mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-11-29 19:08:12 +00:00
138 lines
3.0 KiB
Python
138 lines
3.0 KiB
Python
# 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 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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def H(m):
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return hashlib.sha512(m).digest()
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def expmod(b, e, m):
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if e < 0:
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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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if e & 1:
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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) >> 2, 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) >> 3, q)
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if (x * x - xx) % q != 0:
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x = (x * I) % q
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if x % 2 != 0:
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x = q - x
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return x
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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 scalarmult(P, e):
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if e == 0:
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return [0, 1]
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Q = scalarmult(P, e >> 1)
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Q = edwards(Q, Q)
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if e & 1:
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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 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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def bit(h, i):
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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 = 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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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(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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return encodepoint(R) + encodeint(S)
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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):
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x = q - x
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P = [x, y]
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if not isoncurve(P):
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raise Exception("decoding point that is not on curve")
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return P
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def checkvalid(s, m, pk):
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if len(s) != b >> 2:
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raise Exception("signature length is wrong")
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if len(pk) != b >> 3:
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raise Exception("public-key length is wrong")
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R = decodepoint(s[0:b >> 3])
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A = decodepoint(pk)
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S = decodeint(s[b >> 3:b >> 2])
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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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