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28 lines
900 B
28 lines
900 B
modulus = 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888458477323173057491593855069696241854796396165721416325350064441470418137846398469611935719059908164220784476160001
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assert(modulus.is_prime())
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Fp = GF(modulus)
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generator = Fp(0);
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for i in range(0, 20):
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i = Fp(i);
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neg_i = Fp(-i)
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if not(i.is_primitive_root() or neg_i.is_primitive_root()):
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continue
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elif i.is_primitive_root():
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assert(i.is_primitive_root());
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print("Generator: %d" % i)
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generator = i
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break
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else:
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assert(neg_i.is_primitive_root());
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print("Generator: %d" % neg_i)
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generator = neg_i
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break
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two_adicity = valuation(modulus - 1, 2);
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trace = (modulus - 1) / 2**two_adicity;
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two_adic_root_of_unity = generator^trace
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print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
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