Ring LWE KE

Ring-LWE.sage

from random import randint

def generate_matrix(dimention, modulus):
    array = []
    upper_limit = modulus * dimention
    
    for i in range(0, dimention):
        f = 0
        for j in range(0, dimention):
            f = f + (randrange(modulus, upper_limit) * x^j)
        
        array.append(f)
        
    return Matrix(array)
    
dimention = 8
modulus = 65537
R = PolynomialRing(GF(65537), "X")
X = R.gen()
S = R.quotient(X^1024 + 1, "x")
x = S.gen()

A = generate_matrix(dimention, modulus)
S = generate_matrix(dimention, modulus)
S_ = generate_matrix(dimention, modulus)

B = A.transpose()*S
B_ = A.transpose()*S_

alice = S*B_
bob = S_*B

print alice == bob