Test and reject multimodular arithmetic #9
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Also: - Upgrade test from pseudorandom to proptest - Add method `bits` which returns bitsize
Anticipates faster reduction modulo multimodular primes.
`MASTER_TREE` is populated from a rust expression inside a `lazy_static!` declaration, meaning that it is computed from native rust (so fast) once per thread in which it is needed. This allows faster reduction of large integers modulo up to `N = 512` thirty-two-bit primes.
Specifically, `modular_inverses_sequence` and `product_tree` need to be separate from `multimod`, but depend on the `MODULI` static ref. Solved by introducing `residue_number_system.rs` which contains `MODULI` and associated logic. Now `multimod.rs` depends on all three and adds logic for dealing with multimodular integers.
Specifically: `MODULAR_INVERSES_SEQUENCE`.
SHAKE makes the PRNG expansion deterministic and comparable across implementations.
In the given context, the operands can be assumed to have compatible capacities already.
Also: drop bit capacity tracker. For every multimod arithmetic, the available capacity is assumed to be enough.
Irrelevant for performance.
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This branch records a historical multi-modular / residue number system implementation. In the end it was rejected because 99% of the performance boost came from doing NTT-based came from doing the cyclotomic multiplication using NTT over a u32 field (larger than Falcon's field). The extra 1% does not justify the code complexity nor the compile time.