def MontExp(X, E, N):
# Returns (X^E) mod N
# R = 2**1024
# RN = R % N
# R2N = (R*R) % N;
# A = RN;
# X_tilde = MontMul(X,R2N,N)
# t = helpers.bitlen(E)
# for i in range(0,t):
# A = MontMul(A,A,N)
# if helpers.bit(E,t-i-1) == 1:
# A = MontMul(A,X_tilde,M)
# A = MontMul(A,1,N)
R = 2**1024
RN = R % N
R2N = (R * R) % N
A = RN
X_tilde = MontMul_2bW(X, R2N, N)
t = helpers.bitlen(E)
for i in range(0, t):
A = MontMul_2bW(A, A, N)
if helpers.bit(E, t - i - 1) == 1:
A = MontMul_2bW(A, X_tilde, N)
A = MontMul_2bW(A, 1, N)
return A
def MontMul_512(A, B, M):
# Returns (A*B*Modinv(R,M)) mod M
C = 0
# import pdb; pdb.set_trace()
for i in range(0, 512):
C = MultiPrecisionAdd(C, helpers.bit(A, i) * B, "add")
if (C % 2) != 0:
C = MultiPrecisionAdd(C, M, "add") / 2
C = C / 2
while C >= M:
C = MultiPrecisionAdd(C, M, "sub")
return C
def MontMul(A, B, M):
# Returns (A*B*Modinv(R,M)) mod M
C = 0
for i in range(0, 512):
C = MultiPrecisionAdd(C, helpers.bit(A, i) * B, "add")
if (C % 2) == 0:
C = C / 2
else:
C = MultiPrecisionAdd(C, M, "add") / 2
while C >= M:
C = MultiPrecisionAdd(C, M, "sub")
return C
def MontExp_512(X, E, M):
# Returns (X^E) mod M
R = 2**512
R2 = (R * R) % M
A = R % M
X_tilde = MontMul_512(X, R2, M)
t = helpers.bitlen(E)
for i in range(0, t):
A = MontMul_512(A, A, M)
if helpers.bit(E, t - i - 1) == 1:
A = MontMul_512(A, X_tilde, M)
A = MontMul_512(A, 1, M)
return A
def MontExp_1024(X, E, M):
# Returns (X^E) mod M
R = 2**1024
R2 = (R * R) % M
import pdb
pdb.set_trace()
A = R % M
X_tilde = MontMul_1024(X, R2, M)
t = helpers.bitlen(E)
for i in range(0, t):
A = MontMul_1024(A, A, M)
if helpers.bit(E, t - i - 1) == 1:
A = MontMul_1024(A, X_tilde, M)
A = MontMul_1024(A, 1, M)
return A
def MontExp_1024_print(X, E, M):
# Returns (X^E) mod M
R = 2**1024
R2 = (R * R) % M
A = R % M
X_tilde = MontMul_1024(X, R2, M)
t = helpers.bitlen(E)
for i in range(0, 15):
print "-- Iteration ", str(i)
A = MontMul_1024(A, A, M)
print "\n@ A* A -- ", str(i), " : ", hex(A)
if helpers.bit(E, t - i - 1) == 1:
A = MontMul_1024(A, X_tilde, M)
print "\n@ xtilde * A -- ", str(i), " : ", hex(A)
A = MontMul_1024(A, 1, M)
return A
def MontExp_512(X, E, M):
# Returns (X^E) mod M
R = 2**512
R2 = (R * R) % M
A = R % M
X_tilde = MontMul_512(X, R2, M)
t = helpers.bitlen(E)
for i in range(0, 20):
A = MontMul_512(A, A, M)
if helpers.bit(E, t - i - 1) == 1:
A = MontMul_512(A, X_tilde, M)
#if i >= 505:
print "uint32_t A_test = {" + helpers.WriteConstants(A, 16) + "};"
print " "
A = MontMul_512(A, 1, M)
return A
