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Prad Nukala
@@ -0,0 +1,206 @@
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//
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// Copyright Coinbase, Inc. All Rights Reserved.
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//
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// SPDX-License-Identifier: Apache-2.0
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//
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package fp
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import (
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"math/big"
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"sync"
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"github.com/sonr-io/sonr/crypto/core/curves/native"
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)
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var (
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p256FpInitonce sync.Once
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p256FpParams native.FieldParams
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)
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func P256FpNew() *native.Field {
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return &native.Field{
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Value: [native.FieldLimbs]uint64{},
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Params: getP256FpParams(),
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Arithmetic: p256FpArithmetic{},
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}
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}
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func p256FpParamsInit() {
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// See FIPS 186-3, section D.2.3
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p256FpParams = native.FieldParams{
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R: [native.FieldLimbs]uint64{
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0x0000000000000001,
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0xffffffff00000000,
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0xffffffffffffffff,
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0x00000000fffffffe,
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},
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R2: [native.FieldLimbs]uint64{
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0x0000000000000003,
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0xfffffffbffffffff,
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0xfffffffffffffffe,
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0x00000004fffffffd,
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},
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R3: [native.FieldLimbs]uint64{
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0xfffffffd0000000a,
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0xffffffedfffffff7,
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0x00000005fffffffc,
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0x0000001800000001,
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},
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Modulus: [native.FieldLimbs]uint64{
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0xffffffffffffffff,
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0x00000000ffffffff,
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0x0000000000000000,
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0xffffffff00000001,
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},
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BiModulus: new(big.Int).SetBytes([]byte{
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0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
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}),
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}
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}
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func getP256FpParams() *native.FieldParams {
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p256FpInitonce.Do(p256FpParamsInit)
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return &p256FpParams
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}
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// p256FpArithmetic is a struct with all the methods needed for working
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// in mod q
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type p256FpArithmetic struct{}
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// ToMontgomery converts this field to montgomery form
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func (f p256FpArithmetic) ToMontgomery(out, arg *[native.FieldLimbs]uint64) {
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ToMontgomery((*MontgomeryDomainFieldElement)(out), (*NonMontgomeryDomainFieldElement)(arg))
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}
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// FromMontgomery converts this field from montgomery form
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func (f p256FpArithmetic) FromMontgomery(out, arg *[native.FieldLimbs]uint64) {
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FromMontgomery((*NonMontgomeryDomainFieldElement)(out), (*MontgomeryDomainFieldElement)(arg))
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}
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// Neg performs modular negation
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func (f p256FpArithmetic) Neg(out, arg *[native.FieldLimbs]uint64) {
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Opp((*MontgomeryDomainFieldElement)(out), (*MontgomeryDomainFieldElement)(arg))
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}
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// Square performs modular square
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func (f p256FpArithmetic) Square(out, arg *[native.FieldLimbs]uint64) {
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Square((*MontgomeryDomainFieldElement)(out), (*MontgomeryDomainFieldElement)(arg))
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}
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// Mul performs modular multiplication
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func (f p256FpArithmetic) Mul(out, arg1, arg2 *[native.FieldLimbs]uint64) {
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Mul(
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(*MontgomeryDomainFieldElement)(out),
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(*MontgomeryDomainFieldElement)(arg1),
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(*MontgomeryDomainFieldElement)(arg2),
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)
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}
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// Add performs modular addition
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func (f p256FpArithmetic) Add(out, arg1, arg2 *[native.FieldLimbs]uint64) {
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Add(
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(*MontgomeryDomainFieldElement)(out),
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(*MontgomeryDomainFieldElement)(arg1),
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(*MontgomeryDomainFieldElement)(arg2),
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)
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}
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// Sub performs modular subtraction
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func (f p256FpArithmetic) Sub(out, arg1, arg2 *[native.FieldLimbs]uint64) {
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Sub(
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(*MontgomeryDomainFieldElement)(out),
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(*MontgomeryDomainFieldElement)(arg1),
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(*MontgomeryDomainFieldElement)(arg2),
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)
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}
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// Sqrt performs modular square root
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func (f p256FpArithmetic) Sqrt(wasSquare *int, out, arg *[native.FieldLimbs]uint64) {
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// Use p = 3 mod 4 by Euler's criterion means
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// arg^((p+1)/4 mod p
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var t, c [native.FieldLimbs]uint64
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c1 := [native.FieldLimbs]uint64{
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0x0000_0000_0000_0000,
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0x0000_0000_4000_0000,
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0x4000_0000_0000_0000,
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0x3fff_ffff_c000_0000,
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}
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native.Pow(&t, arg, &c1, getP256FpParams(), f)
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Square((*MontgomeryDomainFieldElement)(&c), (*MontgomeryDomainFieldElement)(&t))
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*wasSquare = (&native.Field{Value: c, Params: getP256FpParams(), Arithmetic: f}).Equal(
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&native.Field{
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Value: *arg, Params: getP256FpParams(), Arithmetic: f,
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},
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)
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Selectznz(out, uint1(*wasSquare), out, &t)
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}
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// Invert performs modular inverse
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func (f p256FpArithmetic) Invert(wasInverted *int, out, arg *[native.FieldLimbs]uint64) {
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// Fermat's Little Theorem
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// a ^ (p - 2) mod p
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//
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// The exponent pattern (from high to low) is:
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// - 32 bits of value 1
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// - 31 bits of value 0
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// - 1 bit of value 1
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// - 96 bits of value 0
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// - 94 bits of value 1
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// - 1 bit of value 0
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// - 1 bit of value 1
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// To speed up the square-and-multiply algorithm, precompute a^(2^31-1).
