EVOLUTION-MANAGER

Edit File: djbec.py

# Ed25519 digital signatures # Based on http://ed25519.cr.yp.to/python/ed25519.py # See also http://ed25519.cr.yp.to/software.html # Adapted by Ron Garret # Sped up considerably using coordinate transforms found on: # http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html # Specifically add-2008-hwcd-4 and dbl-2008-hwcd try: # pragma nocover unicode PY3 = False def asbytes(b): """Convert array of integers to byte string""" return ''.join(chr(x) for x in b) def joinbytes(b): """Convert array of bytes to byte string""" return ''.join(b) def bit(h, i): """Return i'th bit of bytestring h""" return (ord(h[i//8]) >> (i%8)) & 1 except NameError: # pragma nocover PY3 = True asbytes = bytes joinbytes = bytes def bit(h, i): return (h[i//8] >> (i%8)) & 1 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 # Can probably get some extra speedup here by replacing this with # an extended-euclidean, but performance seems OK without that 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 # Faster (!) version based on: # http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html def xpt_add(pt1, pt2): (X1, Y1, Z1, T1) = pt1 (X2, Y2, Z2, T2) = pt2 A = ((Y1-X1)*(Y2+X2)) % q B = ((Y1+X1)*(Y2-X2)) % q C = (Z1*2*T2) % q D = (T1*2*Z2) % q E = (D+C) % q F = (B-A) % q G = (B+A) % q H = (D-C) % q X3 = (E*F) % q Y3 = (G*H) % q Z3 = (F*G) % q T3 = (E*H) % q return (X3, Y3, Z3, T3) def xpt_double (pt): (X1, Y1, Z1, _) = pt A = (X1*X1) B = (Y1*Y1) C = (2*Z1*Z1) D = (-A) % q J = (X1+Y1) % q E = (J*J-A-B) % q G = (D+B) % q F = (G-C) % q H = (D-B) % q X3 = (E*F) % q Y3 = (G*H) % q Z3 = (F*G) % q T3 = (E*H) % q return (X3, Y3, Z3, T3) def pt_xform (pt): (x, y) = pt return (x, y, 1, (x*y)%q) def pt_unxform (pt): (x, y, z, _) = pt return ((x*inv(z))%q, (y*inv(z))%q) def xpt_mult (pt, n): if n==0: return pt_xform((0,1)) _ = xpt_double(xpt_mult(pt, n>>1)) return xpt_add(_, pt) if n&1 else _ def scalarmult(pt, e): return pt_unxform(xpt_mult(pt_xform(pt), e)) def encodeint(y): bits = [(y >> i) & 1 for i in range(b)] e = [(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b//8)] return asbytes(e) def encodepoint(P): x = P[0] y = P[1] bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1] e = [(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b//8)] return asbytes(e) 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)) inter = joinbytes([h[i] for i in range(b//8,b//4)]) r = Hint(inter + 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) v1 = scalarmult(B,S) # v2 = edwards(R,scalarmult(A,h)) v2 = pt_unxform(xpt_add(pt_xform(R), pt_xform(scalarmult(A, h)))) return v1==v2 ########################################################## # # Curve25519 reference implementation by Matthew Dempsky, from: # http://cr.yp.to/highspeed/naclcrypto-20090310.pdf # P = 2 ** 255 - 19 P = q A = 486662 #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, P - 2, P) def add(n, m, d): (xn, zn) = n (xm, zm) = m (xd, zd) = d x = 4 * (xm * xn - zm * zn) ** 2 * zd z = 4 * (xm * zn - zm * xn) ** 2 * xd return (x % P, z % P) def double(n): (xn, zn) = n x = (xn ** 2 - zn ** 2) ** 2 z = 4 * xn * zn * (xn ** 2 + A * xn * zn + zn ** 2) return (x % P, z % P) def curve25519(n, base=9): one = (base,1) two = double(one) # f(m) evaluates to a tuple # containing the mth multiple and the # (m+1)th multiple of base. def f(m): if m == 1: return (one, two) (pm, pm1) = f(m // 2) if (m & 1): return (add(pm, pm1, one), double(pm1)) return (double(pm), add(pm, pm1, one)) ((x,z), _) = f(n) return (x * inv(z)) % P import random def genkey(n=0): n = n or random.randint(0,P) n &= ~7 n &= ~(128 << 8 * 31) n |= 64 << 8 * 31 return n #def str2int(s): # return int(hexlify(s), 16) # # return sum(ord(s[i]) << (8 * i) for i in range(32)) # #def int2str(n): # return unhexlify("%x" % n) # # return ''.join([chr((n >> (8 * i)) & 255) for i in range(32)]) ################################################# def dsa_test(): import os msg = str(random.randint(q,q+q)).encode('utf-8') sk = os.urandom(32) pk = publickey(sk) sig = signature(msg, sk, pk) return checkvalid(sig, msg, pk) def dh_test(): sk1 = genkey() sk2 = genkey() return curve25519(sk1, curve25519(sk2)) == curve25519(sk2, curve25519(sk1))