104 lines
2.4 KiB
Python
104 lines
2.4 KiB
Python
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: 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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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: 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 ''.join([chr(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 ''.join([chr(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 (ord(h[i/8]) >> (i%8)) & 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(''.join([h[i] for i 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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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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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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