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Add field square root algorithms Shanks, Atkin, and Kong #579
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fn kong<F: crate::Field>( | ||
elem: &F, | ||
trace: &F, | ||
c: &F, |
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I didn't know if this variable had a name
}, | ||
/// In the case of 3 mod 4, we can find the square root via an exponentiation, | ||
/// sqrt(a) = a^(p+1)/4. This can be proved using Euler's criterion, a^(p-1)/2 = 1 mod p. | ||
PowerCase3Mod4 { |
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Didn't find any name for this algorithm so I just called it "power"
Co-authored-by: Pratyush Mishra <[email protected]>
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/// * First factor _q - 1 = 2^s t_ where _t_ is odd. | ||
/// * `two_adicity` - _s_. | ||
/// * `quadratic_nonresidue_to_trace` - _c^t_, with random _c_ such that _c^2^(s - 1) = 1_. | ||
/// * `trace_of_modulus_minus_one_div_two` - _(t - 1)/2_. | ||
TonelliShanks { | ||
two_adicity: u32, | ||
quadratic_nonresidue_to_trace: F, | ||
trace_of_modulus_minus_one_div_two: &'static [u64], |
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Just realized my naming is a bit inconsistent with some existing names, this says modulus but I say characteristic. I feel like "characteristic" is more accurate though. Let me know if you think that should be changed.
Hello! I've been doing some work trying to get the algorithms @alexander-zw implemented to actually be called during sqrt calls on the fields - so far they are implemented, but never called. This is proving very difficult for a couple of reasons that you might have easy solutions to (especially @Pratyush). I'll explain how I view the situation
What is the way to go?
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Description
closes: #543 (finishes task #1 but not whole issue)
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