Use full Montgomery mul for BoxedResidue::{mul, square}
#442
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Previously "almost Montgomery multiplications" were used which return a result which is only reduced modulo the bit size of the modulus, but may still equal or exceed the modulus. This commit goes back to using a multiply followed by a full Montgomery reduction, and adds more asserts that the result is fully reduced. This incurs a performance hit, but AMM is likely "unsafe" to use outside of this crate unless we decide to fully encapsulate the inner representation of `*Residue` types. Note that this does not ensure the output of modpow is fully reduced, which is left to be fixed in a followup. This commit includes a regression test from the issue where this was reported (#441) and additionally adds some general proptests for `BoxedResidue::square`.
tarcieri
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Previously "almost Montgomery multiplications" were used which return a result which is only reduced modulo the bit size of the modulus, but may still equal or exceed the modulus.
This commit goes back to using a multiply followed by a full Montgomery reduction, and adds more asserts that the result is fully reduced. This incurs a performance hit, but AMM is likely "unsafe" to use outside of this crate unless we decide to fully encapsulate the inner representation of
*Residuetypes.Note that this does not ensure the output of modpow is fully reduced, which is left to be fixed in a followup.
This commit includes a regression test from the issue where this was reported (#441) and additionally adds some general proptests for
BoxedResidue::square.Closes #441.