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//
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// Courtesy of Thomas Pornin
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//
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var t, r [native.FieldLimbs]uint64
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copy(t[:], arg[:])
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for i := 0; i < 30; i++ {
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f.Square(&t, &t)
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f.Mul(&t, &t, arg)
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}
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copy(r[:], t[:])
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for i := 224; i >= 0; i-- {
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f.Square(&r, &r)
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switch i {
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case 0:
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fallthrough
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case 2:
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fallthrough
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case 192:
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fallthrough
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case 224:
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f.Mul(&r, &r, arg)
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case 3:
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fallthrough
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case 34:
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fallthrough
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case 65:
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f.Mul(&r, &r, &t)
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}
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}
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*wasInverted = (&native.Field{
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Value: *arg,
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Params: getP256FpParams(),
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Arithmetic: f,
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}).IsNonZero()
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Selectznz(out, uint1(*wasInverted), out, &r)
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}
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// FromBytes converts a little endian byte array into a field element
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func (f p256FpArithmetic) FromBytes(out *[native.FieldLimbs]uint64, arg *[native.FieldBytes]byte) {
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FromBytes(out, arg)
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}
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// ToBytes converts a field element to a little endian byte array
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func (f p256FpArithmetic) ToBytes(out *[native.FieldBytes]byte, arg *[native.FieldLimbs]uint64) {
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ToBytes(out, arg)
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}
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// Selectznz performs conditional select.
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// selects arg1 if choice == 0 and arg2 if choice == 1
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func (f p256FpArithmetic) Selectznz(out, arg1, arg2 *[native.FieldLimbs]uint64, choice int) {
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Selectznz(out, uint1(choice), arg1, arg2)
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}
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@@ -0,0 +1,330 @@
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//
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// Copyright Coinbase, Inc. All Rights Reserved.
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//
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// SPDX-License-Identifier: Apache-2.0
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//
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package fp
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import (
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crand "crypto/rand"
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"math/big"
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"math/rand"
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"testing"
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"github.com/stretchr/testify/require"
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"github.com/sonr-io/sonr/crypto/core/curves/native"
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"github.com/sonr-io/sonr/crypto/internal"
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)
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func TestFpSetOne(t *testing.T) {
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fq := P256FpNew().SetOne()
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require.NotNil(t, fq)
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require.Equal(t, fq.Value, getP256FpParams().R)
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}
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func TestFpSetUint64(t *testing.T) {
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act := P256FpNew().SetUint64(1 << 60)
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require.NotNil(t, act)
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// Remember it will be in montgomery form
