mirror of
https://github.com/henrydcase/nobs.git
synced 2024-11-22 23:28:57 +00:00
Kris Kwiatkowski
7efbbf4745
Implementation of Commutative Supersingular Isogeny Diffie Hellman, based on "A faster way to CSIDH" paper (2018/782). * For fast isogeny calculation, implementation converts a curve from Montgomery to Edwards. All calculations are done on Edwards curve and then converted back to Montgomery. * As multiplication in a field Fp511 is most expensive operation the implementation contains multiple multiplications. It has most performant, assembly implementation which uses BMI2 and ADOX/ADCX instructions for modern CPUs. It also contains slower implementation which will run on older CPUs * Benchmarks (Intel SkyLake): BenchmarkGeneratePrivate 6459 172213 ns/op 0 B/op 0 allocs/op BenchmarkGenerateKeyPair 25 45800356 ns/op 0 B/op 0 allocs/op BenchmarkValidate 297 3915983 ns/op 0 B/op 0 allocs/op BenchmarkValidateRandom 184683 6231 ns/op 0 B/op 0 allocs/op BenchmarkValidateGenerated 25 48481306 ns/op 0 B/op 0 allocs/op BenchmarkDerive 19 60928763 ns/op 0 B/op 0 allocs/op BenchmarkDeriveGenerated 8 137342421 ns/op 0 B/op 0 allocs/op BenchmarkXMul 2311 494267 ns/op 1 B/op 0 allocs/op BenchmarkXAdd 2396754 501 ns/op 0 B/op 0 allocs/op BenchmarkXDbl 2072690 571 ns/op 0 B/op 0 allocs/op BenchmarkIsom 78004 15171 ns/op 0 B/op 0 allocs/op BenchmarkFp512Sub 224635152 5.33 ns/op 0 B/op 0 allocs/op BenchmarkFp512Mul 246633255 4.90 ns/op 0 B/op 0 allocs/op BenchmarkCSwap 233228547 5.10 ns/op 0 B/op 0 allocs/op BenchmarkAddRdc 87348240 12.6 ns/op 0 B/op 0 allocs/op BenchmarkSubRdc 95112787 11.7 ns/op 0 B/op 0 allocs/op BenchmarkModExpRdc 25436 46878 ns/op 0 B/op 0 allocs/op BenchmarkMulBmiAsm 19527573 60.1 ns/op 0 B/op 0 allocs/op BenchmarkMulGeneric 7117650 164 ns/op 0 B/op 0 allocs/op * Go code has very similar performance when compared to C implementation. Results from sidh_torturer (4e2996e12d68364761064341cbe1d1b47efafe23) github.com:henrydcase/sidh-torture/csidh | TestName |Go | C | |------------------|----------|----------| |TestSharedSecret | 57.95774 | 57.91092 | |TestKeyGeneration | 62.23614 | 58.12980 | |TestSharedSecret | 55.28988 | 57.23132 | |TestKeyGeneration | 61.68745 | 58.66396 | |TestSharedSecret | 63.19408 | 58.64774 | |TestKeyGeneration | 62.34022 | 61.62539 | |TestSharedSecret | 62.85453 | 68.74503 | |TestKeyGeneration | 52.58518 | 58.40115 | |TestSharedSecret | 50.77081 | 61.91699 | |TestKeyGeneration | 59.91843 | 61.09266 | |TestSharedSecret | 59.97962 | 62.98151 | |TestKeyGeneration | 64.57525 | 56.22863 | |TestSharedSecret | 56.40521 | 55.77447 | |TestKeyGeneration | 67.85850 | 58.52604 | |TestSharedSecret | 60.54290 | 65.14052 | |TestKeyGeneration | 65.45766 | 58.42823 | On average Go implementation is 2% faster.
105 lines
3.0 KiB
Go
105 lines
3.0 KiB
Go
package csidh
|
|
|
|
const (
|
|
// pbits is a bitsize of prime p
|
|
pbits = 511
|
|
// primeCount number of Elkies primes used for constructing p
|
|
primeCount = 74
|
|
// (2*5+1)^74 is roughly 2^256
|
|
expMax = int8(5)
|
|
// size of the limbs, pretty much hardcoded to 64-bit words
|
|
limbBitSize = 64
|
|
// size of the limbs in bytes
|
|
limbByteSize = limbBitSize >> 3
|
|
// Number of limbs for a field element
|
|
numWords = 8
|
|
// PrivateKeySize is a size of cSIDH/512 private key in bytes.
|
|
PrivateKeySize = 37
|
|
// PublicKeySize is a size of cSIDH/512 public key in bytes.
