example.py

#!/usr/bin/sage

from sage.all import *
from sboxU import *
import time



def test_ea(N):
    # generating a random permutation g
    g = random_permutation(N)
    
    # generating the affine transformation
    A = rand_linear_permutation(N)  # A is a SAGE Matrix instance
    a = randint(0, 2**N-1)          # a is a random number of [0,2^n)
    B = rand_linear_permutation(N)  # B is a SAGE Matrix instance
    b = randint(0, 2**N-1)          # a is a random number of [0,2^n)
    f = [oplus(apply_bin_mat(g[apply_bin_mat(oplus(x, a), A)], B), b)
         for x in range(0, 2**N)]
    print("f = (B o g o A)(x + a) + b, where:")
    print("A = \n" + A.str())
    print("a = " + str(a))
    print("B = \n" + B.str())
    print("b = " + str(b))
    print("")
    # recovering the affine equivalence of f and g
    ae = affine_equivalence(f, g)   # the algorithm by Biryukov et al
    if len(ae) == 0:
        print("AE algorithm failed")
    else:
        print("AE relation between f and g rediscovered!")
        print("f = (B o g o A)(x + a) + b, where:")
        print("A = \n" + ae[0].str())
        print("a = " + str(ae[1]))
        print("B = \n" + ae[2].str())
        print("b = " + str(ae[3]))

        
def test_vector_extraction(N):
    z = []
    for x in range(0, 2**(N)+2**(N-1)):
        y = randint(0, 2**N-1)
        if y not in z:
            z.append(y)
    
    for number in ["just one", "all dimensions", "fixed dimension"]:
        #for number in ["all dimensions"]:
        print("\n\n=== {}\n".format(number))
        bases = extract_affine_bases(z, int(N/2), N, number=number)
        print("total = {}".format(len(bases)))
        for b in bases:
            print(str(len(b)) + "  " + pretty_vector(b))

def test_ccz_equivalence(N, n_trials):
    gf = GF(2**N, name="a")
    cube = [(gf.fetch_int(x)**3).integer_representation() for x in range(0, 2**N)]
    print("Should be True:")
    total_time_ccz = 0.0
    for i, g in enumerate(ea_classes_in_the_ccz_class_of(cube)):
        start_time = time.time()
        equiv = are_ccz_equivalent(cube, g)
        elapsed_seconds = float(time.time() - start_time)
        total_time_ccz += elapsed_seconds
        print("{} {:.3f}s".format(equiv, elapsed_seconds))
        if (i == n_trials-1):
            break
    print("average time: {:.3f}s".format(total_time_ccz / n_trials))
    total_time_ccz = 0.0
    print("\nShould be False:")
    for i in range(0, n_trials):
        g = [randint(0, 2**N-1) for i in range(0, 2**N)]
        start_time = time.time()
        equiv = are_ccz_equivalent(cube, g)
        elapsed_seconds = float(time.time() - start_time)
        total_time_ccz += elapsed_seconds
        print("{} {:.3f}s".format(equiv, elapsed_seconds))
    print("average time: {:.3f}s".format(total_time_ccz / n_trials))




if __name__ == '__main__':
    test_ccz_equivalence(8, 10)