65 lines
1.3 KiB
Python
65 lines
1.3 KiB
Python
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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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 radix255(x):
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x = x % q
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if x + x > q: x -= q
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x = [x,0,0,0,0,0,0,0,0,0]
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bits = [26,25,26,25,26,25,26,25,26,25]
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for i in range(9):
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carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
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x[i] -= carry * 2**bits[i]
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x[i + 1] += carry
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result = ""
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for i in range(9):
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result = result+str(x[i])+","
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result = result+str(x[9])
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return result
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Bi = B
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for i in range(32):
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print "{"
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Bij = Bi
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for j in range(8):
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print " {"
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print " {",radix255(Bij[1]+Bij[0]),"},"
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print " {",radix255(Bij[1]-Bij[0]),"},"
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print " {",radix255(2*d*Bij[0]*Bij[1]),"},"
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Bij = edwards(Bij,Bi)
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print " },"
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print "},"
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for k in range(8):
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Bi = edwards(Bi,Bi)
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