def calc_S(v_vec, alpha_degree, GF_step, degree_of_symbol_x, use_latex):
global x
v_alpha = Add()
v_alpha_mod = Add()
for i in range(len(v_vec)):
v_alpha += v_vec[i] * x ** (i * alpha_degree)
v_alpha_mod += v_vec[i] * x ** ((i * alpha_degree) % (2 ** GF_step - 1))
v_alpha_mod = v_alpha_mod.as_poly(x, domain='GF(2)').args[0]
S = sum_alpha(v_alpha_mod, degree_of_symbol_x)
if v_alpha == v_alpha_mod:
if use_latex:
calc = latex(v_alpha)
else:
calc = v_alpha.__str__()
else:
if use_latex:
calc = latex(v_alpha) + ' = ' + latex(v_alpha_mod)
else:
calc = v_alpha.__str__() + ' = ' + v_alpha_mod.__str__()
if S == 0:
return 0, 0, calc
k, l = np.where(degree_of_symbol_x[:-1] == '{:>0{GF}b}'.format(S, GF=GF_step))
return a ** (int(k) - 1), int(k), calc
def degree_mod(pol, mod: int):
if pol.is_Integer or pol.is_Symbol:
return pol
if pol.is_Pow:
return pol.args[0] ** (int(pol.args[1]) % mod)
new_pol = Add()
for i in range(len(pol.args)):
if pol.args[i].is_Integer or pol.args[i].is_Symbol:
new_pol += pol.args[i]
else:
new_pol += pol.args[i].args[0] ** (int(pol.args[i].args[1]) % mod)
if pol.args[-1].is_Integer:
return new_pol.as_poly(a, domain='GF(2)').args[0]
elif pol.args[-1].is_Symbol:
return new_pol.as_poly(pol.args[-1], domain='GF(2)').args[0]
else:
return new_pol.as_poly(pol.args[-1].args[0], domain='GF(2)').args[0]
def get_lambda_3(S1, S3, S5, degree_of_symbol_x, GF_step):
Lambda2_first = Add(S1 ** 2 * S3 + S5)
Lambda2_second = Add(S1 ** 3 + S3)
Lambda2_second = Lambda2_second.as_poly(a, domain='GF(2)').args[0]
Lambda2_second = degree_mod(Lambda2_second, 2 ** GF_step - 1)
Lambda2_second = Lambda2_second.as_poly(a, domain='GF(2)').args[0]
Lambda2_second = sum_alpha(Lambda2_second, degree_of_symbol_x)
if Lambda2_second == 0:
return False, 0, 0
Lambda2_second = '{:>0{GF}b}'.format(Lambda2_second, GF=GF_step)
k, l = np.where(degree_of_symbol_x[:-1] == Lambda2_second)
Lambda2_second = degree_mod(a ** -(int(k) - 1), 2 ** GF_step - 1)
Lambda2_mul = Lambda2_first * Lambda2_second
if not Lambda2_mul.is_Integer:
Lambda2_mul = Lambda2_mul.as_poly().args[0]
Lambda2_mod = degree_mod(Lambda2_mul, 2 ** GF_step - 1)
Lambda2_mod = Lambda2_mod.as_poly(a, domain='GF(2)').args[0]
Lambda2_sum = '{:>0{GF}b}'.format(sum_alpha(Lambda2_mod, degree_of_symbol_x), GF=GF_step)
if Lambda2_sum == '0000':
Lambda2 = 0
else:
k, l = np.where(degree_of_symbol_x[:-1] == Lambda2_sum)
Lambda2 = a ** (int(k) - 1)
Lambda3_first = Add(S1 ** 3 + S3)
Lambda3_second = Add(S1 * Lambda2)
if not Lambda3_second.is_Integer:
Lambda3_second = Lambda3_second.as_poly().args[0]
Lambda3_first = Lambda3_first.as_poly(a, domain='GF(2)').args[0]
Lambda3_second = Lambda3_second.as_poly(a, domain='GF(2)').args[0]
Lambda3_first = degree_mod(Lambda3_first, 2 ** GF_step - 1)
Lambda3_second = degree_mod(Lambda3_second, 2 ** GF_step - 1)
Lambda3 = Lambda3_first + Lambda3_second
Lambda3 = Lambda3.as_poly(a, domain='GF(2)').args[0]
Lambda3 = '{:>0{GF}b}'.format(sum_alpha(Lambda3, degree_of_symbol_x), GF=GF_step)
if Lambda3 == '0000':
Lambda3 = 0
else:
k, l = np.where(degree_of_symbol_x[:-1] == Lambda3)
Lambda3 = a ** (int(k) - 1)
return True, Lambda2, Lambda3
