Add efficient linear combination for Montgomery forms #666
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Signed-off-by: Andrew Whitehead <[email protected]>
Signed-off-by: Andrew Whitehead <[email protected]>
Signed-off-by: Andrew Whitehead <[email protected]>
Signed-off-by: Andrew Whitehead <[email protected]>
tarcieri
reviewed
Sep 19, 2024
| /// This is implemented as a macro to abstract over `const fn` and boxed use cases, since the latter | ||
| /// needs mutable references and thus the unstable `const_mut_refs` feature (rust-lang/rust#57349). | ||
| /// | ||
| // TODO: change this into a `const fn` when `const_mut_refs` is stable |
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Soon! #667
I guess we can add one more macro in the meantime.
tarcieri
reviewed
Sep 19, 2024
| /// We only need the LSB because during reduction this value is multiplied modulo 2**Limb::BITS. | ||
| mod_neg_inv: Limb, | ||
| /// Leading zeros in the modulus, used to choose optimized algorithms | ||
| mod_leading_zeros: u32, |
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Hmm, I get the use cases, but this does seem like a potential sharp edge
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Vartime only!
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Yeah, I'm just worried someone down the road might use it in constant-time use cases
tarcieri
approved these changes
Sep 19, 2024
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This PR implements Algorithm 2 (for B=1) from Efficient Algorithms for Large Prime Characteristic Fields and Their Application to Bilinear Pairings by Patrick Longa: https://eprint.iacr.org/2022/367
This algorithm interleaves schoolbook multiplication and accumulation of multiple terms with the Montgomery reduction. For moduli with one or more leading zeros, this helps to reduce the number of reductions performed. In the
BoxedUintcase this also reduces the number of allocations required. For larger moduli it may be useful to explore the use of larger values of B along with the existing Karatsuba multiplication.As a concrete example, the calculation of
(a•b + c•d) mod musingConstMontyForm, wheremis aU256with at least one leading zero, is reduced from 50 to 32ns in my tests.