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34 lines
1.1 KiB
Python
34 lines
1.1 KiB
Python
import random
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def sample_random(fp, seed):
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rnd = random.Random(seed)
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# Range of the field is 0 ... p - 1
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return fp(rnd.randint(0, fp.p - 1))
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def is_power_of_two(n):
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# Power of two number is represented by a single digit
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# followed by zeroes.
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return n & (n - 1) == 0
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#| ## Choosing roots of unity
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def get_omega(fp, n, seed=None):
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"""
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Given a field, this method returns an n^th root of unity.
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If the seed is not None then this method will return the
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same n'th root of unity for every run with the same seed
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This only makes sense if n is a power of 2.
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"""
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assert is_power_of_two(n)
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# https://crypto.stackexchange.com/questions/63614/finding-the-n-th-root-of-unity-in-a-finite-field
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while True:
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# Sample random x != 0
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x = sample_random(fp, seed)
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# Compute g = x^{(q - 1)/n}
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y = pow(x, (fp.p - 1) // n)
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# If g^{n/2} != 1 then g is a primitive root
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if y != 1 and pow(y, n // 2) != 1:
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assert pow(y, n) == 1, "omega must be 2nd root of unity"
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return y
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