From 68c2e9eedeaa2ad9d9528fbb58adffb0a48365c9 Mon Sep 17 00:00:00 2001 From: Filippo Valsorda Date: Wed, 4 May 2022 09:58:56 -0400 Subject: [PATCH] crypto/elliptic: replace generic P-256 with fiat-crypto For #52182 Change-Id: I8d8b4c3d8299fbd59b0bf48e5c8b7b41c533a2cc Reviewed-on: https://go-review.googlesource.com/c/go/+/360114 TryBot-Result: Gopher Robot Reviewed-by: Roland Shoemaker Run-TryBot: Filippo Valsorda Reviewed-by: Fernando Lobato Meeser --- src/crypto/elliptic/internal/fiat/generate.go | 19 +- src/crypto/elliptic/internal/fiat/p256.go | 135 ++ .../elliptic/internal/fiat/p256_fiat64.go | 1400 +++++++++++++++++ .../elliptic/internal/fiat/p256_invert.go | 84 + .../elliptic/internal/nistec/generate.go | 5 + .../elliptic/internal/nistec/nistec_test.go | 97 +- src/crypto/elliptic/internal/nistec/p256.go | 288 ++++ src/crypto/elliptic/nistec.go | 30 + src/crypto/elliptic/p256.go | 32 - src/crypto/elliptic/p256_asm.go | 20 +- src/crypto/elliptic/p256_generic.go | 477 ------ src/crypto/elliptic/p256_generic_field.go | 705 --------- src/crypto/elliptic/p256_noasm.go | 15 - src/crypto/elliptic/p256_ppc64le.go | 13 +- src/crypto/elliptic/p256_s390x.go | 17 +- 15 files changed, 2045 insertions(+), 1292 deletions(-) create mode 100644 src/crypto/elliptic/internal/fiat/p256.go create mode 100644 src/crypto/elliptic/internal/fiat/p256_fiat64.go create mode 100644 src/crypto/elliptic/internal/fiat/p256_invert.go create mode 100644 src/crypto/elliptic/internal/nistec/p256.go delete mode 100644 src/crypto/elliptic/p256.go delete mode 100644 src/crypto/elliptic/p256_generic.go delete mode 100644 src/crypto/elliptic/p256_generic_field.go delete mode 100644 src/crypto/elliptic/p256_noasm.go diff --git a/src/crypto/elliptic/internal/fiat/generate.go b/src/crypto/elliptic/internal/fiat/generate.go index fd8509de45..3b97307ca3 100644 --- a/src/crypto/elliptic/internal/fiat/generate.go +++ b/src/crypto/elliptic/internal/fiat/generate.go @@ -30,15 +30,16 @@ var curves = []struct { FiatType: "[4]uint64", BytesLen: 28, }, - // The 32-bit pure Go P-256 in crypto/elliptic is still faster than the - // autogenerated code here, regrettably. - // { - // Element: "P256Element", - // Prime: "2^256 - 2^224 + 2^192 + 2^96 - 1", - // Prefix: "p256", - // FiatType: "[4]uint64", - // BytesLen: 32, - // }, + // The P-256 fiat implementation is used only on 32-bit architectures, but + // the uint32 fiat code is for some reason slower than the uint64 one. That + // suggests there is a wide margin for improvement. + { + Element: "P256Element", + Prime: "2^256 - 2^224 + 2^192 + 2^96 - 1", + Prefix: "p256", + FiatType: "[4]uint64", + BytesLen: 32, + }, { Element: "P384Element", Prime: "2^384 - 2^128 - 2^96 + 2^32 - 1", diff --git a/src/crypto/elliptic/internal/fiat/p256.go b/src/crypto/elliptic/internal/fiat/p256.go new file mode 100644 index 0000000000..dfdd0a7c69 --- /dev/null +++ b/src/crypto/elliptic/internal/fiat/p256.go @@ -0,0 +1,135 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by generate.go. DO NOT EDIT. + +package fiat + +import ( + "crypto/subtle" + "errors" +) + +// P256Element is an integer modulo 2^256 - 2^224 + 2^192 + 2^96 - 1. +// +// The zero value is a valid zero element. +type P256Element struct { + // Values are represented internally always in the Montgomery domain, and + // converted in Bytes and SetBytes. + x p256MontgomeryDomainFieldElement +} + +const p256ElementLen = 32 + +type p256UntypedFieldElement = [4]uint64 + +// One sets e = 1, and returns e. +func (e *P256Element) One() *P256Element { + p256SetOne(&e.x) + return e +} + +// Equal returns 1 if e == t, and zero otherwise. +func (e *P256Element) Equal(t *P256Element) int { + eBytes := e.Bytes() + tBytes := t.Bytes() + return subtle.ConstantTimeCompare(eBytes, tBytes) +} + +var p256ZeroEncoding = new(P256Element).Bytes() + +// IsZero returns 1 if e == 0, and zero otherwise. +func (e *P256Element) IsZero() int { + eBytes := e.Bytes() + return subtle.ConstantTimeCompare(eBytes, p256ZeroEncoding) +} + +// Set sets e = t, and returns e. +func (e *P256Element) Set(t *P256Element) *P256Element { + e.x = t.x + return e +} + +// Bytes returns the 32-byte big-endian encoding of e. +func (e *P256Element) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [p256ElementLen]byte + return e.bytes(&out) +} + +func (e *P256Element) bytes(out *[p256ElementLen]byte) []byte { + var tmp p256NonMontgomeryDomainFieldElement + p256FromMontgomery(&tmp, &e.x) + p256ToBytes(out, (*p256UntypedFieldElement)(&tmp)) + p256InvertEndianness(out[:]) + return out[:] +} + +// p256MinusOneEncoding is the encoding of -1 mod p, so p - 1, the +// highest canonical encoding. It is used by SetBytes to check for non-canonical +// encodings such as p + k, 2p + k, etc. +var p256MinusOneEncoding = new(P256Element).Sub( + new(P256Element), new(P256Element).One()).Bytes() + +// SetBytes sets e = v, where v is a big-endian 32-byte encoding, and returns e. +// If v is not 32 bytes or it encodes a value higher than 2^256 - 2^224 + 2^192 + 2^96 - 1, +// SetBytes returns nil and an error, and e is unchanged. +func (e *P256Element) SetBytes(v []byte) (*P256Element, error) { + if len(v) != p256ElementLen { + return nil, errors.New("invalid P256Element encoding") + } + for i := range v { + if v[i] < p256MinusOneEncoding[i] { + break + } + if v[i] > p256MinusOneEncoding[i] { + return nil, errors.New("invalid P256Element encoding") + } + } + var in [p256ElementLen]byte + copy(in[:], v) + p256InvertEndianness(in[:]) + var tmp p256NonMontgomeryDomainFieldElement + p256FromBytes((*p256UntypedFieldElement)(&tmp), &in) + p256ToMontgomery(&e.x, &tmp) + return e, nil +} + +// Add sets e = t1 + t2, and returns e. +func (e *P256Element) Add(t1, t2 *P256Element) *P256Element { + p256Add(&e.x, &t1.x, &t2.x) + return e +} + +// Sub sets e = t1 - t2, and returns e. +func (e *P256Element) Sub(t1, t2 *P256Element) *P256Element { + p256Sub(&e.x, &t1.x, &t2.x) + return e +} + +// Mul sets e = t1 * t2, and returns e. +func (e *P256Element) Mul(t1, t2 *P256Element) *P256Element { + p256Mul(&e.x, &t1.x, &t2.x) + return e +} + +// Square sets e = t * t, and returns e. +func (e *P256Element) Square(t *P256Element) *P256Element { + p256Square(&e.x, &t.x) + return e +} + +// Select sets v to a if cond == 1, and to b if cond == 0. +func (v *P256Element) Select(a, b *P256Element, cond int) *P256Element { + p256Selectznz((*p256UntypedFieldElement)(&v.x), p256Uint1(cond), + (*p256UntypedFieldElement)(&b.x), (*p256UntypedFieldElement)(&a.x)) + return v +} + +func p256InvertEndianness(v []byte) { + for i := 0; i < len(v)/2; i++ { + v[i], v[len(v)-1-i] = v[len(v)-1-i], v[i] + } +} diff --git a/src/crypto/elliptic/internal/fiat/p256_fiat64.go b/src/crypto/elliptic/internal/fiat/p256_fiat64.go new file mode 100644 index 0000000000..75352d5d26 --- /dev/null +++ b/src/crypto/elliptic/internal/fiat/p256_fiat64.go @@ -0,0 +1,1400 @@ +// Code generated by Fiat Cryptography. DO NOT EDIT. +// +// Autogenerated: word_by_word_montgomery --lang Go --no-wide-int --cmovznz-by-mul --relax-primitive-carry-to-bitwidth 32,64 --internal-static --public-function-case camelCase --public-type-case camelCase --private-function-case camelCase --private-type-case camelCase --doc-text-before-function-name '' --doc-newline-before-package-declaration --doc-prepend-header 'Code generated by Fiat Cryptography. DO NOT EDIT.' --package-name fiat --no-prefix-fiat p256 64 '2^256 - 2^224 + 2^192 + 2^96 - 1' mul square add sub one from_montgomery to_montgomery selectznz to_bytes from_bytes +// +// curve description: p256 +// +// machine_wordsize = 64 (from "64") +// +// requested operations: mul, square, add, sub, one, from_montgomery, to_montgomery, selectznz, to_bytes, from_bytes +// +// m = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff (from "2^256 - 2^224 + 2^192 + 2^96 - 1") +// +// +// +// NOTE: In addition to the bounds specified above each function, all +// +// functions synthesized for this Montgomery arithmetic require the +// +// input to be strictly less than the prime modulus (m), and also +// +// require the input to be in the unique saturated representation. +// +// All functions also ensure that these two properties are true of +// +// return values. +// +// +// +// Computed values: +// +// eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) +// +// bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) +// +// twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in +// +// if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256 + +package fiat + +import "math/bits" + +type p256Uint1 uint64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927 +type p256Int1 int64 // We use uint64 instead of a more narrow type for performance reasons; see https://github.com/mit-plv/fiat-crypto/pull/1006#issuecomment-892625927 + +// The type p256MontgomeryDomainFieldElement is a field element in the Montgomery domain. +// +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +type p256MontgomeryDomainFieldElement [4]uint64 + +// The type p256NonMontgomeryDomainFieldElement is a field element NOT in the Montgomery domain. +// +// Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +type p256NonMontgomeryDomainFieldElement [4]uint64 + +// p256CmovznzU64 is a single-word conditional move. +// +// Postconditions: +// +// out1 = (if arg1 = 0 then arg2 else arg3) +// +// Input Bounds: +// +// arg1: [0x0 ~> 0x1] +// arg2: [0x0 ~> 0xffffffffffffffff] +// arg3: [0x0 ~> 0xffffffffffffffff] +// +// Output Bounds: +// +// out1: [0x0 ~> 0xffffffffffffffff] +func p256CmovznzU64(out1 *uint64, arg1 p256Uint1, arg2 uint64, arg3 uint64) { + x1 := (uint64(arg1) * 0xffffffffffffffff) + x2 := ((x1 & arg3) | ((^x1) & arg2)) + *out1 = x2 +} + +// p256Mul multiplies two field elements in the Montgomery domain. +// +// Preconditions: +// +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// +// Postconditions: +// +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +func p256Mul(out1 *p256MontgomeryDomainFieldElement, arg1 *p256MontgomeryDomainFieldElement, arg2 *p256MontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + var x5 uint64 + var x6 uint64 + x6, x5 = bits.Mul64(x4, arg2[3]) + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x4, arg2[2]) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x4, arg2[1]) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x4, arg2[0]) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Add64(x12, x9, uint64(0x0)) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Add64(x10, x7, uint64(p256Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Add64(x8, x5, uint64(p256Uint1(x16))) + x19 := (uint64(p256Uint1(x18)) + x6) + var x20 uint64 + var x21 uint64 + x21, x20 = bits.Mul64(x11, 0xffffffff00000001) + var x22 uint64 + var x23 uint64 + x23, x22 = bits.Mul64(x11, 0xffffffff) + var x24 uint64 + var x25 uint64 + x25, x24 = bits.Mul64(x11, 0xffffffffffffffff) + var x26 uint64 + var x27 uint64 + x26, x27 = bits.Add64(x25, x22, uint64(0x0)) + x28 := (uint64(p256Uint1(x27)) + x23) + var x30 uint64 + _, x30 = bits.Add64(x11, x24, uint64(0x0)) + var x31 uint64 + var x32 uint64 + x31, x32 = bits.Add64(x13, x26, uint64(p256Uint1(x30))) + var x33 uint64 + var x34 uint64 + x33, x34 = bits.Add64(x15, x28, uint64(p256Uint1(x32))) + var x35 uint64 + var x36 uint64 + x35, x36 = bits.Add64(x17, x20, uint64(p256Uint1(x34))) + var x37 uint64 + var x38 uint64 + x37, x38 = bits.Add64(x19, x21, uint64(p256Uint1(x36))) + var x39 uint64 + var x40 uint64 + x40, x39 = bits.Mul64(x1, arg2[3]) + var x41 uint64 + var x42 uint64 + x42, x41 = bits.Mul64(x1, arg2[2]) + var x43 uint64 + var x44 uint64 + x44, x43 = bits.Mul64(x1, arg2[1]) + var x45 uint64 + var x46 uint64 + x46, x45 = bits.Mul64(x1, arg2[0]) + var x47 uint64 + var x48 uint64 + x47, x48 = bits.Add64(x46, x43, uint64(0x0)) + var x49 uint64 + var x50 uint64 + x49, x50 = bits.Add64(x44, x41, uint64(p256Uint1(x48))) + var x51 uint64 + var x52 uint64 + x51, x52 = bits.Add64(x42, x39, uint64(p256Uint1(x50))) + x53 := (uint64(p256Uint1(x52)) + x40) + var x54 uint64 + var x55 uint64 + x54, x55 = bits.Add64(x31, x45, uint64(0x0)) + var x56 uint64 + var x57 uint64 + x56, x57 = bits.Add64(x33, x47, uint64(p256Uint1(x55))) + var x58 uint64 + var x59 uint64 + x58, x59 = bits.Add64(x35, x49, uint64(p256Uint1(x57))) + var x60 uint64 + var x61 uint64 + x60, x61 = bits.Add64(x37, x51, uint64(p256Uint1(x59))) + var x62 uint64 + var x63 uint64 + x62, x63 = bits.Add64(uint64(p256Uint1(x38)), x53, uint64(p256Uint1(x61))) + var x64 uint64 + var x65 uint64 + x65, x64 = bits.Mul64(x54, 0xffffffff00000001) + var x66 uint64 + var x67 uint64 + x67, x66 = bits.Mul64(x54, 0xffffffff) + var x68 uint64 + var x69 uint64 + x69, x68 = bits.Mul64(x54, 0xffffffffffffffff) + var x70 uint64 + var x71 uint64 + x70, x71 = bits.Add64(x69, x66, uint64(0x0)) + x72 := (uint64(p256Uint1(x71)) + x67) + var x74 uint64 + _, x74 = bits.Add64(x54, x68, uint64(0x0)) + var x75 uint64 + var x76 uint64 + x75, x76 = bits.Add64(x56, x70, uint64(p256Uint1(x74))) + var x77 uint64 + var x78 uint64 + x77, x78 = bits.Add64(x58, x72, uint64(p256Uint1(x76))) + var x79 uint64 + var x80 uint64 + x79, x80 = bits.Add64(x60, x64, uint64(p256Uint1(x78))) + var x81 uint64 + var x82 uint64 + x81, x82 = bits.Add64(x62, x65, uint64(p256Uint1(x80))) + x83 := (uint64(p256Uint1(x82)) + uint64(p256Uint1(x63))) + var x84 uint64 + var x85 uint64 + x85, x84 = bits.Mul64(x2, arg2[3]) + var x86 uint64 + var x87 uint64 + x87, x86 = bits.Mul64(x2, arg2[2]) + var x88 uint64 + var x89 uint64 + x89, x88 = bits.Mul64(x2, arg2[1]) + var x90 uint64 + var x91 uint64 + x91, x90 = bits.Mul64(x2, arg2[0]) + var x92 uint64 + var x93 uint64 + x92, x93 = bits.Add64(x91, x88, uint64(0x0)) + var x94 uint64 + var x95 uint64 + x94, x95 = bits.Add64(x89, x86, uint64(p256Uint1(x93))) + var x96 uint64 + var x97 uint64 + x96, x97 = bits.Add64(x87, x84, uint64(p256Uint1(x95))) + x98 := (uint64(p256Uint1(x97)) + x85) + var x99 uint64 + var x100 uint64 + x99, x100 = bits.Add64(x75, x90, uint64(0x0)) + var x101 uint64 + var x102 uint64 + x101, x102 = bits.Add64(x77, x92, uint64(p256Uint1(x100))) + var x103 uint64 + var x104 uint64 + x103, x104 = bits.Add64(x79, x94, uint64(p256Uint1(x102))) + var x105 uint64 + var x106 uint64 + x105, x106 = bits.Add64(x81, x96, uint64(p256Uint1(x104))) + var x107 uint64 + var x108 uint64 + x107, x108 = bits.Add64(x83, x98, uint64(p256Uint1(x106))) + var x109 uint64 + var x110 uint64 + x110, x109 = bits.Mul64(x99, 0xffffffff00000001) + var x111 uint64 + var x112 uint64 + x112, x111 = bits.Mul64(x99, 0xffffffff) + var x113 uint64 + var x114 uint64 + x114, x113 = bits.Mul64(x99, 0xffffffffffffffff) + var x115 uint64 + var x116 uint64 + x115, x116 = bits.Add64(x114, x111, uint64(0x0)) + x117 := (uint64(p256Uint1(x116)) + x112) + var x119 uint64 + _, x119 = bits.Add64(x99, x113, uint64(0x0)) + var x120 uint64 + var x121 uint64 + x120, x121 = bits.Add64(x101, x115, uint64(p256Uint1(x119))) + var x122 uint64 + var x123 uint64 + x122, x123 = bits.Add64(x103, x117, uint64(p256Uint1(x121))) + var x124 uint64 + var x125 uint64 + x124, x125 = bits.Add64(x105, x109, uint64(p256Uint1(x123))) + var x126 uint64 + var x127 uint64 + x126, x127 = bits.Add64(x107, x110, uint64(p256Uint1(x125))) + x128 := (uint64(p256Uint1(x127)) + uint64(p256Uint1(x108))) + var x129 uint64 + var x130 uint64 + x130, x129 = bits.Mul64(x3, arg2[3]) + var x131 uint64 + var x132 uint64 + x132, x131 = bits.Mul64(x3, arg2[2]) + var x133 uint64 + var x134 uint64 + x134, x133 = bits.Mul64(x3, arg2[1]) + var x135 uint64 + var x136 uint64 + x136, x135 = bits.Mul64(x3, arg2[0]) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x136, x133, uint64(0x0)) + var x139 uint64 + var x140 uint64 + x139, x140 = bits.Add64(x134, x131, uint64(p256Uint1(x138))) + var x141 uint64 + var x142 uint64 + x141, x142 = bits.Add64(x132, x129, uint64(p256Uint1(x140))) + x143 := (uint64(p256Uint1(x142)) + x130) + var x144 uint64 + var x145 uint64 + x144, x145 = bits.Add64(x120, x135, uint64(0x0)) + var x146 uint64 + var x147 uint64 + x146, x147 = bits.Add64(x122, x137, uint64(p256Uint1(x145))) + var x148 uint64 + var x149 uint64 + x148, x149 = bits.Add64(x124, x139, uint64(p256Uint1(x147))) + var x150 uint64 + var x151 uint64 + x150, x151 = bits.Add64(x126, x141, uint64(p256Uint1(x149))) + var x152 uint64 + var x153 uint64 + x152, x153 = bits.Add64(x128, x143, uint64(p256Uint1(x151))) + var x154 uint64 + var x155 uint64 + x155, x154 = bits.Mul64(x144, 0xffffffff00000001) + var x156 uint64 + var x157 uint64 + x157, x156 = bits.Mul64(x144, 0xffffffff) + var x158 uint64 + var x159 uint64 + x159, x158 = bits.Mul64(x144, 0xffffffffffffffff) + var x160 uint64 + var x161 uint64 + x160, x161 = bits.Add64(x159, x156, uint64(0x0)) + x162 := (uint64(p256Uint1(x161)) + x157) + var x164 uint64 + _, x164 = bits.Add64(x144, x158, uint64(0x0)) + var x165 uint64 + var x166 uint64 + x165, x166 = bits.Add64(x146, x160, uint64(p256Uint1(x164))) + var x167 uint64 + var x168 uint64 + x167, x168 = bits.Add64(x148, x162, uint64(p256Uint1(x166))) + var x169 uint64 + var x170 uint64 + x169, x170 = bits.Add64(x150, x154, uint64(p256Uint1(x168))) + var x171 uint64 + var x172 uint64 + x171, x172 = bits.Add64(x152, x155, uint64(p256Uint1(x170))) + x173 := (uint64(p256Uint1(x172)) + uint64(p256Uint1(x153))) + var x174 uint64 + var x175 uint64 + x174, x175 = bits.Sub64(x165, 0xffffffffffffffff, uint64(0x0)) + var x176 uint64 + var x177 uint64 + x176, x177 = bits.Sub64(x167, 0xffffffff, uint64(p256Uint1(x175))) + var x178 uint64 + var x179 uint64 + x178, x179 = bits.Sub64(x169, uint64(0x0), uint64(p256Uint1(x177))) + var x180 uint64 + var x181 uint64 + x180, x181 = bits.Sub64(x171, 0xffffffff00000001, uint64(p256Uint1(x179))) + var x183 uint64 + _, x183 = bits.Sub64(x173, uint64(0x0), uint64(p256Uint1(x181))) + var x184 uint64 + p256CmovznzU64(&x184, p256Uint1(x183), x174, x165) + var x185 uint64 + p256CmovznzU64(&x185, p256Uint1(x183), x176, x167) + var x186 uint64 + p256CmovznzU64(&x186, p256Uint1(x183), x178, x169) + var x187 uint64 + p256CmovznzU64(&x187, p256Uint1(x183), x180, x171) + out1[0] = x184 + out1[1] = x185 + out1[2] = x186 + out1[3] = x187 +} + +// p256Square squares a field element in the Montgomery domain. +// +// Preconditions: +// +// 0 ≤ eval arg1 < m +// +// Postconditions: +// +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) * eval (from_montgomery arg1)) mod m +// 0 ≤ eval out1 < m +func p256Square(out1 *p256MontgomeryDomainFieldElement, arg1 *p256MontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + var x5 uint64 + var x6 uint64 + x6, x5 = bits.Mul64(x4, arg1[3]) + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x4, arg1[2]) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x4, arg1[1]) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x4, arg1[0]) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Add64(x12, x9, uint64(0x0)) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Add64(x10, x7, uint64(p256Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Add64(x8, x5, uint64(p256Uint1(x16))) + x19 := (uint64(p256Uint1(x18)) + x6) + var x20 uint64 + var x21 uint64 + x21, x20 = bits.Mul64(x11, 0xffffffff00000001) + var x22 uint64 + var x23 uint64 + x23, x22 = bits.Mul64(x11, 0xffffffff) + var x24 uint64 + var x25 uint64 + x25, x24 = bits.Mul64(x11, 0xffffffffffffffff) + var x26 uint64 + var x27 uint64 + x26, x27 = bits.Add64(x25, x22, uint64(0x0)) + x28 := (uint64(p256Uint1(x27)) + x23) + var x30 uint64 + _, x30 = bits.Add64(x11, x24, uint64(0x0)) + var x31 uint64 + var x32 uint64 + x31, x32 = bits.Add64(x13, x26, uint64(p256Uint1(x30))) + var x33 uint64 + var x34 uint64 + x33, x34 = bits.Add64(x15, x28, uint64(p256Uint1(x32))) + var x35 uint64 + var x36 uint64 + x35, x36 = bits.Add64(x17, x20, uint64(p256Uint1(x34))) + var x37 uint64 + var x38 uint64 + x37, x38 = bits.Add64(x19, x21, uint64(p256Uint1(x36))) + var x39 uint64 + var x40 uint64 + x40, x39 = bits.Mul64(x1, arg1[3]) + var x41 uint64 + var x42 uint64 + x42, x41 = bits.Mul64(x1, arg1[2]) + var x43 uint64 + var x44 uint64 + x44, x43 = bits.Mul64(x1, arg1[1]) + var x45 uint64 + var x46 uint64 + x46, x45 = bits.Mul64(x1, arg1[0]) + var x47 uint64 + var x48 uint64 + x47, x48 = bits.Add64(x46, x43, uint64(0x0)) + var x49 uint64 + var x50 uint64 + x49, x50 = bits.Add64(x44, x41, uint64(p256Uint1(x48))) + var x51 uint64 + var x52 uint64 + x51, x52 = bits.Add64(x42, x39, uint64(p256Uint1(x50))) + x53 := (uint64(p256Uint1(x52)) + x40) + var x54 uint64 + var x55 uint64 + x54, x55 = bits.Add64(x31, x45, uint64(0x0)) + var x56 uint64 + var x57 uint64 + x56, x57 = bits.Add64(x33, x47, uint64(p256Uint1(x55))) + var x58 uint64 + var x59 uint64 + x58, x59 = bits.Add64(x35, x49, uint64(p256Uint1(x57))) + var x60 uint64 + var x61 uint64 + x60, x61 = bits.Add64(x37, x51, uint64(p256Uint1(x59))) + var x62 uint64 + var x63 uint64 + x62, x63 = bits.Add64(uint64(p256Uint1(x38)), x53, uint64(p256Uint1(x61))) + var x64 uint64 + var x65 uint64 + x65, x64 = bits.Mul64(x54, 0xffffffff00000001) + var x66 uint64 + var x67 uint64 + x67, x66 = bits.Mul64(x54, 0xffffffff) + var x68 uint64 + var x69 uint64 + x69, x68 = bits.Mul64(x54, 0xffffffffffffffff) + var x70 uint64 + var x71 uint64 + x70, x71 = bits.Add64(x69, x66, uint64(0x0)) + x72 := (uint64(p256Uint1(x71)) + x67) + var x74 uint64 + _, x74 = bits.Add64(x54, x68, uint64(0x0)) + var x75 uint64 + var x76 uint64 + x75, x76 = bits.Add64(x56, x70, uint64(p256Uint1(x74))) + var x77 uint64 + var x78 uint64 + x77, x78 = bits.Add64(x58, x72, uint64(p256Uint1(x76))) + var x79 uint64 + var x80 uint64 + x79, x80 = bits.Add64(x60, x64, uint64(p256Uint1(x78))) + var x81 uint64 + var x82 uint64 + x81, x82 = bits.Add64(x62, x65, uint64(p256Uint1(x80))) + x83 := (uint64(p256Uint1(x82)) + uint64(p256Uint1(x63))) + var x84 uint64 + var x85 uint64 + x85, x84 = bits.Mul64(x2, arg1[3]) + var x86 uint64 + var x87 uint64 + x87, x86 = bits.Mul64(x2, arg1[2]) + var x88 uint64 + var x89 uint64 + x89, x88 = bits.Mul64(x2, arg1[1]) + var x90 uint64 + var x91 uint64 + x91, x90 = bits.Mul64(x2, arg1[0]) + var x92 uint64 + var x93 uint64 + x92, x93 = bits.Add64(x91, x88, uint64(0x0)) + var x94 uint64 + var x95 uint64 + x94, x95 = bits.Add64(x89, x86, uint64(p256Uint1(x93))) + var x96 uint64 + var x97 uint64 + x96, x97 = bits.Add64(x87, x84, uint64(p256Uint1(x95))) + x98 := (uint64(p256Uint1(x97)) + x85) + var x99 uint64 + var x100 uint64 + x99, x100 = bits.Add64(x75, x90, uint64(0x0)) + var x101 uint64 + var x102 uint64 + x101, x102 = bits.Add64(x77, x92, uint64(p256Uint1(x100))) + var x103 uint64 + var x104 uint64 + x103, x104 = bits.Add64(x79, x94, uint64(p256Uint1(x102))) + var x105 uint64 + var x106 uint64 + x105, x106 = bits.Add64(x81, x96, uint64(p256Uint1(x104))) + var x107 uint64 + var x108 uint64 + x107, x108 = bits.Add64(x83, x98, uint64(p256Uint1(x106))) + var x109 uint64 + var x110 uint64 + x110, x109 = bits.Mul64(x99, 0xffffffff00000001) + var x111 uint64 + var x112 uint64 + x112, x111 = bits.Mul64(x99, 0xffffffff) + var x113 uint64 + var x114 uint64 + x114, x113 = bits.Mul64(x99, 0xffffffffffffffff) + var x115 uint64 + var x116 uint64 + x115, x116 = bits.Add64(x114, x111, uint64(0x0)) + x117 := (uint64(p256Uint1(x116)) + x112) + var x119 uint64 + _, x119 = bits.Add64(x99, x113, uint64(0x0)) + var x120 uint64 + var x121 uint64 + x120, x121 = bits.Add64(x101, x115, uint64(p256Uint1(x119))) + var x122 uint64 + var x123 uint64 + x122, x123 = bits.Add64(x103, x117, uint64(p256Uint1(x121))) + var x124 uint64 + var x125 uint64 + x124, x125 = bits.Add64(x105, x109, uint64(p256Uint1(x123))) + var x126 uint64 + var x127 uint64 + x126, x127 = bits.Add64(x107, x110, uint64(p256Uint1(x125))) + x128 := (uint64(p256Uint1(x127)) + uint64(p256Uint1(x108))) + var x129 uint64 + var x130 uint64 + x130, x129 = bits.Mul64(x3, arg1[3]) + var x131 uint64 + var x132 uint64 + x132, x131 = bits.Mul64(x3, arg1[2]) + var x133 uint64 + var x134 uint64 + x134, x133 = bits.Mul64(x3, arg1[1]) + var x135 uint64 + var x136 uint64 + x136, x135 = bits.Mul64(x3, arg1[0]) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x136, x133, uint64(0x0)) + var x139 uint64 + var x140 uint64 + x139, x140 = bits.Add64(x134, x131, uint64(p256Uint1(x138))) + var x141 uint64 + var x142 uint64 + x141, x142 = bits.Add64(x132, x129, uint64(p256Uint1(x140))) + x143 := (uint64(p256Uint1(x142)) + x130) + var x144 uint64 + var x145 uint64 + x144, x145 = bits.Add64(x120, x135, uint64(0x0)) + var x146 uint64 + var x147 uint64 + x146, x147 = bits.Add64(x122, x137, uint64(p256Uint1(x145))) + var x148 uint64 + var x149 uint64 + x148, x149 = bits.Add64(x124, x139, uint64(p256Uint1(x147))) + var x150 uint64 + var x151 uint64 + x150, x151 = bits.Add64(x126, x141, uint64(p256Uint1(x149))) + var x152 uint64 + var x153 uint64 + x152, x153 = bits.Add64(x128, x143, uint64(p256Uint1(x151))) + var x154 uint64 + var x155 uint64 + x155, x154 = bits.Mul64(x144, 0xffffffff00000001) + var x156 uint64 + var x157 uint64 + x157, x156 = bits.Mul64(x144, 0xffffffff) + var x158 uint64 + var x159 uint64 + x159, x158 = bits.Mul64(x144, 0xffffffffffffffff) + var x160 uint64 + var x161 uint64 + x160, x161 = bits.Add64(x159, x156, uint64(0x0)) + x162 := (uint64(p256Uint1(x161)) + x157) + var x164 uint64 + _, x164 = bits.Add64(x144, x158, uint64(0x0)) + var x165 uint64 + var x166 uint64 + x165, x166 = bits.Add64(x146, x160, uint64(p256Uint1(x164))) + var x167 uint64 + var x168 uint64 + x167, x168 = bits.Add64(x148, x162, uint64(p256Uint1(x166))) + var x169 uint64 + var x170 uint64 + x169, x170 = bits.Add64(x150, x154, uint64(p256Uint1(x168))) + var x171 uint64 + var x172 uint64 + x171, x172 = bits.Add64(x152, x155, uint64(p256Uint1(x170))) + x173 := (uint64(p256Uint1(x172)) + uint64(p256Uint1(x153))) + var x174 uint64 + var x175 uint64 + x174, x175 = bits.Sub64(x165, 0xffffffffffffffff, uint64(0x0)) + var x176 uint64 + var x177 uint64 + x176, x177 = bits.Sub64(x167, 0xffffffff, uint64(p256Uint1(x175))) + var x178 uint64 + var x179 uint64 + x178, x179 = bits.Sub64(x169, uint64(0x0), uint64(p256Uint1(x177))) + var x180 uint64 + var x181 uint64 + x180, x181 = bits.Sub64(x171, 0xffffffff00000001, uint64(p256Uint1(x179))) + var x183 uint64 + _, x183 = bits.Sub64(x173, uint64(0x0), uint64(p256Uint1(x181))) + var x184 uint64 + p256CmovznzU64(&x184, p256Uint1(x183), x174, x165) + var x185 uint64 + p256CmovznzU64(&x185, p256Uint1(x183), x176, x167) + var x186 uint64 + p256CmovznzU64(&x186, p256Uint1(x183), x178, x169) + var x187 uint64 + p256CmovznzU64(&x187, p256Uint1(x183), x180, x171) + out1[0] = x184 + out1[1] = x185 + out1[2] = x186 + out1[3] = x187 +} + +// p256Add adds two field elements in the Montgomery domain. +// +// Preconditions: +// +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// +// Postconditions: +// +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) + eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +func p256Add(out1 *p256MontgomeryDomainFieldElement, arg1 *p256MontgomeryDomainFieldElement, arg2 *p256MontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x1, x2 = bits.Add64(arg1[0], arg2[0], uint64(0x0)) + var x3 uint64 + var x4 uint64 + x3, x4 = bits.Add64(arg1[1], arg2[1], uint64(p256Uint1(x2))) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Add64(arg1[2], arg2[2], uint64(p256Uint1(x4))) + var x7 uint64 + var x8 uint64 + x7, x8 = bits.Add64(arg1[3], arg2[3], uint64(p256Uint1(x6))) + var