def MontExp_1024(A, e, M):
# Returns A^e mod M
return helpers.Modexp(A, e, M) # This is fast
print "M = ", hex(M) # 1024-bits
print "(A*B*R^-1) mod M = ", hex(C) # 1024-bits
print "(A*B*R^-1) mod M = ", hex(D) # 1024-bits
print "error = ", hex(e)
#####################################################
if operation == 4:
print "Test Vector for Montgomery Exponentiation\n"
X = helpers.getRandomInt(1024)
E = helpers.getRandomInt(8)
M = helpers.getModulus(1024)
C = HW.MontExp(X, E, M)
D = helpers.Modexp(X, E, M)
e = C - D
print "X = ", hex(X) # 1024-bits
print "E = ", hex(E) # 8-bits
print "M = ", hex(M) # 1024-bits
print "(X^E) mod M = ", hex(C) # 1024-bits
print "(X^E) mod M = ", hex(D) # 1024-bits
print "error = ", hex(e)
#####################################################
if operation == 5:
print "Test Vector for RSA\n"
X = helpers.getRandomInt(1024)
E = helpers.getRandomInt(16)
N = helpers.getModulus(1024)
# Hardware values
# X = 0xb55708a7f2daa5631117b7d03ec4d7992ccad8d7e22d891db1e03e15ad545a33fc9f444b1a16dbae60d527f8f7118db19d65258cb9977527fbfc19786b18ba76
# E = 0xb1
# M = 0xd9bf2caaf3992d7e456563271a7c22da97d772cf8fb8a8d34756a335657daf63eff091961c4ea3c56066c5822baa68d108e9b45d95aa98852b71d44daca7419f
X = 0xd394854091a4bd576e831c047f8dbd3962c6176e4ac73a271b34d4d64a047fad949e7f5db4f2b561ac3054aa79f1ea1667392a6effc533fdb3910f7e0382a78a3e69c71b718dbfcb525d5ad61c6d04e9a99d80775e84c0ac2581853fb7dbbcbbbcdd23af4d92fcecc53baeeb63951386d4801e7eec875fefcdcc53e97e4d114f
E = 0x8aa7
N = 0xe463552f57f41ea0eba321a7207bedda838f187b75f5ed7af76f70d25b9a2c0d84e0b5943885d4c7682cf637fe44cce70610f8532fcaa42a56867970060e1237bf1feed8fd0f3441ae8bf2c011b530c1cf173a564f448e34b49ba79804bf4901cf6df0c2bc79bc4d90ff37b204f9addb4c4a72d2d9315b454fd2954279c5095d
# M_prime = helpers.Modinv(M, 2**1024)
C = HW.MontExp_1024(X, E, N)
D = helpers.Modexp(X, E, N)
e = C - D
print "X = ", hex(X) # 1024-bits
print "E = ", hex(E) # 16-bits
r = 2**1024
N_prime = (r - helpers.Modinv(N, r))
print "N = ", hex(N) # 1024-bits
print "N_prime = ", hex(N_prime) # 1024-bits
print "(X^E) mod M = ", hex(C) # 1024-bits
print "(X^E) mod M = ", hex(D) # 1024-bits
print "error = ", hex(e)
helpers.print2array(X, 'x', 32)
print "M = ", hex(M) # 512-bits
print "(A*B*R^-1) mod M = ", hex(C) # 512-bits
print "(A*B*R^-1) mod M = ", hex(D) # 512-bits
print "error = ", hex(e)
#####################################################
if operation == 4:
print "Test Vector for Montgomery Exponentiation\n"
X = helpers.getRandomInt(512)
E = helpers.getRandomInt(8)
M = helpers.getModulus(512)
C = HW.MontExp_512(X, E, M)
D = helpers.Modexp(X, E, M)
e = C - D
print "X = ", hex(X) # 512-bits
print "E = ", hex(E) # 8-bits
print "M = ", hex(M) # 512-bits
print "(X^E) mod M = ", hex(C) # 512-bits
print "(X^E) mod M = ", hex(D) # 512-bits
print "error = ", hex(e)
#####################################################
if operation == 5:
print "Test Vector for RSA\n"
print "B = ", hex(B) # 512-bits
print "M = ", hex(M) # 512-bits
print "(A*B*R^-1) mod M = ", hex(C) # 512-bits
print "(A*B*R^-1) mod M = ", hex(D) # 512-bits
#####################################################
if operation == 4:
print "Test Vector for Montgomery Exponentiation\n"
X = helpers.getRandomInt(512)
E = helpers.getRandomInt(8)
M = helpers.getModulus(512)
C = montgomery.MontExp(X, E, M)
D = helpers.Modexp(X, E, M)
print "X = ", hex(X) # 512-bits
print "E = ", hex(E) # 8-bits
print "M = ", hex(M) # 512-bits
print "(X^E) mod M = ", hex(C) # 512-bits
print "(X^E) mod M = ", hex(D) # 512-bits
#####################################################
if operation == 5:
print "Test Vector for RSA\n"
print "\n--- Precomputed Values"