105 lines
2.4 KiB
Python
105 lines
2.4 KiB
Python
|
import hashlib
|
||
|
|
|
||
|
|
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 ''.join([chr(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 ''.join([chr(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b/8)])
|
||
|
|
|
||
|
|
def bit(h,i):
|
||
|
|
return (ord(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(''.join([h[i] for i 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")
|