x9 uint64 + var x10 uint64 + x9, x10 = bits.Sub64(x1, 0xffffffffffffffff, uint64(0x0)) + var x11 uint64 + var x12 uint64 + x11, x12 = bits.Sub64(x3, 0xffffffff, uint64(p256Uint1(x10))) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Sub64(x5, uint64(0x0), uint64(p256Uint1(x12))) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Sub64(x7, 0xffffffff00000001, uint64(p256Uint1(x14))) + var x18 uint64 + _, x18 = bits.Sub64(uint64(p256Uint1(x8)), uint64(0x0), uint64(p256Uint1(x16))) + var x19 uint64 + p256CmovznzU64(&x19, p256Uint1(x18), x9, x1) + var x20 uint64 + p256CmovznzU64(&x20, p256Uint1(x18), x11, x3) + var x21 uint64 + p256CmovznzU64(&x21, p256Uint1(x18), x13, x5) + var x22 uint64 + p256CmovznzU64(&x22, p256Uint1(x18), x15, x7) + out1[0] = x19 + out1[1] = x20 + out1[2] = x21 + out1[3] = x22 +} + +// p256Sub subtracts two field elements in the Montgomery domain. +// +// Preconditions: +// +// 0 ≤ eval arg1 < m +// 0 ≤ eval arg2 < m +// +// Postconditions: +// +// eval (from_montgomery out1) mod m = (eval (from_montgomery arg1) - eval (from_montgomery arg2)) mod m +// 0 ≤ eval out1 < m +func p256Sub(out1 *p256MontgomeryDomainFieldElement, arg1 *p256MontgomeryDomainFieldElement, arg2 *p256MontgomeryDomainFieldElement) { + var x1 uint64 + var x2 uint64 + x1, x2 = bits.Sub64(arg1[0], arg2[0], uint64(0x0)) + var x3 uint64 + var x4 uint64 + x3, x4 = bits.Sub64(arg1[1], arg2[1], uint64(p256Uint1(x2))) + var x5 uint64 + var x6 uint64 + x5, x6 = bits.Sub64(arg1[2], arg2[2], uint64(p256Uint1(x4))) + var x7 uint64 + var x8 uint64 + x7, x8 = bits.Sub64(arg1[3], arg2[3], uint64(p256Uint1(x6))) + var x9 uint64 + p256CmovznzU64(&x9, p256Uint1(x8), uint64(0x0), 0xffffffffffffffff) + var x10 uint64 + var x11 uint64 + x10, x11 = bits.Add64(x1, x9, uint64(0x0)) + var x12 uint64 + var x13 uint64 + x12, x13 = bits.Add64(x3, (x9 & 0xffffffff), uint64(p256Uint1(x11))) + var x14 uint64 + var x15 uint64 + x14, x15 = bits.Add64(x5, uint64(0x0), uint64(p256Uint1(x13))) + var x16 uint64 + x16, _ = bits.Add64(x7, (x9 & 0xffffffff00000001), uint64(p256Uint1(x15))) + out1[0] = x10 + out1[1] = x12 + out1[2] = x14 + out1[3] = x16 +} + +// p256SetOne returns the field element one in the Montgomery domain. +// +// Postconditions: +// +// eval (from_montgomery out1) mod m = 1 mod m +// 0 ≤ eval out1 < m +func p256SetOne(out1 *p256MontgomeryDomainFieldElement) { + out1[0] = uint64(0x1) + out1[1] = 0xffffffff00000000 + out1[2] = 0xffffffffffffffff + out1[3] = 0xfffffffe +} + +// p256FromMontgomery translates a field element out of the Montgomery domain. +// +// Preconditions: +// +// 0 ≤ eval arg1 < m +// +// Postconditions: +// +// eval out1 mod m = (eval arg1 * ((2^64)⁻¹ mod m)^4) mod m +// 0 ≤ eval out1 < m +func p256FromMontgomery(out1 *p256NonMontgomeryDomainFieldElement, arg1 *p256MontgomeryDomainFieldElement) { + x1 := arg1[0] + var x2 uint64 + var x3 uint64 + x3, x2 = bits.Mul64(x1, 0xffffffff00000001) + var x4 uint64 + var x5 uint64 + x5, x4 = bits.Mul64(x1, 0xffffffff) + var x6 uint64 + var x7 uint64 + x7, x6 = bits.Mul64(x1, 0xffffffffffffffff) + var x8 uint64 + var x9 uint64 + x8, x9 = bits.Add64(x7, x4, uint64(0x0)) + var x11 uint64 + _, x11 = bits.Add64(x1, x6, uint64(0x0)) + var x12 uint64 + var x13 uint64 + x12, x13 = bits.Add64(uint64(0x0), x8, uint64(p256Uint1(x11))) + var x14 uint64 + var x15 uint64 + x14, x15 = bits.Add64(x12, arg1[1], uint64(0x0)) + var x16 uint64 + var x17 uint64 + x17, x16 = bits.Mul64(x14, 0xffffffff00000001) + var x18 uint64 + var x19 uint64 + x19, x18 = bits.Mul64(x14, 0xffffffff) + var x20 uint64 + var x21 uint64 + x21, x20 = bits.Mul64(x14, 0xffffffffffffffff) + var x22 uint64 + var x23 uint64 + x22, x23 = bits.Add64(x21, x18, uint64(0x0)) + var x25 uint64 + _, x25 = bits.Add64(x14, x20, uint64(0x0)) + var x26 uint64 + var x27 uint64 + x26, x27 = bits.Add64((uint64(p256Uint1(x15)) + (uint64(p256Uint1(x13)) + (uint64(p256Uint1(x9)) + x5))), x22, uint64(p256Uint1(x25))) + var x28 uint64 + var x29 uint64 + x28, x29 = bits.Add64(x2, (uint64(p256Uint1(x23)) + x19), uint64(p256Uint1(x27))) + var x30 uint64 + var x31 uint64 + x30, x31 = bits.Add64(x3, x16, uint64(p256Uint1(x29))) + var x32 uint64 + var x33 uint64 + x32, x33 = bits.Add64(x26, arg1[2], uint64(0x0)) + var x34 uint64 + var x35 uint64 + x34, x35 = bits.Add64(x28, uint64(0x0), uint64(p256Uint1(x33))) + var x36 uint64 + var x37 uint64 + x36, x37 = bits.Add64(x30, uint64(0x0), uint64(p256Uint1(x35))) + var x38 uint64 + var x39 uint64 + x39, x38 = bits.Mul64(x32, 0xffffffff00000001) + var x40 uint64 + var x41 uint64 + x41, x40 = bits.Mul64(x32, 0xffffffff) + var x42 uint64 + var x43 uint64 + x43, x42 = bits.Mul64(x32, 0xffffffffffffffff) + var x44 uint64 + var x45 uint64 + x44, x45 = bits.Add64(x43, x40, uint64(0x0)) + var x47 uint64 + _, x47 = bits.Add64(x32, x42, uint64(0x0)) + var x48 uint64 + var x49 uint64 + x48, x49 = bits.Add64(x34, x44, uint64(p256Uint1(x47))) + var x50 uint64 + var x51 uint64 + x50, x51 = bits.Add64(x36, (uint64(p256Uint1(x45)) + x41), uint64(p256Uint1(x49))) + var x52 uint64 + var x53 uint64 + x52, x53 = bits.Add64((uint64(p256Uint1(x37)) + (uint64(p256Uint1(x31)) + x17)), x38, uint64(p256Uint1(x51))) + var x54 uint64 + var x55 uint64 + x54, x55 = bits.Add64(x48, arg1[3], uint64(0x0)) + var x56 uint64 + var x57 uint64 + x56, x57 = bits.Add64(x50, uint64(0x0), uint64(p256Uint1(x55))) + var x58 uint64 + var x59 uint64 + x58, x59 = bits.Add64(x52, uint64(0x0), uint64(p256Uint1(x57))) + var x60 uint64 + var x61 uint64 + x61, x60 = bits.Mul64(x54, 0xffffffff00000001) + var x62 uint64 + var x63 uint64 + x63, x62 = bits.Mul64(x54, 0xffffffff) + var x64 uint64 + var x65 uint64 + x65, x64 = bits.Mul64(x54, 0xffffffffffffffff) + var x66 uint64 + var x67 uint64 + x66, x67 = bits.Add64(x65, x62, uint64(0x0)) + var x69 uint64 + _, x69 = bits.Add64(x54, x64, uint64(0x0)) + var x70 uint64 + var x71 uint64 + x70, x71 = bits.Add64(x56, x66, uint64(p256Uint1(x69))) + var x72 uint64 + var x73 uint64 + x72, x73 = bits.Add64(x58, (uint64(p256Uint1(x67)) + x63), uint64(p256Uint1(x71))) + var x74 uint64 + var x75 uint64 + x74, x75 = bits.Add64((uint64(p256Uint1(x59)) + (uint64(p256Uint1(x53)) + x39)), x60, uint64(p256Uint1(x73))) + x76 := (uint64(p256Uint1(x75)) + x61) + var x77 uint64 + var x78 uint64 + x77, x78 = bits.Sub64(x70, 0xffffffffffffffff, uint64(0x0)) + var x79 uint64 + var x80 uint64 + x79, x80 = bits.Sub64(x72, 0xffffffff, uint64(p256Uint1(x78))) + var x81 uint64 + var x82 uint64 + x81, x82 = bits.Sub64(x74, uint64(0x0), uint64(p256Uint1(x80))) + var x83 uint64 + var x84 uint64 + x83, x84 = bits.Sub64(x76, 0xffffffff00000001, uint64(p256Uint1(x82))) + var x86 uint64 + _, x86 = bits.Sub64(uint64(0x0), uint64(0x0), uint64(p256Uint1(x84))) + var x87 uint64 + p256CmovznzU64(&x87, p256Uint1(x86), x77, x70) + var x88 uint64 + p256CmovznzU64(&x88, p256Uint1(x86), x79, x72) + var x89 uint64 + p256CmovznzU64(&x89, p256Uint1(x86), x81, x74) + var x90 uint64 + p256CmovznzU64(&x90, p256Uint1(x86), x83, x76) + out1[0] = x87 + out1[1] = x88 + out1[2] = x89 + out1[3] = x90 +} + +// p256ToMontgomery translates a field element into the Montgomery domain. +// +// Preconditions: +// +// 0 ≤ eval arg1 < m +// +// Postconditions: +// +// eval (from_montgomery out1) mod m = eval arg1 mod m +// 0 ≤ eval out1 < m +func p256ToMontgomery(out1 *p256MontgomeryDomainFieldElement, arg1 *p256NonMontgomeryDomainFieldElement) { + x1 := arg1[1] + x2 := arg1[2] + x3 := arg1[3] + x4 := arg1[0] + var x5 uint64 + var x6 uint64 + x6, x5 = bits.Mul64(x4, 0x4fffffffd) + var x7 uint64 + var x8 uint64 + x8, x7 = bits.Mul64(x4, 0xfffffffffffffffe) + var x9 uint64 + var x10 uint64 + x10, x9 = bits.Mul64(x4, 0xfffffffbffffffff) + var x11 uint64 + var x12 uint64 + x12, x11 = bits.Mul64(x4, 0x3) + var x13 uint64 + var x14 uint64 + x13, x14 = bits.Add64(x12, x9, uint64(0x0)) + var x15 uint64 + var x16 uint64 + x15, x16 = bits.Add64(x10, x7, uint64(p256Uint1(x14))) + var x17 uint64 + var x18 uint64 + x17, x18 = bits.Add64(x8, x5, uint64(p256Uint1(x16))) + var x19 uint64 + var x20 uint64 + x20, x19 = bits.Mul64(x11, 0xffffffff00000001) + var x21 uint64 + var x22 uint64 + x22, x21 = bits.Mul64(x11, 0xffffffff) + var x23 uint64 + var x24 uint64 + x24, x23 = bits.Mul64(x11, 0xffffffffffffffff) + var x25 uint64 + var x26 uint64 + x25, x26 = bits.Add64(x24, x21, uint64(0x0)) + var x28 uint64 + _, x28 = bits.Add64(x11, x23, uint64(0x0)) + var x29 uint64 + var x30 uint64 + x29, x30 = bits.Add64(x13, x25, uint64(p256Uint1(x28))) + var x31 uint64 + var x32 uint64 + x31, x32 = bits.Add64(x15, (uint64(p256Uint1(x26)) + x22), uint64(p256Uint1(x30))) + var x33 uint64 + var x34 uint64 + x33, x34 = bits.Add64(x17, x19, uint64(p256Uint1(x32))) + var x35 uint64 + var x36 uint64 + x35, x36 = bits.Add64((uint64(p256Uint1(x18)) + x6), x20, uint64(p256Uint1(x34))) + var x37 uint64 + var x38 uint64 + x38, x37 = bits.Mul64(x1, 0x4fffffffd) + var x39 uint64 + var x40 uint64 + x40, x39 = bits.Mul64(x1, 0xfffffffffffffffe) + var x41 uint64 + var x42 uint64 + x42, x41 = bits.Mul64(x1, 0xfffffffbffffffff) + var x43 uint64 + var x44 uint64 + x44, x43 = bits.Mul64(x1, 0x3) + var x45 uint64 + var x46 uint64 + x45, x46 = bits.Add64(x44, x41, uint64(0x0)) + var x47 uint64 + var x48 uint64 + x47, x48 = bits.Add64(x42, x39, uint64(p256Uint1(x46))) + var x49 uint64 + var x50 uint64 + x49, x50 = bits.Add64(x40, x37, uint64(p256Uint1(x48))) + var x51 uint64 + var x52 uint64 + x51, x52 = bits.Add64(x29, x43, uint64(0x0)) + var x53 uint64 + var x54 uint64 + x53, x54 = bits.Add64(x31, x45, uint64(p256Uint1(x52))) + var x55 uint64 + var x56 uint64 + x55, x56 = bits.Add64(x33, x47, uint64(p256Uint1(x54))) + var x57 uint64 + var x58 uint64 + x57, x58 = bits.Add64(x35, x49, uint64(p256Uint1(x56))) + var x59 uint64 + var x60 uint64 + x60, x59 = bits.Mul64(x51, 0xffffffff00000001) + var x61 uint64 + var x62 uint64 + x62, x61 = bits.Mul64(x51, 0xffffffff) + var x63 uint64 + var x64 uint64 + x64, x63 = bits.Mul64(x51, 0xffffffffffffffff) + var x65 uint64 + var x66 uint64 + x65, x66 = bits.Add64(x64, x61, uint64(0x0)) + var x68 uint64 + _, x68 = bits.Add64(x51, x63, uint64(0x0)) + var x69 uint64 + var x70 uint64 + x69, x70 = bits.Add64(x53, x65, uint64(p256Uint1(x68))) + var x71 uint64 + var x72 uint64 + x71, x72 = bits.Add64(x55, (uint64(p256Uint1(x66)) + x62), uint64(p256Uint1(x70))) + var x73 uint64 + var x74 uint64 + x73, x74 = bits.Add64(x57, x59, uint64(p256Uint1(x72))) + var x75 uint64 + var x76 uint64 + x75, x76 = bits.Add64(((uint64(p256Uint1(x58)) + uint64(p256Uint1(x36))) + (uint64(p256Uint1(x50)) + x38)), x60, uint64(p256Uint1(x74))) + var x77 uint64 + var x78 uint64 + x78, x77 = bits.Mul64(x2, 0x4fffffffd) + var x79 uint64 + var x80 uint64 + x80, x79 = bits.Mul64(x2, 0xfffffffffffffffe) + var x81 uint64 + var x82 uint64 + x82, x81 = bits.Mul64(x2, 0xfffffffbffffffff) + var x83 uint64 + var x84 uint64 + x84, x83 = bits.Mul64(x2, 0x3) + var x85 uint64 + var x86 uint64 + x85, x86 = bits.Add64(x84, x81, uint64(0x0)) + var x87 uint64 + var x88 uint64 + x87, x88 = bits.Add64(x82, x79, uint64(p256Uint1(x86))) + var x89 uint64 + var x90 uint64 + x89, x90 = bits.Add64(x80, x77, uint64(p256Uint1(x88))) + var x91 uint64 + var x92 uint64 + x91, x92 = bits.Add64(x69, x83, uint64(0x0)) + var x93 uint64 + var x94 uint64 + x93, x94 = bits.Add64(x71, x85, uint64(p256Uint1(x92))) + var x95 uint64 + var x96 uint64 + x95, x96 = bits.Add64(x73, x87, uint64(p256Uint1(x94))) + var x97 uint64 + var x98 uint64 + x97, x98 = bits.Add64(x75, x89, uint64(p256Uint1(x96))) + var x99 uint64 + var x100 uint64 + x100, x99 = bits.Mul64(x91, 0xffffffff00000001) + var x101 uint64 + var x102 uint64 + x102, x101 = bits.Mul64(x91, 0xffffffff) + var x103 uint64 + var x104 uint64 + x104, x103 = bits.Mul64(x91, 0xffffffffffffffff) + var x105 uint64 + var x106 uint64 + x105, x106 = bits.Add64(x104, x101, uint64(0x0)) + var x108 uint64 + _, x108 = bits.Add64(x91, x103, uint64(0x0)) + var x109 uint64 + var x110 uint64 + x109, x110 = bits.Add64(x93, x105, uint64(p256Uint1(x108))) + var x111 uint64 + var x112 uint64 + x111, x112 = bits.Add64(x95, (uint64(p256Uint1(x106)) + x102), uint64(p256Uint1(x110))) + var x113 uint64 + var x114 uint64 + x113, x114 = bits.Add64(x97, x99, uint64(p256Uint1(x112))) + var x115 uint64 + var x116 uint64 + x115, x116 = bits.Add64(((uint64(p256Uint1(x98)) + uint64(p256Uint1(x76))) + (uint64(p256Uint1(x90)) + x78)), x100, uint64(p256Uint1(x114))) + var x117 uint64 + var x118 uint64 + x118, x117 = bits.Mul64(x3, 0x4fffffffd) + var x119 uint64 + var x120 uint64 + x120, x119 = bits.Mul64(x3, 0xfffffffffffffffe) + var x121 uint64 + var x122 uint64 + x122, x121 = bits.Mul64(x3, 0xfffffffbffffffff) + var x123 uint64 + var x124 uint64 + x124, x123 = bits.Mul64(x3, 0x3) + var x125 uint64 + var x126 uint64 + x125, x126 = bits.Add64(x124, x121, uint64(0x0)) + var x127 uint64 + var x128 uint64 + x127, x128 = bits.Add64(x122, x119, uint64(p256Uint1(x126))) + var x129 uint64 + var x130 uint64 + x129, x130 = bits.Add64(x120, x117, uint64(p256Uint1(x128))) + var x131 uint64 + var x132 uint64 + x131, x132 = bits.Add64(x109, x123, uint64(0x0)) + var x133 uint64 + var x134 uint64 + x133, x134 = bits.Add64(x111, x125, uint64(p256Uint1(x132))) + var x135 uint64 + var x136 uint64 + x135, x136 = bits.Add64(x113, x127, uint64(p256Uint1(x134))) + var x137 uint64 + var x138 uint64 + x137, x138 = bits.Add64(x115, x129, uint64(p256Uint1(x136))) + var x139 uint64 + var x140 uint64 + x140, x139 = bits.Mul64(x131, 0xffffffff00000001) + var x141 uint64 + var x142 uint64 + x142, x141 = bits.Mul64(x131, 0xffffffff) + var x143 uint64 + var x144 uint64 + x144, x143 = bits.Mul64(x131, 0xffffffffffffffff) + var x145 