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@ -1,11 +1,12 @@
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# orignal version downloaded from https://ed25519.cr.yp.to/python/ed25519.py
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# modified for Python 3 by Jochen Hoenicke <hoenicke@gmail.com>
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import sys
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import hashlib
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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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q = 2 ** 255 - 19
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l = 2 ** 252 + 27742317777372353535851937790883648493
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def H(m):
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@ -17,7 +18,7 @@ def expmod(b, e, m):
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raise Exception('negative exponent')
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if e == 0:
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return 1
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t = expmod(b, e >> 1, m)**2 % m
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t = expmod(b, e >> 1, m) ** 2 % m
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if e & 1:
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t = (t * b) % m
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return t
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@ -68,35 +69,44 @@ def scalarmult(P, e):
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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 bytes([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b >> 3)])
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if sys.version_info.major < 3:
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return ''.join([chr(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b >> 3)])
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else:
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return bytes([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b >> 3)])
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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 bytes([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b >> 3)])
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if sys.version_info.major < 3:
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return ''.join([chr(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b >> 3)])
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else:
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return bytes([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b >> 3)])
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def bit(h, i):
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return (h[i >> 3] >> (i & 7)) & 1
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if sys.version_info.major < 3:
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return (ord(h[i >> 3]) >> (i & 7)) & 1
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else:
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return (h[i >> 3] >> (i & 7)) & 1
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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 = 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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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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return sum(2 ** i * bit(h, i) for i in range(2 * b))
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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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a = 2 ** (b - 2) + sum(2 ** i * bit(h, i) for i in range(3, b - 2))
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r = Hint(bytes([h[i] for i in range(b >> 3, b >> 2)]) + 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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@ -110,11 +120,11 @@ def isoncurve(P):
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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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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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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):
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x = q - x
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