SRP Adapted for Elliptic Curves

# SRP Adapted for Elliptic Curves - Steven M. Alexander Jr. - 5/6/2014

# NIST Parameters
NIST_p = 115792089210356248762697446949407573530086143415290314195533631308867097853951
NIST_r = 115792089210356248762697446949407573529996955224135760342422259061068512044369
NIST_b = Integer(0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b)
NIST_Px = Integer(0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296)
NIST_Py = Integer(0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5)
NIST_Qx = Integer(0xc97445f45cdef9f0d3e05e1e585fc297235b82b5be8ff3efca67c59852018192)
NIST_Qy = Integer(0xb28ef557ba31dfcbdd21ac46e2a91e3c304f44cb87058ada2cb815151e610046)

# Construct E and Q using NIST parameters
F = GF(NIST_p)
E = EllipticCurve(F, [0, 0, 0, -3, NIST_b])
print "E: " + str(E)
print
Q = E(NIST_Qx, NIST_Qy)
print "Q: " + str(Q) + "\n"

# Use Alice's password hash to determine P
x = Integer(0x4efa264f5ef3e1a5c95736e07544ebf0)
print "MD5 Hash of \"curve\", x = " + str(x)
P = x*Q
print "P = x*Q = " + str(P) + "\n"

#Create Alice's public key
A_a = Integer(0xd103fb3406c351a03578097503d26fa5)
A_A = A_a*Q
print "Alice's secret key a = " + str(A_a)
print "Alice's public key A = a*Q = " + str(A_A) + "\n"

#Give Alice's key to Bob
B_A = A_A

# Create Bob's public key, Bprime
B_b = Integer(0x6abd98d8b311a26ab2cab394e1ecb8af)
print "Bob's secret key b = " + str(B_b)
B_Bprime = B_b*Q
print "Bob's value of Bprime = " + str(B_Bprime) + "\n"

# Generate Tp and Tq
B_r = Integer(0xdfd98dc638b36d4f86712de2e3bd37de)
print "Bob's random value r = " + str(B_r)
B_Tq = B_r*Q
B_Tp = B_r*P
print "Bob's Tq = r*Q = " + str(B_Tq)
print "Bob's Tp = r*P = " + str(B_Tp)

# Mask Bob's public key using Tp
B_B = B_Bprime+B_Tp
print "Bob's value of B = " + str(B_B) + "\n"

# Give B and Tq to Alice
A_Tq = B_Tq
A_B = B_B

# Calculate Alice's Tp
A_Tp = x*A_Tq
A_Bprime = A_B - A_Tp
print "Alice's Tp = " + str(A_Tp)
print "Alice's Bprime = " + str(A_Bprime) + "\n"

# Alice's calculation of the shared key
A_S = A_a*A_Bprime
print "Alice's S = " + str(A_S)

# Bob's calculation of the shared key
B_S = B_b*B_A
print "Bob's S = " + str(B_S)