uint64 + var x146 uint64 + x145, x146 = bits.Add64(x144, x141, uint64(0x0)) + var x148 uint64 + _, x148 = bits.Add64(x131, x143, uint64(0x0)) + var x149 uint64 + var x150 uint64 + x149, x150 = bits.Add64(x133, x145, uint64(p256Uint1(x148))) + var x151 uint64 + var x152 uint64 + x151, x152 = bits.Add64(x135, (uint64(p256Uint1(x146)) + x142), uint64(p256Uint1(x150))) + var x153 uint64 + var x154 uint64 + x153, x154 = bits.Add64(x137, x139, uint64(p256Uint1(x152))) + var x155 uint64 + var x156 uint64 + x155, x156 = bits.Add64(((uint64(p256Uint1(x138)) + uint64(p256Uint1(x116))) + (uint64(p256Uint1(x130)) + x118)), x140, uint64(p256Uint1(x154))) + var x157 uint64 + var x158 uint64 + x157, x158 = bits.Sub64(x149, 0xffffffffffffffff, uint64(0x0)) + var x159 uint64 + var x160 uint64 + x159, x160 = bits.Sub64(x151, 0xffffffff, uint64(p256Uint1(x158))) + var x161 uint64 + var x162 uint64 + x161, x162 = bits.Sub64(x153, uint64(0x0), uint64(p256Uint1(x160))) + var x163 uint64 + var x164 uint64 + x163, x164 = bits.Sub64(x155, 0xffffffff00000001, uint64(p256Uint1(x162))) + var x166 uint64 + _, x166 = bits.Sub64(uint64(p256Uint1(x156)), uint64(0x0), uint64(p256Uint1(x164))) + var x167 uint64 + p256CmovznzU64(&x167, p256Uint1(x166), x157, x149) + var x168 uint64 + p256CmovznzU64(&x168, p256Uint1(x166), x159, x151) + var x169 uint64 + p256CmovznzU64(&x169, p256Uint1(x166), x161, x153) + var x170 uint64 + p256CmovznzU64(&x170, p256Uint1(x166), x163, x155) + out1[0] = x167 + out1[1] = x168 + out1[2] = x169 + out1[3] = x170 +} + +// p256Selectznz is a multi-limb conditional select. +// +// Postconditions: +// +// eval out1 = (if arg1 = 0 then eval arg2 else eval arg3) +// +// Input Bounds: +// +// arg1: [0x0 ~> 0x1] +// arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// +// Output Bounds: +// +// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +func p256Selectznz(out1 *[4]uint64, arg1 p256Uint1, arg2 *[4]uint64, arg3 *[4]uint64) { + var x1 uint64 + p256CmovznzU64(&x1, arg1, arg2[0], arg3[0]) + var x2 uint64 + p256CmovznzU64(&x2, arg1, arg2[1], arg3[1]) + var x3 uint64 + p256CmovznzU64(&x3, arg1, arg2[2], arg3[2]) + var x4 uint64 + p256CmovznzU64(&x4, arg1, arg2[3], arg3[3]) + out1[0] = x1 + out1[1] = x2 + out1[2] = x3 + out1[3] = x4 +} + +// p256ToBytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order. +// +// Preconditions: +// +// 0 ≤ eval arg1 < m +// +// Postconditions: +// +// out1 = map (λ x, ⌊((eval arg1 mod m) mod 2^(8 * (x + 1))) / 2^(8 * x)⌋) [0..31] +// +// Input Bounds: +// +// arg1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +// +// Output Bounds: +// +// out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +func p256ToBytes(out1 *[32]uint8, arg1 *[4]uint64) { + x1 := arg1[3] + x2 := arg1[2] + x3 := arg1[1] + x4 := arg1[0] + x5 := (uint8(x4) & 0xff) + x6 := (x4 >> 8) + x7 := (uint8(x6) & 0xff) + x8 := (x6 >> 8) + x9 := (uint8(x8) & 0xff) + x10 := (x8 >> 8) + x11 := (uint8(x10) & 0xff) + x12 := (x10 >> 8) + x13 := (uint8(x12) & 0xff) + x14 := (x12 >> 8) + x15 := (uint8(x14) & 0xff) + x16 := (x14 >> 8) + x17 := (uint8(x16) & 0xff) + x18 := uint8((x16 >> 8)) + x19 := (uint8(x3) & 0xff) + x20 := (x3 >> 8) + x21 := (uint8(x20) & 0xff) + x22 := (x20 >> 8) + x23 := (uint8(x22) & 0xff) + x24 := (x22 >> 8) + x25 := (uint8(x24) & 0xff) + x26 := (x24 >> 8) + x27 := (uint8(x26) & 0xff) + x28 := (x26 >> 8) + x29 := (uint8(x28) & 0xff) + x30 := (x28 >> 8) + x31 := (uint8(x30) & 0xff) + x32 := uint8((x30 >> 8)) + x33 := (uint8(x2) & 0xff) + x34 := (x2 >> 8) + x35 := (uint8(x34) & 0xff) + x36 := (x34 >> 8) + x37 := (uint8(x36) & 0xff) + x38 := (x36 >> 8) + x39 := (uint8(x38) & 0xff) + x40 := (x38 >> 8) + x41 := (uint8(x40) & 0xff) + x42 := (x40 >> 8) + x43 := (uint8(x42) & 0xff) + x44 := (x42 >> 8) + x45 := (uint8(x44) & 0xff) + x46 := uint8((x44 >> 8)) + x47 := (uint8(x1) & 0xff) + x48 := (x1 >> 8) + x49 := (uint8(x48) & 0xff) + x50 := (x48 >> 8) + x51 := (uint8(x50) & 0xff) + x52 := (x50 >> 8) + x53 := (uint8(x52) & 0xff) + x54 := (x52 >> 8) + x55 := (uint8(x54) & 0xff) + x56 := (x54 >> 8) + x57 := (uint8(x56) & 0xff) + x58 := (x56 >> 8) + x59 := (uint8(x58) & 0xff) + x60 := uint8((x58 >> 8)) + out1[0] = x5 + out1[1] = x7 + out1[2] = x9 + out1[3] = x11 + out1[4] = x13 + out1[5] = x15 + out1[6] = x17 + out1[7] = x18 + out1[8] = x19 + out1[9] = x21 + out1[10] = x23 + out1[11] = x25 + out1[12] = x27 + out1[13] = x29 + out1[14] = x31 + out1[15] = x32 + out1[16] = x33 + out1[17] = x35 + out1[18] = x37 + out1[19] = x39 + out1[20] = x41 + out1[21] = x43 + out1[22] = x45 + out1[23] = x46 + out1[24] = x47 + out1[25] = x49 + out1[26] = x51 + out1[27] = x53 + out1[28] = x55 + out1[29] = x57 + out1[30] = x59 + out1[31] = x60 +} + +// p256FromBytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order. +// +// Preconditions: +// +// 0 ≤ bytes_eval arg1 < m +// +// Postconditions: +// +// eval out1 mod m = bytes_eval arg1 mod m +// 0 ≤ eval out1 < m +// +// Input Bounds: +// +// arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]] +// +// Output Bounds: +// +// out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]] +func p256FromBytes(out1 *[4]uint64, arg1 *[32]uint8) { + x1 := (uint64(arg1[31]) << 56) + x2 := (uint64(arg1[30]) << 48) + x3 := (uint64(arg1[29]) << 40) + x4 := (uint64(arg1[28]) << 32) + x5 := (uint64(arg1[27]) << 24) + x6 := (uint64(arg1[26]) << 16) + x7 := (uint64(arg1[25]) << 8) + x8 := arg1[24] + x9 := (uint64(arg1[23]) << 56) + x10 := (uint64(arg1[22]) << 48) + x11 := (uint64(arg1[21]) << 40) + x12 := (uint64(arg1[20]) << 32) + x13 := (uint64(arg1[19]) << 24) + x14 := (uint64(arg1[18]) << 16) + x15 := (uint64(arg1[17]) << 8) + x16 := arg1[16] + x17 := (uint64(arg1[15]) << 56) + x18 := (uint64(arg1[14]) << 48) + x19 := (uint64(arg1[13]) << 40) + x20 := (uint64(arg1[12]) << 32) + x21 := (uint64(arg1[11]) << 24) + x22 := (uint64(arg1[10]) << 16) + x23 := (uint64(arg1[9]) << 8) + x24 := arg1[8] + x25 := (uint64(arg1[7]) << 56) + x26 := (uint64(arg1[6]) << 48) + x27 := (uint64(arg1[5]) << 40) + x28 := (uint64(arg1[4]) << 32) + x29 := (uint64(arg1[3]) << 24) + x30 := (uint64(arg1[2]) << 16) + x31 := (uint64(arg1[1]) << 8) + x32 := arg1[0] + x33 := (x31 + uint64(x32)) + x34 := (x30 + x33) + x35 := (x29 + x34) + x36 := (x28 + x35) + x37 := (x27 + x36) + x38 := (x26 + x37) + x39 := (x25 + x38) + x40 := (x23 + uint64(x24)) + x41 := (x22 + x40) + x42 := (x21 + x41) + x43 := (x20 + x42) + x44 := (x19 + x43) + x45 := (x18 + x44) + x46 := (x17 + x45) + x47 := (x15 + uint64(x16)) + x48 := (x14 + x47) + x49 := (x13 + x48) + x50 := (x12 + x49) + x51 := (x11 + x50) + x52 := (x10 + x51) + x53 := (x9 + x52) + x54 := (x7 + uint64(x8)) + x55 := (x6 + x54) + x56 := (x5 + x55) + x57 := (x4 + x56) + x58 := (x3 + x57) + x59 := (x2 + x58) + x60 := (x1 + x59) + out1[0] = x39 + out1[1] = x46 + out1[2] = x53 + out1[3] = x60 +} diff --git a/src/crypto/elliptic/internal/fiat/p256_invert.go b/src/crypto/elliptic/internal/fiat/p256_invert.go new file mode 100644 index 0000000000..d0101e1d4f --- /dev/null +++ b/src/crypto/elliptic/internal/fiat/p256_invert.go @@ -0,0 +1,84 @@ +// Copyright 2021 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by addchain. DO NOT EDIT. + +package fiat + +// Invert sets e = 1/x, and returns e. +// +// If x == 0, Invert returns e = 0. +func (e *P256Element) Invert(x *P256Element) *P256Element { + // Inversion is implemented as exponentiation with exponent p − 2. + // The sequence of 12 multiplications and 255 squarings is derived from the + // following addition chain generated with github.com/mmcloughlin/addchain v0.4.0. + // + // _10 = 2*1 + // _11 = 1 + _10 + // _110 = 2*_11 + // _111 = 1 + _110 + // _111000 = _111 << 3 + // _111111 = _111 + _111000 + // x12 = _111111 << 6 + _111111 + // x15 = x12 << 3 + _111 + // x16 = 2*x15 + 1 + // x32 = x16 << 16 + x16 + // i53 = x32 << 15 + // x47 = x15 + i53 + // i263 = ((i53 << 17 + 1) << 143 + x47) << 47 + // return (x47 + i263) << 2 + 1 + // + + var z = new(P256Element).Set(e) + var t0 = new(P256Element) + var t1 = new(P256Element) + + z.Square(x) + z.Mul(x, z) + z.Square(z) + z.Mul(x, z) + t0.Square(z) + for s := 1; s < 3; s++ { + t0.Square(t0) + } + t0.Mul(z, t0) + t1.Square(t0) + for s := 1; s < 6; s++ { + t1.Square(t1) + } + t0.Mul(t0, t1) + for s := 0; s < 3; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + t0.Square(z) + t0.Mul(x, t0) + t1.Square(t0) + for s := 1; s < 16; s++ { + t1.Square(t1) + } + t0.Mul(t0, t1) + for s := 0; s < 15; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + for s := 0; s < 17; s++ { + t0.Square(t0) + } + t0.Mul(x, t0) + for s := 0; s < 143; s++ { + t0.Square(t0) + } + t0.Mul(z, t0) + for s := 0; s < 47; s++ { + t0.Square(t0) + } + z.Mul(z, t0) + for s := 0; s < 2; s++ { + z.Square(z) + } + z.Mul(x, z) + + return e.Set(z) +} diff --git a/src/crypto/elliptic/internal/nistec/generate.go b/src/crypto/elliptic/internal/nistec/generate.go index 52b14f8424..a7c9d00db4 100644 --- a/src/crypto/elliptic/internal/nistec/generate.go +++ b/src/crypto/elliptic/internal/nistec/generate.go @@ -28,6 +28,11 @@ var curves = []struct { Element: "fiat.P224Element", Params: elliptic.P224().Params(), }, + { + P: "P256", + Element: "fiat.P256Element", + Params: elliptic.P256().Params(), + }, { P: "P384", Element: "fiat.P384Element", diff --git a/src/crypto/elliptic/internal/nistec/nistec_test.go b/src/crypto/elliptic/internal/nistec/nistec_test.go index 4eae998c5d..9fde2f4fa1 100644 --- a/src/crypto/elliptic/internal/nistec/nistec_test.go +++ b/src/crypto/elliptic/internal/nistec/nistec_test.go @@ -5,6 +5,7 @@ package nistec_test import ( + "bytes" "crypto/elliptic/internal/nistec" "math/rand" "os" @@ -19,7 +20,21 @@ func TestAllocations(t *testing.T) { t.Run("P224", func(t *testing.T) { if allocs := testing.AllocsPerRun(100, func() { p := nistec.NewP224Generator() - scalar := make([]byte, 66) + scalar := make([]byte, 28) + rand.Read(scalar) + p.ScalarMult(p, scalar) + out := p.Bytes() + if _, err := p.SetBytes(out); err != nil { + t.Fatal(err) + } + }); allocs > 0 { + t.Errorf("expected zero allocations, got %0.1f", allocs) + } + }) + t.Run("P256", func(t *testing.T) { + if allocs := testing.AllocsPerRun(100, func() { + p := nistec.NewP256Generator() + scalar := make([]byte, 32) rand.Read(scalar) p.ScalarMult(p, scalar) out := p.Bytes() @@ -33,7 +48,7 @@ func TestAllocations(t *testing.T) { t.Run("P384", func(t *testing.T) { if allocs := testing.AllocsPerRun(100, func() { p := nistec.NewP384Generator() - scalar := make([]byte, 66) + scalar := make([]byte, 48) rand.Read(scalar) p.ScalarMult(p, scalar) out := p.Bytes() @@ -60,35 +75,65 @@ func TestAllocations(t *testing.T) { }) } +type nistPoint[T any] interface { + Bytes() []byte + SetBytes([]byte) (T, error) + Add(T, T) T + Double(T) T + ScalarMult(T, []byte) T +} + +func TestEquivalents(t *testing.T) { + t.Run("P224", func(t *testing.T) { + testEquivalents(t, nistec.NewP224Point, nistec.NewP224Generator) + }) + t.Run("P256", func(t *testing.T) { + testEquivalents(t, nistec.NewP256Point, nistec.NewP256Generator) + }) + t.Run("P384", func(t *testing.T) { + testEquivalents(t, nistec.NewP384Point, nistec.NewP384Generator) + }) + t.Run("P521", func(t *testing.T) { + testEquivalents(t, nistec.NewP521Point, nistec.NewP521Generator) + }) +} + +func testEquivalents[P nistPoint[P]](t *testing.T, newPoint, newGenerator func() P) { + p := newGenerator() + + p1 := newPoint().Double(p) + p2 := newPoint().Add(p, p) + p3 := newPoint().ScalarMult(p, []byte{2}) + + if !bytes.Equal(p1.Bytes(), p2.Bytes()) { + t.Error("P+P != 2*P") + } + if !bytes.Equal(p1.Bytes(), p3.Bytes()) { + t.Error("P+P != [2]P") + } +} + func BenchmarkScalarMult(b *testing.B) { b.Run("P224", func(b *testing.B) { - scalar := make([]byte, 66) - rand.Read(scalar) - p := nistec.NewP224Generator() - b.ReportAllocs() - b.ResetTimer() - for i := 0; i < b.N; i++ { - p.ScalarMult(p, scalar) - } + benchmarkScalarMult(b, nistec.NewP224Generator(), 28) + }) + b.Run("P256", func(b *testing.B) { + benchmarkScalarMult(b, nistec.NewP256Generator(), 32) }) b.Run("P384", func(b *testing.B) { - scalar := make([]byte, 66) - rand.Read(scalar) - p := nistec.NewP384Generator() - b.ReportAllocs() - b.ResetTimer() - for i := 0; i < b.N; i++ { - p.ScalarMult(p, scalar) - } + benchmarkScalarMult(b, nistec.NewP384Generator(), 48) }) b.Run("P521", func(b *testing.B) { - scalar := make([]byte, 66) - rand.Read(scalar) - p := nistec.NewP521Generator() - b.ReportAllocs() - b.ResetTimer() - for i := 0; i < b.N; i++ { - p.ScalarMult(p, scalar) - } + benchmarkScalarMult(b, nistec.NewP521Generator(), 66) }) } + +func benchmarkScalarMult[P nistPoint[P]](b *testing.B, p P, scalarSize int) { + scalar := make([]byte, scalarSize) + rand.Read(scalar) + b.ReportAllocs() + b.ResetTimer() + for i := 0; i < b.N; i++ { + p.ScalarMult(p, scalar) + } +} diff --git a/src/crypto/elliptic/internal/nistec/p256.go b/src/crypto/elliptic/internal/nistec/p256.go new file mode 100644 index 0000000000..e3f172767b --- /dev/null +++ b/src/crypto/elliptic/internal/nistec/p256.go @@ -0,0 +1,288 @@ +// Copyright 2022 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +// Code generated by generate.go. DO NOT EDIT. + +package nistec + +import ( + "crypto/elliptic/internal/fiat" + "crypto/subtle" + "errors" +) + +var p256B, _ = new(fiat.P256Element).SetBytes([]byte{0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7, 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc, 0x65, 0x1d, 0x6, 0xb0, 0xcc, 0x53, 0xb0, 0xf6, 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b}) + +var p256G, _ = NewP256Point().SetBytes([]byte{0x4, 0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2, 0x77, 0x3, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0, 