158 lines
4.0 KiB
Python
158 lines
4.0 KiB
Python
# The reference Ed25519 software is in the public domain.
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# Source: https://ed25519.cr.yp.to/python/ed25519.py
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#
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# Parts Copyright (c) 2016 The MoneroPy Developers. Released under the BSD 3-Clause
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from binascii import hexlify, unhexlify
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import hashlib
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import operator as _oper
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import sys as _sys
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# Set up byte handling for Python 2 or 3
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if _sys.version_info.major == 2: # pragma: no cover
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int2byte = chr
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range = xrange
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def indexbytes(buf, i):
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return ord(buf[i])
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def intlist2bytes(l):
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return b"".join(chr(c) for c in l)
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else: # pragma: no cover
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indexbytes = _oper.getitem
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intlist2bytes = bytes
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int2byte = _oper.methodcaller("to_bytes", 1, "big")
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b = 256
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q = 2**255 - 19
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l = 2**252 + 27742317777372353535851937790883648493
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def expmod(b, e, m):
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if e == 0: return 1
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t = expmod(b, e//2, m)**2 % m
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if e & 1: t = (t*b) % m
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return t
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def inv(x):
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return expmod(x, q-2, q)
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d = -121665 * inv(121666)
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I = expmod(2, (q-1)//4, q)
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def xrecover(y):
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xx = (y*y-1) * inv(d*y*y+1)
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x = expmod(xx, (q+3)//8, q)
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if (x*x - xx) % q != 0: x = (x*I) % q
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if x % 2 != 0: x = q-x
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return x
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def compress(P):
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zinv = inv(P[2])
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return (P[0] * zinv % q, P[1] * zinv % q)
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def decompress(P):
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return (P[0], P[1], 1, P[0]*P[1] % q)
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By = 4 * inv(5)
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Bx = xrecover(By)
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B = [Bx%q, By%q]
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def edwards(P, Q):
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x1 = P[0]
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y1 = P[1]
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x2 = Q[0]
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y2 = Q[1]
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x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
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y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
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return [x3%q, y3%q]
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def add(P, Q):
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A = (P[1]-P[0])*(Q[1]-Q[0]) % q
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B = (P[1]+P[0])*(Q[1]+Q[0]) % q
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C = 2 * P[3] * Q[3] * d % q
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D = 2 * P[2] * Q[2] % q
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E = B-A
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F = D-C
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G = D+C
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H = B+A
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return (E*F, G*H, F*G, E*H)
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def add_compressed(P, Q):
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return compress(add(decompress(P), decompress(Q)))
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def scalarmult(P, e):
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if e == 0: return [0, 1]
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Q = scalarmult(P, e//2)
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Q = edwards(Q, Q)
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if e & 1: Q = edwards(Q, P)
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return Q
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def encodeint(y):
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bits = [(y >> i) & 1 for i in range(b)]
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return b''.join([int2byte(sum([bits[i*8 + j] << j for j in range(8)])) for i in range(b//8)])
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def encodepoint(P):
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x = P[0]
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y = P[1]
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bits = [(y >> i) & 1 for i in range(b-1)] + [x & 1]
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return b''.join([int2byte(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b//8)])
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def bit(h, i):
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return (indexbytes(h, i//8) >> (i%8)) & 1
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def isoncurve(P):
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x = P[0]
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y = P[1]
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return (-x*x + y*y - 1 - d*x*x*y*y) % q == 0
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def decodeint(s):
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return sum(2**i * bit(s, i) for i in range(0, b))
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def decodepoint(s):
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y = sum(2**i * bit(s, i) for i in range(0, b-1))
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x = xrecover(y)
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if x & 1 != bit(s, b-1): x = q - x
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P = [x, y]
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if not isoncurve(P): raise Exception("decoding point that is not on curve")
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return P
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# These are unused but let's keep them
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#def H(m):
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# return hashlib.sha512(m).digest()
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#
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#def Hint(m):
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# h = H(m)
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# return sum(2**i * bit(h, i) for i in range(2*b))
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#
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#def publickey(sk):
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# h = H(sk)
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# a = 2**(b-2) + sum(2**i * bit(h, i) for i in range(3, b-2))
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# A = scalarmult(B, a)
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# return encodepoint(A)
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#
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#def signature(m, sk, pk):
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# h = H(sk)
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# a = 2**(b-2) + sum(2**i * bit(h, i) for i in range(3, b-2))
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# r = Hint(intlist2bytes([indexbytes(h, j) for j in range(b//8, b//4)]) + m)
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# R = scalarmult(B, r)
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# S = (r + Hint(encodepoint(R)+pk+m) * a) % l
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# return encodepoint(R) + encodeint(S)
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#
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#def checkvalid(s, m, pk):
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# if len(s) != b//4: raise Exception("signature length is wrong")
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# if len(pk) != b//8: raise Exception("public-key length is wrong")
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# R = decodepoint(s[0:b//8])
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# A = decodepoint(pk)
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# S = decodeint(s[b//8:b//4])
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# h = Hint(encodepoint(R) + pk + m)
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# if scalarmult(B, S) != edwards(R, scalarmult(A, h)):
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# raise Exception("signature does not pass verification")
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def public_from_secret(k):
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keyInt = decodeint(k)
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aB = scalarmult(B, keyInt)
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return encodepoint(aB)
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def public_from_secret_hex(hk):
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return hexlify(public_from_secret(unhexlify(hk))).decode()
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