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28 lines
899 B
28 lines
899 B
modulus = 5237311370989869175293026848905079641021338739994243633972937865128169101571388346632361720473792365177258871486054600656048925740061347509722287043067341250552640264308621296888446513816907173362124418513727200975392177480577
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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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