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96, 0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0xf, 0x9e, 0x16, 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5}) + +const p256ElementLength = 32 + +// P256Point is a P256 point. The zero value is NOT valid. +type P256Point struct { + // The point is represented in projective coordinates (X:Y:Z), + // where x = X/Z and y = Y/Z. + x, y, z *fiat.P256Element +} + +// NewP256Point returns a new P256Point representing the point at infinity point. +func NewP256Point() *P256Point { + return &P256Point{ + x: new(fiat.P256Element), + y: new(fiat.P256Element).One(), + z: new(fiat.P256Element), + } +} + +// NewP256Generator returns a new P256Point set to the canonical generator. +func NewP256Generator() *P256Point { + return (&P256Point{ + x: new(fiat.P256Element), + y: new(fiat.P256Element), + z: new(fiat.P256Element), + }).Set(p256G) +} + +// Set sets p = q and returns p. +func (p *P256Point) Set(q *P256Point) *P256Point { + p.x.Set(q.x) + p.y.Set(q.y) + p.z.Set(q.z) + return p +} + +// SetBytes sets p to the compressed, uncompressed, or infinity value encoded in +// b, as specified in SEC 1, Version 2.0, Section 2.3.4. If the point is not on +// the curve, it returns nil and an error, and the receiver is unchanged. +// Otherwise, it returns p. +func (p *P256Point) SetBytes(b []byte) (*P256Point, error) { + switch { + // Point at infinity. + case len(b) == 1 && b[0] == 0: + return p.Set(NewP256Point()), nil + + // Uncompressed form. + case len(b) == 1+2*p256ElementLength && b[0] == 4: + x, err := new(fiat.P256Element).SetBytes(b[1 : 1+p256ElementLength]) + if err != nil { + return nil, err + } + y, err := new(fiat.P256Element).SetBytes(b[1+p256ElementLength:]) + if err != nil { + return nil, err + } + if err := p256CheckOnCurve(x, y); err != nil { + return nil, err + } + p.x.Set(x) + p.y.Set(y) + p.z.One() + return p, nil + + // Compressed form + case len(b) == 1+p256ElementLength && b[0] == 0: + return nil, errors.New("unimplemented") // TODO(filippo) + + default: + return nil, errors.New("invalid P256 point encoding") + } +} + +func p256CheckOnCurve(x, y *fiat.P256Element) error { + // x³ - 3x + b. + x3 := new(fiat.P256Element).Square(x) + x3.Mul(x3, x) + + threeX := new(fiat.P256Element).Add(x, x) + threeX.Add(threeX, x) + + x3.Sub(x3, threeX) + x3.Add(x3, p256B) + + // y² = x³ - 3x + b + y2 := new(fiat.P256Element).Square(y) + + if x3.Equal(y2) != 1 { + return errors.New("P256 point not on curve") + } + return nil +} + +// Bytes returns the uncompressed or infinity encoding of p, as specified in +// SEC 1, Version 2.0, Section 2.3.3. Note that the encoding of the point at +// infinity is shorter than all other encodings. +func (p *P256Point) Bytes() []byte { + // This function is outlined to make the allocations inline in the caller + // rather than happen on the heap. + var out [133]byte + return p.bytes(&out) +} + +func (p *P256Point) bytes(out *[133]byte) []byte { + if p.z.IsZero() == 1 { + return append(out[:0], 0) + } + + zinv := new(fiat.P256Element).Invert(p.z) + xx := new(fiat.P256Element).Mul(p.x, zinv) + yy := new(fiat.P256Element).Mul(p.y, zinv) + + buf := append(out[:0], 4) + buf = append(buf, xx.Bytes()...) + buf = append(buf, yy.Bytes()...) + return buf +} + +// Add sets q = p1 + p2, and returns q. The points may overlap. +func (q *P256Point) Add(p1, p2 *P256Point) *P256Point { + // Complete addition formula for a = -3 from "Complete addition formulas for + // prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2. + + t0 := new(fiat.P256Element).Mul(p1.x, p2.x) // t0 := X1 * X2 + t1 := new(fiat.P256Element).Mul(p1.y, p2.y) // t1 := Y1 * Y2 + t2 := new(fiat.P256Element).Mul(p1.z, p2.z) // t2 := Z1 * Z2 + t3 := new(fiat.P256Element).Add(p1.x, p1.y) // t3 := X1 + Y1 + t4 := new(fiat.P256Element).Add(p2.x, p2.y) // t4 := X2 + Y2 + t3.Mul(t3, t4) // t3 := t3 * t4 + t4.Add(t0, t1) // t4 := t0 + t1 + t3.Sub(t3, t4) // t3 := t3 - t4 + t4.Add(p1.y, p1.z) // t4 := Y1 + Z1 + x3 := new(fiat.P256Element).Add(p2.y, p2.z) // X3 := Y2 + Z2 + t4.Mul(t4, x3) // t4 := t4 * X3 + x3.Add(t1, t2) // X3 := t1 + t2 + t4.Sub(t4, x3) // t4 := t4 - X3 + x3.Add(p1.x, p1.z) // X3 := X1 + Z1 + y3 := new(fiat.P256Element).Add(p2.x, p2.z) // Y3 := X2 + Z2 + x3.Mul(x3, y3) // X3 := X3 * Y3 + y3.Add(t0, t2) // Y3 := t0 + t2 + y3.Sub(x3, y3) // Y3 := X3 - Y3 + z3 := new(fiat.P256Element).Mul(p256B, t2) // Z3 := b * t2 + x3.Sub(y3, z3) // X3 := Y3 - Z3 + z3.Add(x3, x3) // Z3 := X3 + X3 + x3.Add(x3, z3) // X3 := X3 + Z3 + z3.Sub(t1, x3) // Z3 := t1 - X3 + x3.Add(t1, x3) // X3 := t1 + X3 + y3.Mul(p256B, y3) // Y3 := b * Y3 + t1.Add(t2, t2) // t1 := t2 + t2 + t2.Add(t1, t2) // t2 := t1 + t2 + y3.Sub(y3, t2) // Y3 := Y3 - t2 + y3.Sub(y3, t0) // Y3 := Y3 - t0 + t1.Add(y3, y3) // t1 := Y3 + Y3 + y3.Add(t1, y3) // Y3 := t1 + Y3 + t1.Add(t0, t0) // t1 := t0 + t0 + t0.Add(t1, t0) // t0 := t1 + t0 + t0.Sub(t0, t2) // t0 := t0 - t2 + t1.Mul(t4, y3) // t1 := t4 * Y3 + t2.Mul(t0, y3) // t2 := t0 * Y3 + y3.Mul(x3, z3) // Y3 := X3 * Z3 + y3.Add(y3, t2) // Y3 := Y3 + t2 + x3.Mul(t3, x3) // X3 := t3 * X3 + x3.Sub(x3, t1) // X3 := X3 - t1 + z3.Mul(t4, z3) // Z3 := t4 * Z3 + t1.Mul(t3, t0) // t1 := t3 * t0 + z3.Add(z3, t1) // Z3 := Z3 + t1 + + q.x.Set(x3) + q.y.Set(y3) + q.z.Set(z3) + return q +} + +// Double sets q = p + p, and returns q. The points may overlap. +func (q *P256Point) Double(p *P256Point) *P256Point { + // Complete addition formula for a = -3 from "Complete addition formulas for + // prime order elliptic curves" (https://eprint.iacr.org/2015/1060), §A.2. + + t0 := new(fiat.P256Element).Square(p.x) // t0 := X ^ 2 + t1 := new(fiat.P256Element).Square(p.y) // t1 := Y ^ 2 + t2 := new(fiat.P256Element).Square(p.z) // t2 := Z ^ 2 + t3 := new(fiat.P256Element).Mul(p.x, p.y) // t3 := X * Y + t3.Add(t3, t3) // t3 := t3 + t3 + z3 := new(fiat.P256Element).Mul(p.x, p.z) // Z3 := X * Z + z3.Add(z3, z3) // Z3 := Z3 + Z3 + y3 := new(fiat.P256Element).Mul(p256B, t2) // Y3 := b * t2 + y3.Sub(y3, z3) // Y3 := Y3 - Z3 + x3 := new(fiat.P256Element).Add(y3, y3) // X3 := Y3 + Y3 + y3.Add(x3, y3) // Y3 := X3 + Y3 + x3.Sub(t1, y3) // X3 := t1 - Y3 + y3.Add(t1, y3) // Y3 := t1 + Y3 + y3.Mul(x3, y3) // Y3 := X3 * Y3 + x3.Mul(x3, t3) // X3 := X3 * t3 + t3.Add(t2, t2) // t3 := t2 + t2 + t2.Add(t2, t3) // t2 := t2 + t3 + z3.Mul(p256B, z3) // Z3 := b * Z3 + z3.Sub(z3, t2) // Z3 := Z3 - t2 + z3.Sub(z3, t0) // Z3 := Z3 - t0 + t3.Add(z3, z3) // t3 := Z3 + Z3 + z3.Add(z3, t3) // Z3 := Z3 + t3 + t3.Add(t0, t0) // t3 := t0 + t0 + t0.Add(t3, t0) // t0 := t3 + t0 + t0.Sub(t0, t2) // t0 := t0 - t2 + t0.Mul(t0, z3) // t0 := t0 * Z3 + y3.Add(y3, t0) // Y3 := Y3 + t0 + t0.Mul(p.y, p.z) // t0 := Y * Z + t0.Add(t0, t0) // t0 := t0 + t0 + z3.Mul(t0, z3) // Z3 := t0 * Z3 + x3.Sub(x3, z3) // X3 := X3 - Z3 + z3.Mul(t0, t1) // Z3 := t0 * t1 + z3.Add(z3, z3) // Z3 := Z3 + Z3 + z3.Add(z3, z3) // Z3 := Z3 + Z3 + + q.x.Set(x3) + q.y.Set(y3) + q.z.Set(z3) + return q +} + +// Select sets q to p1 if cond == 1, and to p2 if cond == 0. +func (q *P256Point) Select(p1, p2 *P256Point, cond int) *P256Point { + q.x.Select(p1.x, p2.x, cond) + q.y.Select(p1.y, p2.y, cond) + q.z.Select(p1.z, p2.z, cond) + return q +} + +// ScalarMult sets p = scalar * q, and returns p. +func (p *P256Point) ScalarMult(q *P256Point, scalar []byte) *P256Point { + // table holds the first 16 multiples of q. The explicit newP256Point calls + // get inlined, letting the allocations live on the stack. + var table = [16]*P256Point{ + NewP256Point(), NewP256Point(), NewP256Point(), NewP256Point(), + NewP256Point(), NewP256Point(), NewP256Point(), NewP256Point(), + NewP256Point(), NewP256Point(), NewP256Point(), NewP256Point(), + NewP256Point(), NewP256Point(), NewP256Point(), NewP256Point(), + } + for i := 1; i < 16; i++ { + table[i].Add(table[i-1], q) + } + + // Instead of doing the classic double-and-add chain, we do it with a + // four-bit window: we double four times, and then add [0-15]P. + t := NewP256Point() + p.Set(NewP256Point()) + for _, byte := range scalar { + p.Double(p) + p.Double(p) + p.Double(p) + p.Double(p) + + for i := uint8(0); i < 16; i++ { + cond := subtle.ConstantTimeByteEq(byte>>4, i) + t.Select(table[i], t, cond) + } + p.Add(p, t) + + p.Double(p) + p.Double(p) + p.Double(p) + p.Double(p) + + for i := uint8(0); i < 16; i++ { + cond := subtle.ConstantTimeByteEq(byte&0b1111, i) + t.Select(table[i], t, cond) + } + p.Add(p, t) + } + + return p +} diff --git a/src/crypto/elliptic/nistec.go b/src/crypto/elliptic/nistec.go index c6f170b3f0..2a95380e06 100644 --- a/src/crypto/elliptic/nistec.go +++ b/src/crypto/elliptic/nistec.go @@ -29,6 +29,36 @@ func initP224() { } } +var p256Params CurveParams + +var p256 Curve = &nistCurve[*nistec.P256Point]{ + params: &p256Params, + newPoint: nistec.NewP256Point, + newGenerator: nistec.NewP256Generator, +} + +var initP256Arch func() + +func initP256() { + p256Params = CurveParams{ + Name: "P-256", + BitSize: 256, + // FIPS 186-4, section D.1.2.3 + P: bigFromDecimal("115792089210356248762697446949407573530086143415290314195533631308867097853951"), + N: bigFromDecimal("115792089210356248762697446949407573529996955224135760342422259061068512044369"), + B: bigFromHex("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b"), + Gx: bigFromHex("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296"), + Gy: bigFromHex("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5"), + } + + // P-256 is implemented by various different backends, including a generic + // 32-bit constant-time one in internal/nistec, which is used when assembly + // implementations are not available, or not appropriate for the hardware. + if initP256Arch != nil { + initP256Arch() + } +} + var p384 = &nistCurve[*nistec.P384Point]{ newPoint: nistec.NewP384Point, newGenerator: nistec.NewP384Generator, diff --git a/src/crypto/elliptic/p256.go b/src/crypto/elliptic/p256.go deleted file mode 100644 index 97ecda5a8e..0000000000 --- a/src/crypto/elliptic/p256.go +++ /dev/null @@ -1,32 +0,0 @@ -// Copyright 2021 The Go Authors. All rights reserved. -// Use of this source code is governed by a BSD-style -// license that can be found in the LICENSE file. - -package elliptic - -// P-256 is implemented by various different backends, including a generic -// 32-bit constant-time one in p256_generic.go, which is used when assembly -// implementations are not available, or not appropriate for the hardware. - -import "math/big" - -var p256Params *CurveParams - -// RInverse contains 1/R mod p, the inverse of the Montgomery constant 2^257. -var p256RInverse *big.Int - -func initP256() { - // See FIPS 186-3, section D.2.3 - p256Params = &CurveParams{Name: "P-256"} - p256Params.P, _ = new(big.Int).SetString("115792089210356248762697446949407573530086143415290314195533631308867097853951", 10) - p256Params.N, _ = new(big.Int).SetString("115792089210356248762697446949407573529996955224135760342422259061068512044369", 10) - p256Params.B, _ = new(big.Int).SetString("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16) - p256Params.Gx, _ = new(big.Int).SetString("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16) - p256Params.Gy, _ = new(big.Int).SetString("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16) - p256Params.BitSize = 256 - - p256RInverse, _ = new(big.Int).SetString("7fffffff00000001fffffffe8000000100000000ffffffff0000000180000000", 16) - - // Arch-specific initialization, i.e. let a platform dynamically pick a P256 implementation - initP256Arch() -} diff --git a/src/crypto/elliptic/p256_asm.go b/src/crypto/elliptic/p256_asm.go index ce80282ed6..f8335bc85c 100644 --- a/src/crypto/elliptic/p256_asm.go +++ b/src/crypto/elliptic/p256_asm.go @@ -32,10 +32,10 @@ type p256Point struct { xyz [12]uint64 } -var p256 p256Curve - -func initP256Arch() { - p256 = p256Curve{p256Params} +func init() { + initP256Arch = func() { + p256 = p256Curve{&p256Params} + } } func (curve p256Curve) Params() *CurveParams { @@ -120,9 +120,9 @@ func (curve p256Curve) Inverse(k *big.Int) *big.Int { k = new(big.Int).Neg(k) } - if k.Cmp(p256.N) >= 0 { + if k.Cmp(p256Params.N) >= 0 { // This should never happen. - k = new(big.Int).Mod(k, p256.N) + k = new(big.Int).Mod(k, p256Params.N) } // table will store precomputed powers of x. @@ -218,8 +218,8 @@ func fromBig(out []uint64, big *big.Int) { func p256GetScalar(out []uint64, in []byte) { n := new(big.Int).SetBytes(in) - if n.Cmp(p256.N) >= 0 { - n.Mod(n, p256.N) + if n.Cmp(p256Params.N) >= 0 { + n.Mod(n, p256Params.N) } fromBig(out, n) } @@ -230,10 +230,10 @@ func p256GetScalar(out []uint64, in []byte) { var rr = []uint64{0x0000000000000003, 0xfffffffbffffffff, 0xfffffffffffffffe, 0x00000004fffffffd} func maybeReduceModP(in *big.Int) *big.Int { - if in.Cmp(p256.P) < 0 { + if in.Cmp(p256Params.P) < 0 { return in } - return new(big.Int).Mod(in, p256.P) + return new(big.Int).Mod(in, p256Params.P) } func (curve p256Curve) CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int) { diff --git a/src/crypto/elliptic/p256_generic.go b/src/crypto/elliptic/p256_generic.go deleted file mode 100644 index 22dde23109..0000000000 --- a/src/crypto/elliptic/p256_generic.go +++ /dev/null @@ -1,477 +0,0 @@ -// Copyright 2013 The Go Authors. All rights reserved. -// Use of this source code is governed by a BSD-style -// license that can be found in the LICENSE file. - -//go:build !amd64 && !arm64 - -package elliptic - -// This file contains a constant-time, 32-bit implementation of P256. - -import "math/big" - -type p256Curve struct { - *CurveParams -} - -func (curve p256Curve) Params() *CurveParams { - return curve.CurveParams -} - -// p256GetScalar endian-swaps the big-endian scalar value from in and