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require.Equal(t, act.Value[0], uint64(0x100000000fffffff))
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}
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func TestFpAdd(t *testing.T) {
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lhs := P256FpNew().SetOne()
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rhs := P256FpNew().SetOne()
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exp := P256FpNew().SetUint64(2)
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res := P256FpNew().Add(lhs, rhs)
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require.NotNil(t, res)
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require.Equal(t, 1, res.Equal(exp))
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// Fuzz test
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for i := 0; i < 25; i++ {
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// Divide by 4 to prevent overflow false errors
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l := rand.Uint64() >> 2
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r := rand.Uint64() >> 2
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e := l + r
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lhs.SetUint64(l)
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rhs.SetUint64(r)
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exp.SetUint64(e)
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a := P256FpNew().Add(lhs, rhs)
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require.NotNil(t, a)
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require.Equal(t, exp, a)
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}
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}
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func TestFpSub(t *testing.T) {
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lhs := P256FpNew().SetOne()
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rhs := P256FpNew().SetOne()
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exp := P256FpNew().SetZero()
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res := P256FpNew().Sub(lhs, rhs)
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require.NotNil(t, res)
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require.Equal(t, 1, res.Equal(exp))
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// Fuzz test
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for i := 0; i < 25; i++ {
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// Divide by 4 to prevent overflow false errors
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l := rand.Uint64() >> 2
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r := rand.Uint64() >> 2
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if l < r {
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l, r = r, l
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}
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e := l - r
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lhs.SetUint64(l)
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rhs.SetUint64(r)
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exp.SetUint64(e)
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a := P256FpNew().Sub(lhs, rhs)
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require.NotNil(t, a)
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require.Equal(t, exp, a)
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}
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}
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func TestFpMul(t *testing.T) {
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lhs := P256FpNew().SetOne()
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rhs := P256FpNew().SetOne()
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exp := P256FpNew().SetOne()
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res := P256FpNew().Mul(lhs, rhs)
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require.NotNil(t, res)
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require.Equal(t, 1, res.Equal(exp))
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// Fuzz test
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for i := 0; i < 25; i++ {
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// Divide by 4 to prevent overflow false errors
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l := rand.Uint32()
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r := rand.Uint32()
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e := uint64(l) * uint64(r)
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lhs.SetUint64(uint64(l))
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rhs.SetUint64(uint64(r))
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exp.SetUint64(e)
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a := P256FpNew().Mul(lhs, rhs)
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require.NotNil(t, a)
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require.Equal(t, exp, a)
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}
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}
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func TestFpDouble(t *testing.T) {
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a := P256FpNew().SetUint64(2)
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e := P256FpNew().SetUint64(4)
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require.Equal(t, e, P256FpNew().Double(a))
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for i := 0; i < 25; i++ {
