69 lines
1.4 KiB
Python
69 lines
1.4 KiB
Python
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import math
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k = 31
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F = GF(2)
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var = 'x'
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PR = PolynomialRing(F, var)
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p = PR.irreducible_element(k)
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gamma = PR.random_element(k)
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exp = 10
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target = gamma^exp % p
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def polynomial_power_in_Z2(q, exp, p, var):
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if exp == 0:
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return 1
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if q.degree() == p.degree():
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q += p
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res = q
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for i in range(2, exp+1):
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res = multiply_polynomials_in_Z2(res, q, p, var)
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return res
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def polynomial_power_in_Z2_V2(q, exp, p, var):
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if exp == 0:
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return 1
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if q.degree() == p.degree():
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q += p
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log2deg = math.floor(math.log2(exp)) + 1
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arr = [0]*log2deg
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arr[0] = q
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for i in range(1, log2deg):
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arr[i] = multiply_polynomials_in_Z2(arr[i-1], arr[i-1], p, var)
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res = PR(1)
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for i, b in enumerate(bin(exp)[:1:-1]):
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if b == '1':
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res = multiply_polynomials_in_Z2(res, arr[i], p, var)
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return res
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def multiply_polynomials_in_Z2(q1, q2, p, var):
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if q1.degree() > p.degree():
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raise ValueError('Unsupported!')
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if q1.degree() == p.degree():
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q1 += p
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arr = [0]*(q2.degree()+1)
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arr[0] = q1
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for i in range(1, q2.degree()+1):
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arr[i] = arr[i-1]*PR(var)
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if arr[i].degree() == p.degree():
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arr[i] += p
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return sum(arr[i] for i in q2.exponents())
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print(target)
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res = polynomial_power_in_Z2(gamma, exp, p, var)
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print(res)
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res = polynomial_power_in_Z2_V2(gamma, exp, p, var)
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print(res)
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