writes it -// to out. If the scalar is equal or greater than the order of the group, it's -// reduced modulo that order. -func p256GetScalar(out *[32]byte, in []byte) { - n := new(big.Int).SetBytes(in) - var scalarBytes []byte - - if n.Cmp(p256Params.N) >= 0 || len(in) > len(out) { - n.Mod(n, p256Params.N) - scalarBytes = n.Bytes() - } else { - scalarBytes = in - } - - for i, v := range scalarBytes { - out[len(scalarBytes)-(1+i)] = v - } -} - -func (p256Curve) ScalarBaseMult(scalar []byte) (x, y *big.Int) { - var scalarReversed [32]byte - p256GetScalar(&scalarReversed, scalar) - - var x1, y1, z1 [p256Limbs]uint32 - p256ScalarBaseMult(&x1, &y1, &z1, &scalarReversed) - return p256ToAffine(&x1, &y1, &z1) -} - -func (p256Curve) ScalarMult(bigX, bigY *big.Int, scalar []byte) (x, y *big.Int) { - var scalarReversed [32]byte - p256GetScalar(&scalarReversed, scalar) - - var px, py, x1, y1, z1 [p256Limbs]uint32 - p256FromBig(&px, bigX) - p256FromBig(&py, bigY) - p256ScalarMult(&x1, &y1, &z1, &px, &py, &scalarReversed) - return p256ToAffine(&x1, &y1, &z1) -} - -// p256Precomputed contains precomputed values to aid the calculation of scalar -// multiples of the base point, G. It's actually two, equal length, tables -// concatenated. -// -// The first table contains (x,y) field element pairs for 16 multiples of the -// base point, G. -// -// Index | Index (binary) | Value -// 0 | 0000 | 0G (all zeros, omitted) -// 1 | 0001 | G -// 2 | 0010 | 2**64G -// 3 | 0011 | 2**64G + G -// 4 | 0100 | 2**128G -// 5 | 0101 | 2**128G + G -// 6 | 0110 | 2**128G + 2**64G -// 7 | 0111 | 2**128G + 2**64G + G -// 8 | 1000 | 2**192G -// 9 | 1001 | 2**192G + G -// 10 | 1010 | 2**192G + 2**64G -// 11 | 1011 | 2**192G + 2**64G + G -// 12 | 1100 | 2**192G + 2**128G -// 13 | 1101 | 2**192G + 2**128G + G -// 14 | 1110 | 2**192G + 2**128G + 2**64G -// 15 | 1111 | 2**192G + 2**128G + 2**64G + G -// -// The second table follows the same style, but the terms are 2**32G, -// 2**96G, 2**160G, 2**224G. -// -// This is ~2KB of data. -var p256Precomputed = [p256Limbs * 2 * 15 * 2]uint32{ - 0x11522878, 0xe730d41, 0xdb60179, 0x4afe2ff, 0x12883add, 0xcaddd88, 0x119e7edc, 0xd4a6eab, 0x3120bee, - 0x1d2aac15, 0xf25357c, 0x19e45cdd, 0x5c721d0, 0x1992c5a5, 0xa237487, 0x154ba21, 0x14b10bb, 0xae3fe3, - 0xd41a576, 0x922fc51, 0x234994f, 0x60b60d3, 0x164586ae, 0xce95f18, 0x1fe49073, 0x3fa36cc, 0x5ebcd2c, - 0xb402f2f, 0x15c70bf, 0x1561925c, 0x5a26704, 0xda91e90, 0xcdc1c7f, 0x1ea12446, 0xe1ade1e, 0xec91f22, - 0x26f7778, 0x566847e, 0xa0bec9e, 0x234f453, 0x1a31f21a, 0xd85e75c, 0x56c7109, 0xa267a00, 0xb57c050, - 0x98fb57, 0xaa837cc, 0x60c0792, 0xcfa5e19, 0x61bab9e, 0x589e39b, 0xa324c5, 0x7d6dee7, 0x2976e4b, - 0x1fc4124a, 0xa8c244b, 0x1ce86762, 0xcd61c7e, 0x1831c8e0, 0x75774e1, 0x1d96a5a9, 0x843a649, 0xc3ab0fa, - 0x6e2e7d5, 0x7673a2a, 0x178b65e8, 0x4003e9b, 0x1a1f11c2, 0x7816ea, 0xf643e11, 0x58c43df, 0xf423fc2, - 0x19633ffa, 0x891f2b2, 0x123c231c, 0x46add8c, 0x54700dd, 0x59e2b17, 0x172db40f, 0x83e277d, 0xb0dd609, - 0xfd1da12, 0x35c6e52, 0x19ede20c, 0xd19e0c0, 0x97d0f40, 0xb015b19, 0x449e3f5, 0xe10c9e, 0x33ab581, - 0x56a67ab, 0x577734d, 0x1dddc062, 0xc57b10d, 0x149b39d, 0x26a9e7b, 0xc35df9f, 0x48764cd, 0x76dbcca, - 0xca4b366, 0xe9303ab, 0x1a7480e7, 0x57e9e81, 0x1e13eb50, 0xf466cf3, 0x6f16b20, 0x4ba3173, 0xc168c33, - 0x15cb5439, 0x6a38e11, 0x73658bd, 0xb29564f, 0x3f6dc5b, 0x53b97e, 0x1322c4c0, 0x65dd7ff, 0x3a1e4f6, - 0x14e614aa, 0x9246317, 0x1bc83aca, 0xad97eed, 0xd38ce4a, 0xf82b006, 0x341f077, 0xa6add89, 0x4894acd, - 0x9f162d5, 0xf8410ef, 0x1b266a56, 0xd7f223, 0x3e0cb92, 0xe39b672, 0x6a2901a, 0x69a8556, 0x7e7c0, - 0x9b7d8d3, 0x309a80, 0x1ad05f7f, 0xc2fb5dd, 0xcbfd41d, 0x9ceb638, 0x1051825c, 0xda0cf5b, 0x812e881, - 0x6f35669, 0x6a56f2c, 0x1df8d184, 0x345820, 0x1477d477, 0x1645db1, 0xbe80c51, 0xc22be3e, 0xe35e65a, - 0x1aeb7aa0, 0xc375315, 0xf67bc99, 0x7fdd7b9, 0x191fc1be, 0x61235d, 0x2c184e9, 0x1c5a839, 0x47a1e26, - 0xb7cb456, 0x93e225d, 0x14f3c6ed, 0xccc1ac9, 0x17fe37f3, 0x4988989, 0x1a90c502, 0x2f32042, 0xa17769b, - 0xafd8c7c, 0x8191c6e, 0x1dcdb237, 0x16200c0, 0x107b32a1, 0x66c08db, 0x10d06a02, 0x3fc93, 0x5620023, - 0x16722b27, 0x68b5c59, 0x270fcfc, 0xfad0ecc, 0xe5de1c2, 0xeab466b, 0x2fc513c, 0x407f75c, 0xbaab133, - 0x9705fe9, 0xb88b8e7, 0x734c993, 0x1e1ff8f, 0x19156970, 0xabd0f00, 0x10469ea7, 0x3293ac0, 0xcdc98aa, - 0x1d843fd, 0xe14bfe8, 0x15be825f, 0x8b5212, 0xeb3fb67, 0x81cbd29, 0xbc62f16, 0x2b6fcc7, 0xf5a4e29, - 0x13560b66, 0xc0b6ac2, 0x51ae690, 0xd41e271, 0xf3e9bd4, 0x1d70aab, 0x1029f72, 0x73e1c35, 0xee70fbc, - 0xad81baf, 0x9ecc49a, 0x86c741e, 0xfe6be30, 0x176752e7, 0x23d416, 0x1f83de85, 0x27de188, 0x66f70b8, - 0x181cd51f, 0x96b6e4c, 0x188f2335, 0xa5df759, 0x17a77eb6, 0xfeb0e73, 0x154ae914, 0x2f3ec51, 0x3826b59, - 0xb91f17d, 0x1c72949, 0x1362bf0a, 0xe23fddf, 0xa5614b0, 0xf7d8f, 0x79061, 0x823d9d2, 0x8213f39, - 0x1128ae0b, 0xd095d05, 0xb85c0c2, 0x1ecb2ef, 0x24ddc84, 0xe35e901, 0x18411a4a, 0xf5ddc3d, 0x3786689, - 0x52260e8, 0x5ae3564, 0x542b10d, 0x8d93a45, 0x19952aa4, 0x996cc41, 0x1051a729, 0x4be3499, 0x52b23aa, - 0x109f307e, 0x6f5b6bb, 0x1f84e1e7, 0x77a0cfa, 0x10c4df3f, 0x25a02ea, 0xb048035, 0xe31de66, 0xc6ecaa3, - 0x28ea335, 0x2886024, 0x1372f020, 0xf55d35, 0x15e4684c, 0xf2a9e17, 0x1a4a7529, 0xcb7beb1, 0xb2a78a1, - 0x1ab21f1f, 0x6361ccf, 0x6c9179d, 0xb135627, 0x1267b974, 0x4408bad, 0x1cbff658, 0xe3d6511, 0xc7d76f, - 0x1cc7a69, 0xe7ee31b, 0x54fab4f, 0x2b914f, 0x1ad27a30, 0xcd3579e, 0xc50124c, 0x50daa90, 0xb13f72, - 0xb06aa75, 0x70f5cc6, 0x1649e5aa, 0x84a5312, 0x329043c, 0x41c4011, 0x13d32411, 0xb04a838, 0xd760d2d, - 0x1713b532, 0xbaa0c03, 0x84022ab, 0x6bcf5c1, 0x2f45379, 0x18ae070, 0x18c9e11e, 0x20bca9a, 0x66f496b, - 0x3eef294, 0x67500d2, 0xd7f613c, 0x2dbbeb, 0xb741038, 0xe04133f, 0x1582968d, 0xbe985f7, 0x1acbc1a, - 0x1a6a939f, 0x33e50f6, 0xd665ed4, 0xb4b7bd6, 0x1e5a3799, 0x6b33847, 0x17fa56ff, 0x65ef930, 0x21dc4a, - 0x2b37659, 0x450fe17, 0xb357b65, 0xdf5efac, 0x15397bef, 0x9d35a7f, 0x112ac15f, 0x624e62e, 0xa90ae2f, - 0x107eecd2, 0x1f69bbe, 0x77d6bce, 0x5741394, 0x13c684fc, 0x950c910, 0x725522b, 0xdc78583, 0x40eeabb, - 0x1fde328a, 0xbd61d96, 0xd28c387, 0x9e77d89, 0x12550c40, 0x759cb7d, 0x367ef34, 0xae2a960, 0x91b8bdc, - 0x93462a9, 0xf469ef, 0xb2e9aef, 0xd2ca771, 0x54e1f42, 0x7aaa49, 0x6316abb, 0x2413c8e, 0x5425bf9, - 0x1bed3e3a, 0xf272274, 0x1f5e7326, 0x6416517, 0xea27072, 0x9cedea7, 0x6e7633, 0x7c91952, 0xd806dce, - 0x8e2a7e1, 0xe421e1a, 0x418c9e1, 0x1dbc890, 0x1b395c36, 0xa1dc175, 0x1dc4ef73, 0x8956f34, 0xe4b5cf2, - 0x1b0d3a18, 0x3194a36, 0x6c2641f, 0xe44124c, 0xa2f4eaa, 0xa8c25ba, 0xf927ed7, 0x627b614, 0x7371cca, - 0xba16694, 0x417bc03, 0x7c0a7e3, 0x9c35c19, 0x1168a205, 0x8b6b00d, 0x10e3edc9, 0x9c19bf2, 0x5882229, - 0x1b2b4162, 0xa5cef1a, 0x1543622b, 0x9bd433e, 0x364e04d, 0x7480792, 0x5c9b5b3, 0xe85ff25, 0x408ef57, - 0x1814cfa4, 0x121b41b, 0xd248a0f, 0x3b05222, 0x39bb16a, 0xc75966d, 0xa038113, 0xa4a1769, 0x11fbc6c, - 0x917e50e, 0xeec3da8, 0x169d6eac, 0x10c1699, 0xa416153, 0xf724912, 0x15cd60b7, 0x4acbad9, 0x5efc5fa, - 0xf150ed7, 0x122b51, 0x1104b40a, 0xcb7f442, 0xfbb28ff, 0x6ac53ca, 0x196142cc, 0x7bf0fa9, 0x957651, - 0x4e0f215, 0xed439f8, 0x3f46bd5, 0x5ace82f, 0x110916b6, 0x6db078, 0xffd7d57, 0xf2ecaac, 0xca86dec, - 0x15d6b2da, 0x965ecc9, 0x1c92b4c2, 0x1f3811, 0x1cb080f5, 0x2d8b804, 0x19d1c12d, 0xf20bd46, 0x1951fa7, - 0xa3656c3, 0x523a425, 0xfcd0692, 0xd44ddc8, 0x131f0f5b, 0xaf80e4a, 0xcd9fc74, 0x99bb618, 0x2db944c, - 0xa673090, 0x1c210e1, 0x178c8d23, 0x1474383, 0x10b8743d, 0x985a55b, 0x2e74779, 0x576138, 0x9587927, - 0x133130fa, 0xbe05516, 0x9f4d619, 0xbb62570, 0x99ec591, 0xd9468fe, 0x1d07782d, 0xfc72e0b, 0x701b298, - 0x1863863b, 0x85954b8, 0x121a0c36, 0x9e7fedf, 0xf64b429, 0x9b9d71e, 0x14e2f5d8, 0xf858d3a, 0x942eea8, - 0xda5b765, 0x6edafff, 0xa9d18cc, 0xc65e4ba, 0x1c747e86, 0xe4ea915, 0x1981d7a1, 0x8395659, 0x52ed4e2, - 0x87d43b7, 0x37ab11b, 0x19d292ce, 0xf8d4692, 0x18c3053f, 0x8863e13, 0x4c146c0, 0x6bdf55a, 0x4e4457d, - 0x16152289, 0xac78ec2, 0x1a59c5a2, 0x2028b97, 0x71c2d01, 0x295851f, 0x404747b, 0x878558d, 0x7d29aa4, - 0x13d8341f, 0x8daefd7, 0x139c972d, 0x6b7ea75, 0xd4a9dde, 0xff163d8, 0x81d55d7, 0xa5bef68, 0xb7b30d8, - 0xbe73d6f, 0xaa88141, 0xd976c81, 0x7e7a9cc, 0x18beb771, 0xd773cbd, 0x13f51951, 0x9d0c177, 0x1c49a78, -} - -// Group operations: -// -// Elements of the elliptic curve group are represented in Jacobian -// coordinates: (x, y, z). An affine point (x', y') is x'=x/z**2, y'=y/z**3 in -// Jacobian form. - -// p256PointDouble sets {xOut,yOut,zOut} = 2*{x,y,z}. -// -// See https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l -func p256PointDouble(xOut, yOut, zOut, x, y, z *[p256Limbs]uint32) { - var delta, gamma, alpha, beta, tmp, tmp2 [p256Limbs]uint32 - - p256Square(&delta, z) - p256Square(&gamma, y) - p256Mul(&beta, x, &gamma) - - p256Sum(&tmp, x, &delta) - p256Diff(&tmp2, x, &delta) - p256Mul(&alpha, &tmp, &tmp2) - p256Scalar3(&alpha) - - p256Sum(&tmp, y, z) - p256Square(&tmp, &tmp) - p256Diff(&tmp, &tmp, &gamma) - p256Diff(zOut, &tmp, &delta) - - p256Scalar4(&beta) - p256Square(xOut, &alpha) - p256Diff(xOut, xOut, &beta) - p256Diff(xOut, xOut, &beta) - - p256Diff(&tmp, &beta, xOut) - p256Mul(&tmp, &alpha, &tmp) - p256Square(&tmp2, &gamma) - p256Scalar8(&tmp2) - p256Diff(yOut, &tmp, &tmp2) -} - -// p256PointAddMixed sets {xOut,yOut,zOut} = {x1,y1,z1} + {x2,y2,1}. -// (i.e. the second point is affine.) -// -// See https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl -// -// Note that this function does not handle P+P, infinity+P nor P+infinity -// correctly. -func p256PointAddMixed(xOut, yOut, zOut, x1, y1, z1, x2, y2 *[p256Limbs]uint32) { - var z1z1, z1z1z1, s2, u2, h, i, j, r, rr, v, tmp [p256Limbs]uint32 - - p256Square(&z1z1, z1) - p256Sum(&tmp, z1, z1) - - p256Mul(&u2, x2, &z1z1) - p256Mul(&z1z1z1, z1, &z1z1) - p256Mul(&s2, y2, &z1z1z1) - p256Diff(&h, &u2, x1) - p256Sum(&i, &h, &h) - p256Square(&i, &i) - p256Mul(&j, &h, &i) - p256Diff(&r, &s2, y1) - p256Sum(&r, &r, &r) - p256Mul(&v, x1, &i) - - p256Mul(zOut, &tmp, &h) - p256Square(&rr, &r) - p256Diff(xOut, &rr, &j) - p256Diff(xOut, xOut, &v) - p256Diff(xOut, xOut, &v) - - p256Diff(&tmp, &v, xOut) - p256Mul(yOut, &tmp, &r) - p256Mul(&tmp, y1, &j) - p256Diff(yOut, yOut, &tmp) - p256Diff(yOut, yOut, &tmp) -} - -// p256PointAdd sets {xOut,yOut,zOut} = {x1,y1,z1} + {x2,y2,z2}. -// -// See https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl -// -// Note that this function does not handle P+P, infinity+P nor P+infinity -// correctly. -func p256PointAdd(xOut, yOut, zOut, x1, y1, z1, x2, y2, z2 *[p256Limbs]uint32) { - var z1z1, z1z1z1, z2z2, z2z2z2, s1, s2, u1, u2, h, i, j, r, rr, v, tmp [p256Limbs]uint32 - - p256Square(&z1z1, z1) - p256Square(&z2z2, z2) - p256Mul(&u1, x1, &z2z2) - - p256Sum(&tmp, z1, z2) - p256Square(&tmp, &tmp) - p256Diff(&tmp, &tmp, &z1z1) - p256Diff(&tmp, &tmp, &z2z2) - - p256Mul(&z2z2z2, z2, &z2z2) - p256Mul(&s1, y1, &z2z2z2) - - p256Mul(&u2, x2, &z1z1) - p256Mul(&z1z1z1, z1, &z1z1) - p256Mul(&s2, y2, &z1z1z1) - p256Diff(&h, &u2, &u1) - p256Sum(&i, &h, &h) - p256Square(&i, &i) - p256Mul(&j, &h, &i) - p256Diff(&r, &s2, &s1) - p256Sum(&r, &r, &r) - p256Mul(&v, &u1, &i) - - p256Mul(zOut, &tmp, &h) - p256Square(&rr, &r) - p256Diff(xOut, &rr, &j) - p256Diff(xOut, xOut, &v) - p256Diff(xOut, xOut, &v) - - p256Diff(&tmp, &v, xOut) - p256Mul(yOut, &tmp, &r) - p256Mul(&tmp, &s1, &j) - p256Diff(yOut, yOut, &tmp) - p256Diff(yOut, yOut, &tmp) -} - -// p256SelectAffinePoint sets {out_x,out_y} to the index'th entry of table. -// -// On entry: index < 16, table[0] must be zero. -func p256SelectAffinePoint(xOut, yOut *[p256Limbs]uint32, table []uint32, index uint32) { - for i := range xOut { - xOut[i] = 0 - } - for i := range yOut { - yOut[i] = 0 - } - - for i := uint32(1); i < 16; i++ { - mask := i ^ index - mask |= mask >> 2 - mask |= mask >> 1 - mask &= 1 - mask-- - for j := range xOut { - xOut[j] |= table[0] & mask - table = table[1:] - } - for j := range yOut { - yOut[j] |= table[0] & mask - table = table[1:] - } - } -} - -// p256SelectJacobianPoint sets {out_x,out_y,out_z} to the index'th entry of -// table. -// -// On entry: index < 16, table[0] must be zero. -func p256SelectJacobianPoint(xOut, yOut, zOut *[p256Limbs]uint32, table *[16][3][p256Limbs]uint32, index uint32) { - for i := range xOut { - xOut[i] = 0 - } - for i := range yOut { - yOut[i] = 0 - } - for i := range zOut { - zOut[i] = 0 - } - - // The implicit value at index 0 is all zero. We don't need to perform that - // iteration of the loop because we already set out_* to zero. - for i := uint32(1); i < 16; i++ { - mask := i ^ index - mask |= mask >> 2 - mask |= mask >> 1 - mask &= 1 - mask-- - for j := range xOut { - xOut[j] |= table[i][0][j] & mask - } - for j := range yOut { - yOut[j] |= table[i][1][j] & mask - } - for j := range zOut { - zOut[j] |= table[i][2][j] & mask - } - } -} - -// p256GetBit returns the bit'th bit of scalar. -func p256GetBit(scalar *[32]uint8, bit uint) uint32 { - return uint32(((scalar[bit>>3]) >> (bit & 7)) & 1) -} - -// p256ScalarBaseMult sets {xOut,yOut,zOut} = scalar*G where scalar is a -// little-endian number. Note that the value of scalar must be less than the -// order of the group. -func p256ScalarBaseMult(xOut, yOut, zOut *[p256Limbs]uint32, scalar *[32]uint8) { - nIsInfinityMask := ^uint32(0) - var pIsNoninfiniteMask, mask, tableOffset uint32 - var px, py, tx, ty, tz [p256Limbs]uint32 - - for i := range xOut { - xOut[i] = 0 - } - for i := range yOut { - yOut[i] = 0 - } - for i := range zOut { - zOut[i] = 0 - } - - // The loop adds bits at positions 0, 64, 128 and 192, followed by - // positions 32,96,160 and 224 and does this 32 times. - for i := uint(0); i < 32; i++ { - if i != 0 { - p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) - } - tableOffset = 0 - for j := uint(0); j <= 32; j += 32 { - bit0 := p256GetBit(scalar, 31-i+j) - bit1 := p256GetBit(scalar, 95-i+j) - bit2 := p256GetBit(scalar, 159-i+j) - bit3 := p256GetBit(scalar, 223-i+j) - index := bit0 | (bit1 << 1) | (bit2 << 2) | (bit3 << 3) - - p256SelectAffinePoint(&px, &py, p256Precomputed[tableOffset:], index) - tableOffset += 30 * p256Limbs - - // Since scalar is less than the order of the group, we know that - // {xOut,yOut,zOut} != {px,py,1}, unless both are zero, which we handle - // below. - p256PointAddMixed(&tx, &ty, &tz, xOut, yOut, zOut, &px, &py) - // The result of pointAddMixed is incorrect if {xOut,yOut,zOut} is zero - // (a.k.a. the point at infinity). We handle that situation by - // copying the point from the table. - p256CopyConditional(xOut, &px, nIsInfinityMask) - p256CopyConditional(yOut, &py, nIsInfinityMask) - p256CopyConditional(zOut, &p256One, nIsInfinityMask) - - // Equally, the result is also wrong if the point from the table is - // zero, which happens when the index is zero. We handle that by - // only copying from {tx,ty,tz} to {xOut,yOut,zOut} if index != 0. - pIsNoninfiniteMask = nonZeroToAllOnes(index) - mask = pIsNoninfiniteMask & ^nIsInfinityMask - p256CopyConditional(xOut, &tx, mask) - p256CopyConditional(yOut, &ty, mask) - p256CopyConditional(zOut, &tz, mask) - // If p was not zero, then n is now non-zero. - nIsInfinityMask &^= pIsNoninfiniteMask - } - } -} - -// p256PointToAffine converts a Jacobian point to an affine point. If the input -// is the point at infinity then it returns (0, 0) in constant time. -func p256PointToAffine(xOut, yOut, x, y, z *[p256Limbs]uint32) { - var zInv, zInvSq [p256Limbs]uint32 - - p256Invert(&zInv, z) - p256Square(&zInvSq, &zInv) - p256Mul(xOut, x, &zInvSq) - p256Mul(&zInv, &zInv, &zInvSq) - p256Mul(yOut, y, &zInv) -} - -// p256ToAffine returns a pair of *big.Int containing the affine representation -// of {x,y,z}. -func p256ToAffine(x, y, z *[p256Limbs]uint32) (xOut, yOut *big.Int) { - var xx, yy [p256Limbs]uint32 - p256PointToAffine(&xx, &yy, x, y, z) - return p256ToBig(&xx), p256ToBig(&yy) -} - -// p256ScalarMult sets {xOut,yOut,zOut} = scalar*{x,y}. -func p256ScalarMult(xOut, yOut, zOut, x, y *[p256Limbs]uint32, scalar *[32]uint8) { - var px, py, pz, tx, ty, tz [p256Limbs]uint32 - var precomp [16][3][p256Limbs]uint32 - var nIsInfinityMask, index, pIsNoninfiniteMask, mask uint32 - - // We precompute 0,1,2,... times {x,y}. - precomp[1][0] = *x - precomp[1][1] = *y - precomp[1][2] = p256One - - for i := 2; i < 16; i += 2 { - p256PointDouble(&precomp[i][0], &precomp[i][1], &precomp[i][2], &precomp[i/2][0], &precomp[i/2][1], &precomp[i/2][2]) - p256PointAddMixed(&precomp[i+1][0], &precomp[i+1][1], &precomp[i+1][2], &precomp[i][0], &precomp[i][1], &precomp[i][2], x, y) - } - - for i := range xOut { - xOut[i] = 0 - } - for i := range yOut { - yOut[i] = 0 - } - for i := range zOut { - zOut[i] = 0 - } - nIsInfinityMask = ^uint32(0) - - // We add in a window of four bits each iteration and do this 64 times. - for i := 0; i < 64; i++ { - if i != 0 { - p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) - p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) - p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) - p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) - } - - index = uint32(scalar[31-i/2]) - if (i & 1) == 1 { - index &= 15 - } else { - index >>= 4 - } - - // See the comments in scalarBaseMult about handling infinities. - p256SelectJacobianPoint(&px, &py, &pz, &precomp, index) - p256PointAdd(&tx, &ty, &tz, xOut, yOut, zOut, &px, &py, &pz) - p256CopyConditional(xOut, &px, nIsInfinityMask) - p256CopyConditional(yOut, &py, nIsInfinityMask) - p256CopyConditional(zOut, &pz, nIsInfinityMask) - - pIsNoninfiniteMask = nonZeroToAllOnes(index) - mask = pIsNoninfiniteMask & ^nIsInfinityMask - p256CopyConditional(xOut, &tx, mask) - p256CopyConditional(yOut, &ty, mask) - p256CopyConditional(zOut, &tz, mask) - nIsInfinityMask &^= pIsNoninfiniteMask - } -} diff --git a/src/crypto/elliptic/p256_generic_field.go b/src/crypto/elliptic/p256_generic_field.go deleted file mode 100644 index 5824946ba4..0000000000 --- a/src/crypto/elliptic/p256_generic_field.go +++ /dev/null @@ -1,705 +0,0 @@ -// Copyright 2013 The Go Authors. All rights reserved. -// Use of this source code is governed by a BSD-style -// license that can be found in the LICENSE file. - -//go:build !amd64 && !arm64 - -package elliptic - -import "math/big" - -// Field elements are represented as nine, unsigned 32-bit words. -// -// The value of a field element is: -// x[0] + (x[1] * 2**29) + (x[2] * 2**57) + ... + (x[8] * 2**228) -// -// That is, each limb is alternately 29 or 28-bits wide in little-endian -// order. -// -// This means that a field element hits 2**257, rather than 2**256 as we would -// like. A 28, 29, ... pattern would cause us to hit 2**256, but that causes -// problems when multiplying as terms end up one bit short of a limb which -// would require much bit-shifting to correct. -// -// Finally, the values stored in a field element are in Montgomery form. So the -// value |y| is stored as (y*R) mod p, where p is the P-256 prime and R is -// 2**257. - -const ( - p256Limbs = 9 - bottom29Bits = 0x1fffffff -) - -var ( - // p256One is the number 1 as a field element. - p256One = [p256Limbs]uint32{2, 0, 0, 0xffff800, 0x1fffffff, 0xfffffff, 0x1fbfffff, 0x1ffffff, 0} - p256Zero = [p256Limbs]uint32{0, 0, 0, 0, 0, 0, 0, 0, 0} - // p256P is the prime modulus as a field element. - p256P = [p256Limbs]uint32{0x1fffffff, 0xfffffff, 0x1fffffff, 0x3ff, 0, 0, 0x200000, 0xf000000, 0xfffffff} - // p2562P is the twice prime modulus as a field element. - p2562P = [p256Limbs]uint32{0x1ffffffe, 0xfffffff, 0x1fffffff, 0x7ff, 0, 0, 0x400000, 0xe000000, 0x1fffffff} -) - -// Field element operations: - -const bottom28Bits = 0xfffffff - -// nonZeroToAllOnes returns: -// -// 0xffffffff for 0 < x <= 2**31 -// 0 for x == 0 or x > 2**31. -func nonZeroToAllOnes(x uint32) uint32 { - return ((x - 1) >> 31) - 1 -} - -// p256ReduceCarry adds a multiple of p in order to cancel |carry|, -// which is a term at 2**257. -// -// On entry: carry < 2**3, inout[0,2,...] < 2**29, inout[1,3,...] < 2**28. -// On exit: inout[0,2,..] < 2**30, inout[1,3,...] < 2**29. -func p256ReduceCarry(inout *[p256Limbs]uint32, carry uint32) { - carry_mask := nonZeroToAllOnes(carry) - - inout[0] += carry << 1 - inout[3] += 0x10000000 & carry_mask - // carry < 2**3 thus (carry << 11) < 2**14 and we added 2**28 in the - // previous line therefore this doesn't underflow. - inout[3] -= carry << 11 - inout[4] += (0x20000000 - 1) & carry_mask - inout[5] += (0x10000000 - 1) & carry_mask - inout[6] += (0x20000000 - 1) & carry_mask - inout[6] -= carry << 22 - // This may underflow if carry is non-zero but, if so, we'll fix it in the - // next line. - inout[7] -= 1 & carry_mask - inout[7] += carry << 25 -} - -// p256Sum sets out = in+in2. -// -// On entry: in[i]+in2[i] must not overflow a 32-bit word. -// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -func p256Sum(out, in, in2 *[p256Limbs]uint32) { - carry := uint32(0) - for i := 0; ; i++ { - out[i] = in[i] + in2[i] - out[i] += carry - carry = out[i] >> 29 - out[i] &= bottom29Bits - - i++ - if i == p256Limbs { - break - } - - out[i] = in[i] + in2[i] - out[i] += carry - carry = out[i] >> 28 - out[i] &= bottom28Bits - } - - p256ReduceCarry(out, carry) -} - -const ( - two30m2 = 1<<30 - 1<<2 - two30p13m2 = 1<<30 + 1<<13 - 1<<2 - two31m2 = 1<<31 - 1<<2 - two31m3 = 1<<31 - 1<<3 - two31p24m2 = 1<<31 + 1<<24 - 1<<2 - two30m27m2 = 1<<30 - 1<<27 - 1<<2 -) - -// p256Zero31 is 0 mod p. -var p256Zero31 = [p256Limbs]uint32{two31m3, two30m2, two31m2, two30p13m2, two31m2, two30m2, two31p24m2, two30m27m2, two31m2} - -// p256Diff sets out = in-in2. -// -// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29 and -// in2[0,2,...] < 2**30, in2[1,3,...] < 2**29. -// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -func p256Diff(out, in, in2 *[p256Limbs]uint32) { - var carry uint32 - - for i := 0; ; i++ { - out[i] = in[i] - in2[i] - out[i] += p256Zero31[i] - out[i] += carry - carry = out[i] >> 29 - out[i] &= bottom29Bits - - i++ - if i == p256Limbs { - break - } - - out[i] = in[i] - in2[i] - out[i] += p256Zero31[i] - out[i] += carry - carry = out[i] >> 28 - out[i] &= bottom28Bits - } - - p256ReduceCarry(out, carry) -} - -// p256ReduceDegree sets out = tmp/R mod p where tmp contains 64-bit words with -// the same 29,28,... bit positions as a field element. -// -// The values in field elements are in Montgomery form: x*R mod p where R = -// 2**257. Since we just multiplied two Montgomery values together, the result -// is x*y*R*R mod p. We wish to divide by R in order for the result also to be -// in Montgomery form. -// -// On entry: tmp[i] < 2**64. -// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -func p256ReduceDegree(out *[p256Limbs]uint32, tmp [17]uint64) { - // The following table may be helpful when reading this code: - // - // Limb number: 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10... - // Width (bits): 29| 28| 29| 28| 29| 28| 29| 28| 29| 28| 29 - // Start bit: 0 | 29| 57| 86|114|143|171|200|228|257|285 - // (odd phase): 0 | 28| 57| 85|114|142|171|199|228|256|285 - var tmp2 [18]uint32 - var carry, x, xMask uint32 - - // tmp contains 64-bit words with the same 29,28,29-bit positions as a - // field element. So the top of an element of tmp might overlap with - // another element two positions down. The following loop eliminates - // this overlap. - tmp2[0] = uint32(tmp[0]) & bottom29Bits - - tmp2[1] = uint32(tmp[0]) >> 29 - tmp2[1] |= (uint32(tmp[0]>>32) << 3) & bottom28Bits - tmp2[1] += uint32(tmp[1]) & bottom28Bits - carry = tmp2[1] >> 28 - tmp2[1] &= bottom28Bits - - for i := 2; i < 17; i++ { - tmp2[i] = (uint32(tmp[i-2] >> 32)) >> 25 - tmp2[i] += (uint32(tmp[i-1])) >> 28 - tmp2[i] += (uint32(tmp[i-1]>>32) << 4) & bottom29Bits - tmp2[i] += uint32(tmp[i]) & bottom29Bits - tmp2[i] += carry - carry = tmp2[i] >> 29 - tmp2[i] &= bottom29Bits - - i++ - if i == 17 { - break - } - tmp2[i] = uint32(tmp[i-2]>>32) >> 25 - tmp2[i] += uint32(tmp[i-1]) >> 29 - tmp2[i] += ((uint32(tmp[i-1] >> 32)) << 3) & bottom28Bits - tmp2[i] += uint32(tmp[i]) & bottom28Bits - tmp2[i] += carry - carry = tmp2[i] >> 28 - tmp2[i] &= bottom28Bits - } - - tmp2[17] = uint32(tmp[15]>>32) >> 25 - tmp2[17] += uint32(tmp[16]) >> 29 - tmp2[17] += uint32(tmp[16]>>32) << 3 - tmp2[17] += carry - - // Montgomery elimination of terms: - // - // Since R is 2**257, we can divide by R with a bitwise shift if we can - // ensure that the right-most 257 bits are all zero. We can make that true - // by adding multiplies of p without affecting the value. - // - // So we eliminate limbs from right to left. Since the bottom 29 bits of p - // are all ones, then by adding tmp2[0]*p to tmp2 we'll make tmp2[0] == 0. - // We can do that for 8 further limbs and then right shift to eliminate the - // extra factor of R. - for i := 0; ; i += 2 { - tmp2[i+1] += tmp2[i] >> 29 - x = tmp2[i] & bottom29Bits - xMask = nonZeroToAllOnes(x) - tmp2[i] = 0 - - // The bounds calculations for this loop are tricky. Each iteration of - // the loop eliminates two words by adding values to words to their - // right. - // - // The following table contains the amounts added to each word (as an - // offset from the value of i at the top of the loop). The amounts are - // accounted for from the first and second half of the loop separately - // and are written as, for example, 28 to mean a value <2**28. - // - // Word: 3 4 5 6 7 8 9 10 - // Added in top half: 28 11 29 21 29 28 - // 28 29 - // 29 - // Added in bottom half: 29 10 28 21 28 28 - // 29 - // - // The value that is currently offset 7 will be offset 5 for the next - // iteration and then offset 3 for the iteration after that. Therefore - // the total value added will be the values added at 7, 5 and 3. - // - // The following table accumulates these values. The sums at the bottom - // are written as, for example, 29+28, to mean a value < 2**29+2**28. - // - // Word: 3 4 5 6 7 8 9 10 11 12 13 - // 28 11 10 29 21 29 28 28 28 28 28 - // 29 28 11 28 29 28 29 28 29 28 - // 29 28 21 21 29 21 29 21 - // 10 29 28 21 28 21 28 - // 28 29 28 29 28 29 28 - // 11 10 29 10 29 10 - // 29 28 11 28 11 - // 29 29 - // -------------------------------------------- - // 30+ 31+ 30+ 31+ 30+ - // 28+ 29+ 28+ 29+ 21+ - // 21+ 28+ 21+ 28+ 10 - // 10 21+ 10 21+ - // 11 11 - // - // So the greatest amount is added to tmp2[10] and tmp2[12]. If - // tmp2[10/12] has an initial value of <2**29, then the maximum value - // will be < 2**31 + 2**30 + 2**28 + 2**21 + 2**11, which is < 2**32, - // as required. - tmp2[i+3] += (x << 10) & bottom28Bits - tmp2[i+4] += (x >> 18) - - tmp2[i+6] += (x << 21) & bottom29Bits - tmp2[i+7] += x >> 8 - - // At position 200, which is the starting bit position for word 7, we - // have a factor of 0xf000000 = 2**28 - 2**24. - tmp2[i+7] += 0x10000000 & xMask - tmp2[i+8] += (x - 1) & xMask - tmp2[i+7] -= (x << 24) & bottom28Bits - tmp2[i+8] -= x >> 4 - - tmp2[i+8] += 0x20000000 & xMask - tmp2[i+8] -= x - tmp2[i+8] += (x << 28) & bottom29Bits - tmp2[i+9] += ((x >> 1) - 1) & xMask - - if i+1 == p256Limbs { - break - } - tmp2[i+2] += tmp2[i+1] >> 28 - x = tmp2[i+1] & bottom28Bits - xMask = nonZeroToAllOnes(x) - tmp2[i+1] = 0 - - tmp2[i+4] += (x << 11) & bottom29Bits - tmp2[i+5] += (x >> 18) - - tmp2[i+7] += (x << 21) & bottom28Bits - tmp2[i+8] += x >> 7 - - // At position 199, which is the starting bit of the 8th word when - // dealing with a context starting on an odd word, we have a factor of - // 0x1e000000 = 2**29 - 2**25. Since we have not updated i, the 