|
|
PublicKeySize = 64
|
|
// SharedSecretSize is a size of cSIDH/512 shared secret in bytes.
|
|
SharedSecretSize = 64
|
|
)
|
|
|
|
var (
|
|
// Elkies primes up to 374 + prime 587
|
|
// p = 4 * product(primes) - 1
|
|
primes = [primeCount]uint64{
|
|
0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025,
|
|
0x0029, 0x002B, 0x002F, 0x0035, 0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053,
|
|
0x0059, 0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F, 0x0083, 0x0089, 0x008B,
|
|
0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD, 0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5,
|
|
0x00C7, 0x00D3, 0x00DF, 0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
|
|
0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137, 0x0139, 0x013D, 0x014B,
|
|
0x0151, 0x015B, 0x015D, 0x0161, 0x0167, 0x016F, 0x0175, 0x024B}
|
|
|
|
p = fp{
|
|
0x1B81B90533C6C87B, 0xC2721BF457ACA835,
|
|
0x516730CC1F0B4F25, 0xA7AAC6C567F35507,
|
|
0x5AFBFCC69322C9CD, 0xB42D083AEDC88C42,
|
|
0xFC8AB0D15E3E4C4A, 0x65B48E8F740F89BF,
|
|
}
|
|
|
|
/* Montgomery R = 2^512 mod p */
|
|
one = fp{
|
|
0xC8FC8DF598726F0A, 0x7B1BC81750A6AF95,
|
|
0x5D319E67C1E961B4, 0xB0AA7275301955F1,
|
|
0x4A080672D9BA6C64, 0x97A5EF8A246EE77B,
|
|
0x06EA9E5D4383676A, 0x3496E2E117E0EC80,
|
|
}
|
|
|
|
// 2 in Montgomery domain
|
|
two = fp{
|
|
0x767762E5FD1E1599, 0x33C5743A49A0B6F6,
|
|
0x68FC0C0364C77443, 0xB9AA1E24F83F56DB,
|
|
0x3914101F20520EFB, 0x7B1ED6D95B1542B4,
|
|
0x114A8BE928C8828A, 0x03793732BBB24F40,
|
|
}
|
|
|
|
// -2 in Montgomery domain
|
|
twoNeg = fp{
|
|
0xA50A561F36A8B2E2, 0x8EACA7BA0E0BF13E,
|
|
0xE86B24C8BA43DAE2, 0xEE00A8A06FB3FE2B,
|
|
0x21E7ECA772D0BAD1, 0x390E316192B3498E,
|
|
0xEB4024E83575C9C0, 0x623B575CB85D3A7F,
|
|
}
|
|
|
|
// 4 in Montgomery domain
|
|
four = fp{
|
|
0xECEEC5CBFA3C2B32, 0x678AE87493416DEC,
|
|
0xD1F81806C98EE886, 0x73543C49F07EADB6,
|
|
0x7228203E40A41DF7, 0xF63DADB2B62A8568,
|
|
0x229517D251910514, 0x06F26E6577649E80,
|
|
}
|
|
|
|
// 4 * sqrt(p)
|
|
fourSqrtP = fp{
|
|
0x17895E71E1A20B3F, 0x38D0CD95F8636A56,
|
|
0x142B9541E59682CD, 0x856F1399D91D6592,
|
|
0x0000000000000002,
|
|
}
|
|
|
|
// -p^-1 mod 2^64
|
|
pNegInv = fp{
|
|
0x66c1301f632e294d,
|
|
}
|
|
|
|
// (p-1)/2. Used as exponent, hence not in
|
|
// montgomery domain
|
|
pMin1By2 = fp{
|
|
0x8DC0DC8299E3643D, 0xE1390DFA2BD6541A,
|
|
0xA8B398660F85A792, 0xD3D56362B3F9AA83,
|
|
0x2D7DFE63499164E6, 0x5A16841D76E44621,
|
|
0xFE455868AF1F2625, 0x32DA4747BA07C4DF,
|
|
}
|
|
|
|
// p-1 mod 2^64. Used as exponent, hence not
|
|
// in montgomery domain
|
|
pMin1 = fp{
|
|
0x1B81B90533C6C879, 0xC2721BF457ACA835,
|
|
0x516730CC1F0B4F25, 0xA7AAC6C567F35507,
|
|
0x5AFBFCC69322C9CD, 0xB42D083AEDC88C42,
|
|
0xFC8AB0D15E3E4C4A, 0x65B48E8F740F89BF,
|
|
}
|
|
)
|