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tv := rand.Uint32()
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ttv := uint64(tv) * 2
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a = P256FpNew().SetUint64(uint64(tv))
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e = P256FpNew().SetUint64(ttv)
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require.Equal(t, e, P256FpNew().Double(a))
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}
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}
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func TestFpSquare(t *testing.T) {
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a := P256FpNew().SetUint64(4)
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e := P256FpNew().SetUint64(16)
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require.Equal(t, e, a.Square(a))
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for i := 0; i < 25; i++ {
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j := rand.Uint32()
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exp := uint64(j) * uint64(j)
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e.SetUint64(exp)
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a.SetUint64(uint64(j))
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require.Equal(t, e, a.Square(a))
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}
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}
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func TestFpNeg(t *testing.T) {
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g := P256FpNew().SetUint64(7)
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a := P256FpNew().SetOne()
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a.Neg(a)
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e := P256FpNew().SetRaw(&[native.FieldLimbs]uint64{0xfffffffffffffffe, 0x00000001ffffffff, 0x0000000000000000, 0xfffffffe00000002})
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require.Equal(t, e, a)
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a.Neg(g)
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e = P256FpNew().SetRaw(&[native.FieldLimbs]uint64{0xfffffffffffffff8, 0x00000007ffffffff, 0x0000000000000000, 0xfffffff800000008})
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require.Equal(t, e, a)
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}
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|
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func TestFpExp(t *testing.T) {
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e := P256FpNew().SetUint64(8)
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a := P256FpNew().SetUint64(2)
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by := P256FpNew().SetUint64(3)
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require.Equal(t, e, a.Exp(a, by))
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}
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|
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func TestFpSqrt(t *testing.T) {
|
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t1 := P256FpNew().SetUint64(2)
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t2 := P256FpNew().Neg(t1)
|
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t3 := P256FpNew().Square(t1)
|
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_, wasSquare := t3.Sqrt(t3)
|
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|
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require.True(t, wasSquare)
|
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require.Equal(t, 1, t1.Equal(t3)|t2.Equal(t3))
|
||||
t1.SetUint64(3)
|
||||
_, wasSquare = P256FpNew().Sqrt(t1)
|
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require.False(t, wasSquare)
|
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}
|
||||
|
||||
func TestFpInvert(t *testing.T) {
|
||||
twoInv := P256FpNew().SetRaw(&[native.FieldLimbs]uint64{0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8000000000000000})
|
||||
two := P256FpNew().SetUint64(2)
|
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a, inverted := P256FpNew().Invert(two)
|
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require.True(t, inverted)
|
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require.Equal(t, a, twoInv)
|
||||
|
||||
rootOfUnity := P256FpNew().SetLimbs(&[native.FieldLimbs]uint64{0x8619a9e760c01d0c, 0xa883c4fba37998df, 0x45607580b6eabd98, 0xf252b002544b2f99})
|
||||
rootOfUnityInv := P256FpNew().SetRaw(&[native.FieldLimbs]uint64{0x2609d8ab477f96d1, 0x6e5f128fb20a0f24, 0xe4d636874d99643b, 0x376080cc1f2a3735})
|
||||
a, inverted = P256FpNew().Invert(rootOfUnity)
|
||||
require.True(t, inverted)
|
||||
require.Equal(t, a, rootOfUnityInv)
|
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|
||||
lhs := P256FpNew().SetUint64(9)
|
||||
rhs := P256FpNew().SetUint64(3)
|
||||
rhsInv, inverted := P256FpNew().Invert(rhs)
|
||||
require.True(t, inverted)
|
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require.Equal(t, rhs, P256FpNew().Mul(lhs, rhsInv))
|
||||
|
||||
rhs.SetZero()
|
||||
_, inverted = P256FpNew().Invert(rhs)
|
||||
require.False(t, inverted)
|
||||
}
|
||||
|
||||
func TestFpCMove(t *testing.T) {
|
||||
t1 := P256FpNew().SetUint64(5)
|
||||
t2 := P256FpNew().SetUint64(10)
|
||||
require.Equal(t, t1, P256FpNew().CMove(t1, t2, 0))
|
||||
require.Equal(t, t2, P256FpNew().CMove(t1, t2, 1))
|
||||
}
|
||||
|
||||
func TestFpBytes(t *testing.T) {
|
||||
t1 := P256FpNew().SetUint64(99)
|
||||
seq := t1.Bytes()
|
||||
t2, err := P256FpNew().SetBytes(&seq)
|
||||
require.NoError(t, err)
|
||||