8th - // word from i+1 is i+8. - tmp2[i+8] += 0x20000000 & xMask - tmp2[i+9] += (x - 1) & xMask - tmp2[i+8] -= (x << 25) & bottom29Bits - tmp2[i+9] -= x >> 4 - - tmp2[i+9] += 0x10000000 & xMask - tmp2[i+9] -= x - tmp2[i+10] += (x - 1) & xMask - } - - // We merge the right shift with a carry chain. The words above 2**257 have - // widths of 28,29,... which we need to correct when copying them down. - carry = 0 - for i := 0; i < 8; i++ { - // The maximum value of tmp2[i + 9] occurs on the first iteration and - // is < 2**30+2**29+2**28. Adding 2**29 (from tmp2[i + 10]) is - // therefore safe. - out[i] = tmp2[i+9] - out[i] += carry - out[i] += (tmp2[i+10] << 28) & bottom29Bits - carry = out[i] >> 29 - out[i] &= bottom29Bits - - i++ - out[i] = tmp2[i+9] >> 1 - out[i] += carry - carry = out[i] >> 28 - out[i] &= bottom28Bits - } - - out[8] = tmp2[17] - out[8] += carry - carry = out[8] >> 29 - out[8] &= bottom29Bits - - p256ReduceCarry(out, carry) -} - -// p256Square sets out=in*in. -// -// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29. -// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -func p256Square(out, in *[p256Limbs]uint32) { - var tmp [17]uint64 - - tmp[0] = uint64(in[0]) * uint64(in[0]) - tmp[1] = uint64(in[0]) * (uint64(in[1]) << 1) - tmp[2] = uint64(in[0])*(uint64(in[2])<<1) + - uint64(in[1])*(uint64(in[1])<<1) - tmp[3] = uint64(in[0])*(uint64(in[3])<<1) + - uint64(in[1])*(uint64(in[2])<<1) - tmp[4] = uint64(in[0])*(uint64(in[4])<<1) + - uint64(in[1])*(uint64(in[3])<<2) + - uint64(in[2])*uint64(in[2]) - tmp[5] = uint64(in[0])*(uint64(in[5])<<1) + - uint64(in[1])*(uint64(in[4])<<1) + - uint64(in[2])*(uint64(in[3])<<1) - tmp[6] = uint64(in[0])*(uint64(in[6])<<1) + - uint64(in[1])*(uint64(in[5])<<2) + - uint64(in[2])*(uint64(in[4])<<1) + - uint64(in[3])*(uint64(in[3])<<1) - tmp[7] = uint64(in[0])*(uint64(in[7])<<1) + - uint64(in[1])*(uint64(in[6])<<1) + - uint64(in[2])*(uint64(in[5])<<1) + - uint64(in[3])*(uint64(in[4])<<1) - // tmp[8] has the greatest value of 2**61 + 2**60 + 2**61 + 2**60 + 2**60, - // which is < 2**64 as required. - tmp[8] = uint64(in[0])*(uint64(in[8])<<1) + - uint64(in[1])*(uint64(in[7])<<2) + - uint64(in[2])*(uint64(in[6])<<1) + - uint64(in[3])*(uint64(in[5])<<2) + - uint64(in[4])*uint64(in[4]) - tmp[9] = uint64(in[1])*(uint64(in[8])<<1) + - uint64(in[2])*(uint64(in[7])<<1) + - uint64(in[3])*(uint64(in[6])<<1) + - uint64(in[4])*(uint64(in[5])<<1) - tmp[10] = uint64(in[2])*(uint64(in[8])<<1) + - uint64(in[3])*(uint64(in[7])<<2) + - uint64(in[4])*(uint64(in[6])<<1) + - uint64(in[5])*(uint64(in[5])<<1) - tmp[11] = uint64(in[3])*(uint64(in[8])<<1) + - uint64(in[4])*(uint64(in[7])<<1) + - uint64(in[5])*(uint64(in[6])<<1) - tmp[12] = uint64(in[4])*(uint64(in[8])<<1) + - uint64(in[5])*(uint64(in[7])<<2) + - uint64(in[6])*uint64(in[6]) - tmp[13] = uint64(in[5])*(uint64(in[8])<<1) + - uint64(in[6])*(uint64(in[7])<<1) - tmp[14] = uint64(in[6])*(uint64(in[8])<<1) + - uint64(in[7])*(uint64(in[7])<<1) - tmp[15] = uint64(in[7]) * (uint64(in[8]) << 1) - tmp[16] = uint64(in[8]) * uint64(in[8]) - - p256ReduceDegree(out, tmp) -} - -// p256Mul sets out=in*in2. -// -// On entry: in[0,2,...] < 2**30, in[1,3,...] < 2**29 and -// in2[0,2,...] < 2**30, in2[1,3,...] < 2**29. -// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -func p256Mul(out, in, in2 *[p256Limbs]uint32) { - var tmp [17]uint64 - - tmp[0] = uint64(in[0]) * uint64(in2[0]) - tmp[1] = uint64(in[0])*(uint64(in2[1])<<0) + - uint64(in[1])*(uint64(in2[0])<<0) - tmp[2] = uint64(in[0])*(uint64(in2[2])<<0) + - uint64(in[1])*(uint64(in2[1])<<1) + - uint64(in[2])*(uint64(in2[0])<<0) - tmp[3] = uint64(in[0])*(uint64(in2[3])<<0) + - uint64(in[1])*(uint64(in2[2])<<0) + - uint64(in[2])*(uint64(in2[1])<<0) + - uint64(in[3])*(uint64(in2[0])<<0) - tmp[4] = uint64(in[0])*(uint64(in2[4])<<0) + - uint64(in[1])*(uint64(in2[3])<<1) + - uint64(in[2])*(uint64(in2[2])<<0) + - uint64(in[3])*(uint64(in2[1])<<1) + - uint64(in[4])*(uint64(in2[0])<<0) - tmp[5] = uint64(in[0])*(uint64(in2[5])<<0) + - uint64(in[1])*(uint64(in2[4])<<0) + - uint64(in[2])*(uint64(in2[3])<<0) + - uint64(in[3])*(uint64(in2[2])<<0) + - uint64(in[4])*(uint64(in2[1])<<0) + - uint64(in[5])*(uint64(in2[0])<<0) - tmp[6] = uint64(in[0])*(uint64(in2[6])<<0) + - uint64(in[1])*(uint64(in2[5])<<1) + - uint64(in[2])*(uint64(in2[4])<<0) + - uint64(in[3])*(uint64(in2[3])<<1) + - uint64(in[4])*(uint64(in2[2])<<0) + - uint64(in[5])*(uint64(in2[1])<<1) + - uint64(in[6])*(uint64(in2[0])<<0) - tmp[7] = uint64(in[0])*(uint64(in2[7])<<0) + - uint64(in[1])*(uint64(in2[6])<<0) + - uint64(in[2])*(uint64(in2[5])<<0) + - uint64(in[3])*(uint64(in2[4])<<0) + - uint64(in[4])*(uint64(in2[3])<<0) + - uint64(in[5])*(uint64(in2[2])<<0) + - uint64(in[6])*(uint64(in2[1])<<0) + - uint64(in[7])*(uint64(in2[0])<<0) - // tmp[8] has the greatest value but doesn't overflow. See logic in - // p256Square. - tmp[8] = uint64(in[0])*(uint64(in2[8])<<0) + - uint64(in[1])*(uint64(in2[7])<<1) + - uint64(in[2])*(uint64(in2[6])<<0) + - uint64(in[3])*(uint64(in2[5])<<1) + - uint64(in[4])*(uint64(in2[4])<<0) + - uint64(in[5])*(uint64(in2[3])<<1) + - uint64(in[6])*(uint64(in2[2])<<0) + - uint64(in[7])*(uint64(in2[1])<<1) + - uint64(in[8])*(uint64(in2[0])<<0) - tmp[9] = uint64(in[1])*(uint64(in2[8])<<0) + - uint64(in[2])*(uint64(in2[7])<<0) + - uint64(in[3])*(uint64(in2[6])<<0) + - uint64(in[4])*(uint64(in2[5])<<0) + - uint64(in[5])*(uint64(in2[4])<<0) + - uint64(in[6])*(uint64(in2[3])<<0) + - uint64(in[7])*(uint64(in2[2])<<0) + - uint64(in[8])*(uint64(in2[1])<<0) - tmp[10] = uint64(in[2])*(uint64(in2[8])<<0) + - uint64(in[3])*(uint64(in2[7])<<1) + - uint64(in[4])*(uint64(in2[6])<<0) + - uint64(in[5])*(uint64(in2[5])<<1) + - uint64(in[6])*(uint64(in2[4])<<0) + - uint64(in[7])*(uint64(in2[3])<<1) + - uint64(in[8])*(uint64(in2[2])<<0) - tmp[11] = uint64(in[3])*(uint64(in2[8])<<0) + - uint64(in[4])*(uint64(in2[7])<<0) + - uint64(in[5])*(uint64(in2[6])<<0) + - uint64(in[6])*(uint64(in2[5])<<0) + - uint64(in[7])*(uint64(in2[4])<<0) + - uint64(in[8])*(uint64(in2[3])<<0) - tmp[12] = uint64(in[4])*(uint64(in2[8])<<0) + - uint64(in[5])*(uint64(in2[7])<<1) + - uint64(in[6])*(uint64(in2[6])<<0) + - uint64(in[7])*(uint64(in2[5])<<1) + - uint64(in[8])*(uint64(in2[4])<<0) - tmp[13] = uint64(in[5])*(uint64(in2[8])<<0) + - uint64(in[6])*(uint64(in2[7])<<0) + - uint64(in[7])*(uint64(in2[6])<<0) + - uint64(in[8])*(uint64(in2[5])<<0) - tmp[14] = uint64(in[6])*(uint64(in2[8])<<0) + - uint64(in[7])*(uint64(in2[7])<<1) + - uint64(in[8])*(uint64(in2[6])<<0) - tmp[15] = uint64(in[7])*(uint64(in2[8])<<0) + - uint64(in[8])*(uint64(in2[7])<<0) - tmp[16] = uint64(in[8]) * (uint64(in2[8]) << 0) - - p256ReduceDegree(out, tmp) -} - -func p256Assign(out, in *[p256Limbs]uint32) { - *out = *in -} - -// p256Invert calculates |out| = |in|^{-1} -// -// Based on Fermat's Little Theorem: -// -// a^p = a (mod p) -// a^{p-1} = 1 (mod p) -// a^{p-2} = a^{-1} (mod p) -func p256Invert(out, in *[p256Limbs]uint32) { - var ftmp, ftmp2 [p256Limbs]uint32 - - // each e_I will hold |in|^{2^I - 1} - var e2, e4, e8, e16, e32, e64 [p256Limbs]uint32 - - p256Square(&ftmp, in) // 2^1 - p256Mul(&ftmp, in, &ftmp) // 2^2 - 2^0 - p256Assign(&e2, &ftmp) - p256Square(&ftmp, &ftmp) // 2^3 - 2^1 - p256Square(&ftmp, &ftmp) // 2^4 - 2^2 - p256Mul(&ftmp, &ftmp, &e2) // 2^4 - 2^0 - p256Assign(&e4, &ftmp) - p256Square(&ftmp, &ftmp) // 2^5 - 2^1 - p256Square(&ftmp, &ftmp) // 2^6 - 2^2 - p256Square(&ftmp, &ftmp) // 2^7 - 2^3 - p256Square(&ftmp, &ftmp) // 2^8 - 2^4 - p256Mul(&ftmp, &ftmp, &e4) // 2^8 - 2^0 - p256Assign(&e8, &ftmp) - for i := 0; i < 8; i++ { - p256Square(&ftmp, &ftmp) - } // 2^16 - 2^8 - p256Mul(&ftmp, &ftmp, &e8) // 2^16 - 2^0 - p256Assign(&e16, &ftmp) - for i := 0; i < 16; i++ { - p256Square(&ftmp, &ftmp) - } // 2^32 - 2^16 - p256Mul(&ftmp, &ftmp, &e16) // 2^32 - 2^0 - p256Assign(&e32, &ftmp) - for i := 0; i < 32; i++ { - p256Square(&ftmp, &ftmp) - } // 2^64 - 2^32 - p256Assign(&e64, &ftmp) - p256Mul(&ftmp, &ftmp, in) // 2^64 - 2^32 + 2^0 - for i := 0; i < 192; i++ { - p256Square(&ftmp, &ftmp) - } // 2^256 - 2^224 + 2^192 - - p256Mul(&ftmp2, &e64, &e32) // 2^64 - 2^0 - for i := 0; i < 16; i++ { - p256Square(&ftmp2, &ftmp2) - } // 2^80 - 2^16 - p256Mul(&ftmp2, &ftmp2, &e16) // 2^80 - 2^0 - for i := 0; i < 8; i++ { - p256Square(&ftmp2, &ftmp2) - } // 2^88 - 2^8 - p256Mul(&ftmp2, &ftmp2, &e8) // 2^88 - 2^0 - for i := 0; i < 4; i++ { - p256Square(&ftmp2, &ftmp2) - } // 2^92 - 2^4 - p256Mul(&ftmp2, &ftmp2, &e4) // 2^92 - 2^0 - p256Square(&ftmp2, &ftmp2) // 2^93 - 2^1 - p256Square(&ftmp2, &ftmp2) // 2^94 - 2^2 - p256Mul(&ftmp2, &ftmp2, &e2) // 2^94 - 2^0 - p256Square(&ftmp2, &ftmp2) // 2^95 - 2^1 - p256Square(&ftmp2, &ftmp2) // 2^96 - 2^2 - p256Mul(&ftmp2, &ftmp2, in) // 2^96 - 3 - - p256Mul(out, &ftmp2, &ftmp) // 2^256 - 2^224 + 2^192 + 2^96 - 3 -} - -// p256Scalar3 sets out=3*out. -// -// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -func p256Scalar3(out *[p256Limbs]uint32) { - var carry uint32 - - for i := 0; ; i++ { - out[i] *= 3 - out[i] += carry - carry = out[i] >> 29 - out[i] &= bottom29Bits - - i++ - if i == p256Limbs { - break - } - - out[i] *= 3 - out[i] += carry - carry = out[i] >> 28 - out[i] &= bottom28Bits - } - - p256ReduceCarry(out, carry) -} - -// p256Scalar4 sets out=4*out. -// -// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -func p256Scalar4(out *[p256Limbs]uint32) { - var carry, nextCarry uint32 - - for i := 0; ; i++ { - nextCarry = out[i] >> 27 - out[i] <<= 2 - out[i] &= bottom29Bits - out[i] += carry - carry = nextCarry + (out[i] >> 29) - out[i] &= bottom29Bits - - i++ - if i == p256Limbs { - break - } - nextCarry = out[i] >> 26 - out[i] <<= 2 - out[i] &= bottom28Bits - out[i] += carry - carry = nextCarry + (out[i] >> 28) - out[i] &= bottom28Bits - } - - p256ReduceCarry(out, carry) -} - -// p256Scalar8 sets out=8*out. -// -// On entry: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -// On exit: out[0,2,...] < 2**30, out[1,3,...] < 2**29. -func p256Scalar8(out *[p256Limbs]uint32) { - var carry, nextCarry uint32 - - for i := 0; ; i++ { - nextCarry = out[i] >> 26 - out[i] <<= 3 - out[i] &= bottom29Bits - out[i] += carry - carry = nextCarry + (out[i] >> 29) - out[i] &= bottom29Bits - - i++ - if i == p256Limbs { - break - } - nextCarry = out[i] >> 25 - out[i] <<= 3 - out[i] &= bottom28Bits - out[i] += carry - carry = nextCarry + (out[i] >> 28) - out[i] &= bottom28Bits - } - - p256ReduceCarry(out, carry) -} - -// p256CopyConditional sets out=in if mask = 0xffffffff in constant time. -// -// On entry: mask is either 0 or 0xffffffff. -func p256CopyConditional(out, in *[p256Limbs]uint32, mask uint32) { - for i := 0; i < p256Limbs; i++ { - tmp := mask & (in[i] ^ out[i]) - out[i] ^= tmp - } -} - -// p256FromBig sets out = R*in. -func p256FromBig(out *[p256Limbs]uint32, in *big.Int) { - tmp := new(big.Int).Lsh(in, 257) - tmp.Mod(tmp, p256Params.P) - - for i := 0; i < p256Limbs; i++ { - if bits := tmp.Bits(); len(bits) > 0 { - out[i] = uint32(bits[0]) & bottom29Bits - } else { - out[i] = 0 - } - tmp.Rsh(tmp, 29) - - i++ - if i == p256Limbs { - break - } - - if bits := tmp.Bits(); len(bits) > 0 { - out[i] = uint32(bits[0]) & bottom28Bits - } else { - out[i] = 0 - } - tmp.Rsh(tmp, 28) - } -} - -// p256ToBig returns a *big.Int containing the value of in. -func p256ToBig(in *[p256Limbs]uint32) *big.Int { - result, tmp := new(big.Int), new(big.Int) - - result.SetInt64(int64(in[p256Limbs-1])) - for i := p256Limbs - 2; i >= 0; i-- { - if (i & 1) == 0 { - result.Lsh(result, 29) - } else { - result.Lsh(result, 28) - } - tmp.SetInt64(int64(in[i])) - result.Add(result, tmp) - } - - result.Mul(result, p256RInverse) - result.Mod(result, p256Params.P) - return result -} diff --git a/src/crypto/elliptic/p256_noasm.go b/src/crypto/elliptic/p256_noasm.go deleted file mode 100644 index 380ea66ac3..0000000000 --- a/src/crypto/elliptic/p256_noasm.go +++ /dev/null @@ -1,15 +0,0 @@ -// Copyright 2016 The Go Authors. All rights reserved. -// Use of this source code is governed by a BSD-style -// license that can be found in the LICENSE file. - -//go:build !amd64 && !s390x && !arm64 && !ppc64le -// +build !amd64,!s390x,!arm64,!ppc64le - -package elliptic - -var p256 p256Curve - -func initP256Arch() { - // Use pure Go constant-time implementation. - p256 = p256Curve{p256Params} -} diff --git a/src/crypto/elliptic/p256_ppc64le.go b/src/crypto/elliptic/p256_ppc64le.go index 3867a87e1f..12021d038c 100644 --- a/src/crypto/elliptic/p256_ppc64le.go +++ b/src/crypto/elliptic/p256_ppc64le.go @@ -27,14 +27,13 @@ type p256Point struct { z [32]byte } -var ( - p256 Curve - p256PreFast *[37][64]p256Point -) +var p256PreFast *[37][64]p256Point -func initP256Arch() { - p256 = p256CurveFast{p256Params} - initTable() +func init() { + initP256Arch = func() { + p256 = p256CurveFast{&p256Params} + initTable() + } } func (curve p256CurveFast) Params() *CurveParams { diff --git a/src/crypto/elliptic/p256_s390x.go b/src/crypto/elliptic/p256_s390x.go index b7331ebbfd..a8b2b07005 100644 --- a/src/crypto/elliptic/p256_s390x.go +++ b/src/crypto/elliptic/p256_s390x.go @@ -28,10 +28,7 @@ type p256Point struct { z [32]byte } -var ( - p256 Curve - p256PreFast *[37][64]p256Point -) +var p256PreFast *[37][64]p256Point //go:noescape func p256MulInternalTrampolineSetup() @@ -51,15 +48,13 @@ func p256SqrInternalVX() //go:noescape func p256SqrInternalVMSL() -func initP256Arch() { +func init() { if cpu.S390X.HasVX { - p256 = p256CurveFast{p256Params} - initTable() - return + initP256Arch = func() { + p256 = p256CurveFast{&p256Params} + initTable() + } } - - // No vector support, use pure Go implementation. - p256 = p256Curve{p256Params} } func (curve p256CurveFast) Params() *CurveParams { -- 2.50.0