wownero-python/monero/ed25519.py

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2018-02-22 04:41:20 +00:00
# The reference Ed25519 software is in the public domain.
# Source: https://ed25519.cr.yp.to/python/ed25519.py
#
# Parts Copyright (c) 2016 The MoneroPy Developers. Released under the BSD 3-Clause
import hashlib
import operator as _oper
import sys as _sys
# Set up byte handling for Python 2 or 3
if _sys.version_info.major == 2:
int2byte = chr
range = xrange
def indexbytes(buf, i):
return ord(buf[i])
def intlist2bytes(l):
return b"".join(chr(c) for c in l)
else:
indexbytes = _oper.getitem
intlist2bytes = bytes
int2byte = _oper.methodcaller("to_bytes", 1, "big")
b = 256
q = 2**255 - 19
l = 2**252 + 27742317777372353535851937790883648493
def H(m):
return hashlib.sha512(m).digest()
def expmod(b, e, m):
if e == 0: return 1
t = expmod(b, e//2, m)**2 % m
if e & 1: t = (t*b) % m
return t
def inv(x):
return expmod(x, q-2, q)
d = -121665 * inv(121666)
I = expmod(2, (q-1)//4, q)
def xrecover(y):
xx = (y*y-1) * inv(d*y*y+1)
x = expmod(xx, (q+3)//8, q)
if (x*x - xx) % q != 0: x = (x*I) % q
if x % 2 != 0: x = q-x
return x
By = 4 * inv(5)
Bx = xrecover(By)
B = [Bx%q, By%q]
def edwards(P, Q):
x1 = P[0]
y1 = P[1]
x2 = Q[0]
y2 = Q[1]
x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
return [x3%q, y3%q]
def scalarmult(P, e):
if e == 0: return [0, 1]
Q = scalarmult(P, e//2)
Q = edwards(Q, Q)
if e & 1: Q = edwards(Q, P)
return Q
def encodeint(y):
bits = [(y >> i) & 1 for i in range(b)]
return b''.join([int2byte(sum([bits[i*8 + j] << j for j in range(8)])) for i in range(b//8)])
def encodepoint(P):
x = P[0]
y = P[1]
bits = [(y >> i) & 1 for i in range(b-1)] + [x & 1]
return b''.join([int2byte(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b//8)])
def bit(h, i):
return (indexbytes(h, i//8) >> (i%8)) & 1
def publickey(sk):
h = H(sk)
a = 2**(b-2) + sum(2**i * bit(h, i) for i in range(3, b-2))
A = scalarmult(B, a)
return encodepoint(A)
def Hint(m):
h = H(m)
return sum(2**i * bit(h, i) for i in range(2*b))
def signature(m, sk, pk):
h = H(sk)
a = 2**(b-2) + sum(2**i * bit(h, i) for i in range(3, b-2))
r = Hint(intlist2bytes([indexbytes(h, j) for j in range(b//8, b//4)]) + m)
R = scalarmult(B, r)
S = (r + Hint(encodepoint(R)+pk+m) * a) % l
return encodepoint(R) + encodeint(S)
def isoncurve(P):
x = P[0]
y = P[1]
return (-x*x + y*y - 1 - d*x*x*y*y) % q == 0
def decodeint(s):
return sum(2**i * bit(s, i) for i in range(0, b))
def decodepoint(s):
y = sum(2**i * bit(s, i) for i in range(0, b-1))
x = xrecover(y)
if x & 1 != bit(s, b-1): x = q - x
P = [x, y]
if not isoncurve(P): raise Exception("decoding point that is not on curve")
return P
def checkvalid(s, m, pk):
if len(s) != b//4: raise Exception("signature length is wrong")
if len(pk) != b//8: raise Exception("public-key length is wrong")
R = decodepoint(s[0:b//8])
A = decodepoint(pk)
S = decodeint(s[b//8:b//4])
h = Hint(encodepoint(R) + pk + m)
if scalarmult(B, S) != edwards(R, scalarmult(A, h)):
raise Exception("signature does not pass verification")
# This is from https://github.com/monero-project/mininero by Shen Noether with The Monero Project
def scalarmultbase(e):
if e == 0: return [0, 1]
Q = scalarmult(B, e//2)
Q = edwards(Q, Q)
if e & 1: Q = edwards(Q, B)
return Q