base.py (1511B)
1 # Future imports for Python 2.7, mandatory in 3.0 2 from __future__ import division 3 from __future__ import print_function 4 from __future__ import unicode_literals 5 6 b = 256 7 q = 2**255 - 19 8 l = 2**252 + 27742317777372353535851937790883648493 9 10 def expmod(b,e,m): 11 if e == 0: return 1 12 t = expmod(b,e/2,m)**2 % m 13 if e & 1: t = (t*b) % m 14 return t 15 16 def inv(x): 17 return expmod(x,q-2,q) 18 19 d = -121665 * inv(121666) 20 I = expmod(2,(q-1)/4,q) 21 22 def xrecover(y): 23 xx = (y*y-1) * inv(d*y*y+1) 24 x = expmod(xx,(q+3)/8,q) 25 if (x*x - xx) % q != 0: x = (x*I) % q 26 if x % 2 != 0: x = q-x 27 return x 28 29 By = 4 * inv(5) 30 Bx = xrecover(By) 31 B = [Bx % q,By % q] 32 33 def edwards(P,Q): 34 x1 = P[0] 35 y1 = P[1] 36 x2 = Q[0] 37 y2 = Q[1] 38 x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2) 39 y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2) 40 return [x3 % q,y3 % q] 41 42 def radix255(x): 43 x = x % q 44 if x + x > q: x -= q 45 x = [x,0,0,0,0,0,0,0,0,0] 46 bits = [26,25,26,25,26,25,26,25,26,25] 47 for i in range(9): 48 carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i] 49 x[i] -= carry * 2**bits[i] 50 x[i + 1] += carry 51 result = "" 52 for i in range(9): 53 result = result+str(x[i])+"," 54 result = result+str(x[9]) 55 return result 56 57 Bi = B 58 for i in range(32): 59 print("{") 60 Bij = Bi 61 for j in range(8): 62 print(" {") 63 print(" {",radix255(Bij[1]+Bij[0]),"},") 64 print(" {",radix255(Bij[1]-Bij[0]),"},") 65 print(" {",radix255(2*d*Bij[0]*Bij[1]),"},") 66 Bij = edwards(Bij,Bi) 67 print(" },") 68 print("},") 69 for k in range(8): 70 Bi = edwards(Bi,Bi)