require.Equal(t, t1, t2)
|
||||
|
||||
for i := 0; i < 25; i++ {
|
||||
t1.SetUint64(rand.Uint64())
|
||||
seq = t1.Bytes()
|
||||
_, err = t2.SetBytes(&seq)
|
||||
require.NoError(t, err)
|
||||
require.Equal(t, t1, t2)
|
||||
}
|
||||
}
|
||||
|
||||
func TestFpCmp(t *testing.T) {
|
||||
tests := []struct {
|
||||
a *native.Field
|
||||
b *native.Field
|
||||
e int
|
||||
}{
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{2731658267414164836, 14655288906067898431, 6537465423330262322, 8306191141697566219}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{6472764012681988529, 10848812988401906064, 2961825807536828898, 4282183981941645679}),
|
||||
e: 1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{8023004109510539223, 4652004072850285717, 1877219145646046927, 383214385093921911}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{10099384440823804262, 16139476942229308465, 8636966320777393798, 5435928725024696785}),
|
||||
e: -1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{3741840066202388211, 12165774400417314871, 16619312580230515379, 16195032234110087705}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{3905865991286066744, 543690822309071825, 17963103015950210055, 3745476720756119742}),
|
||||
e: 1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{16660853697936147788, 7799793619412111108, 13515141085171033220, 2641079731236069032}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{17790588295388238399, 571847801379669440, 14537208974498222469, 12792570372087452754}),
|
||||
e: -1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{3912839285384959186, 2701177075110484070, 6453856448115499033, 6475797457962597458}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{1282566391665688512, 13503640416992806563, 2962240104675990153, 3374904770947067689}),
|
||||
e: 1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{5716631803409360103, 7859567470082614154, 12747956220853330146, 18434584096087315020}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{16317076441459028418, 12854146980376319601, 2258436689269031143, 9531877130792223752}),
|
||||
e: 1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{17955191469941083403, 10350326247207200880, 17263512235150705075, 12700328451238078022}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{6767595547459644695, 7146403825494928147, 12269344038346710612, 9122477829383225603}),
|
||||
e: 1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{17099388671847024438, 6426264987820696548, 10641143464957227405, 7709745403700754098}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{10799154372990268556, 17178492485719929374, 5705777922258988797, 8051037767683567782}),
|
||||
e: -1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{4567139260680454325, 1629385880182139061, 16607020832317899145, 1261011562621553200}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{13487234491304534488, 17872642955936089265, 17651026784972590233, 9468934643333871559}),
|
||||
e: -1,
|
||||
},
|
||||
{
|
||||
a: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{18071070103467571798, 11787850505799426140, 10631355976141928593, 4867785203635092610}),
|
||||
b: P256FpNew().SetRaw(&[native.FieldLimbs]uint64{12596443599426461624, 10176122686151524591, 17075755296887483439, 6726169532695070719}),
|
||||
e: -1,
|
||||
},
|
||||
}
|
||||
|
||||
for _, test := range tests {
|
||||
require.Equal(t, test.e, test.a.Cmp(test.b))
|
||||
require.Equal(t, -test.e, test.b.Cmp(test.a))
|
||||
require.Equal(t, 0, test.a.Cmp(test.a))
|
||||
require.Equal(t, 0, test.b.Cmp(test.b))
|
||||
}
|
||||
}
|
||||
|
||||
func TestFpBigInt(t *testing.T) {
|
||||
t1 := P256FpNew().SetBigInt(big.NewInt(9999))
|
||||
t2 := P256FpNew().SetBigInt(t1.BigInt())
|
||||
require.Equal(t, t1, t2)
|
||||
|
||||
e := P256FpNew().SetRaw(&[native.FieldLimbs]uint64{0x515151513f3f3f3e, 0xc9c9c9cb36363636, 0xb7b7b7b79c9c9c9c, 0xfffffffeaeaeaeaf})
|
||||
b := new(
|
||||
big.Int,
|
||||
).SetBytes([]byte{9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9})
|
||||
t1.SetBigInt(b)
|
||||
require.Equal(t, e, t1)
|
||||
e.Value[0] = 0xaeaeaeaec0c0c0c1
|
||||
e.Value[1] = 0x36363635c9c9c9c9
|
||||
e.Value[2] = 0x4848484863636363
|
||||
e.Value[3] = 0x0000000051515151
|
||||
b.Neg(b)
|
||||
t1.SetBigInt(b)
|
||||
require.Equal(t, e, t1)
|
||||
}
|
||||
|
||||
func TestFpSetBytesWide(t *testing.T) {
|
||||
e := P256FpNew().SetRaw(&[native.FieldLimbs]uint64{0xccdefd48c77805bc, 0xe935dc2db86364d6, 0xca8ee6e5870a020e, 0x4c94bf4467f3b5bf})
|
||||
|
||||
a := P256FpNew().SetBytesWide(&[64]byte{
|
||||
0x69, 0x23, 0x5a, 0x0b, 0xce, 0x0c, 0xa8, 0x64,
|
||||
0x3c, 0x78, 0xbc, 0x01, 0x05, 0xef, 0xf2, 0x84,
|
||||
0xde, 0xbb, 0x6b, 0xc8, 0x63, 0x5e, 0x6e, 0x69,
|
||||
0x62, 0xcc, 0xc6, 0x2d, 0xf5, 0x72, 0x40, 0x92,
|
||||
0x28, 0x11, 0xd6, 0xc8, 0x07, 0xa5, 0x88, 0x82,
|
||||
0xfe, 0xe3, 0x97, 0xf6, 0x1e, 0xfb, 0x2e, 0x3b,
|
||||
0x27, 0x5f, 0x85, 0x06, 0x8d, 0x99, 0xa4, 0x75,
|
||||
0xc0, 0x2c, 0x71, 0x69, 0x9e, 0x58, 0xea, 0x52,
|
||||
})
|
||||
require.Equal(t, e, a)
|
||||
}
|
||||
|
||||
func TestFpSetBytesWideBigInt(t *testing.T) {
|
||||
params := getP256FpParams()
|
||||
var tv2 [64]byte
|
||||
for i := 0; i < 25; i++ {
|
||||
_, _ = crand.Read(tv2[:])
|
||||
e := new(big.Int).SetBytes(tv2[:])
|
||||
e.Mod(e, params.BiModulus)
|
||||
|
||||
tv := internal.ReverseScalarBytes(tv2[:])
|
||||
copy(tv2[:], tv)
|
||||
a := P256FpNew().SetBytesWide(&tv2)
|
||||
require.Equal(t, 0, e.Cmp(a.BigInt()))
|
||||
}
|
||||
}
|
||||
Executable
+1463
File diff suppressed because it is too large
Load Diff
Reference in New Issue
Block a user