RustCrypto / crypto-bigint

Cryptography-oriented big integer library with constant-time, stack-allocated (no_std-friendly) implementations of modern formulas
Apache License 2.0
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Determine and document `BoxedUint` widening arithmetic semantics #312

Open tarcieri opened 1 year ago

tarcieri commented 1 year ago

Arithmetic with BoxedUint needs to deal with values whose number of limbs don't match. This is true of Uint as well, but there everything is nicely type safe.

So far the internal BoxedUint::chain operation (which addition and subtraction are implemented in terms of) handles widening to the widest of the two inputs.

The wrapping_* and checked_* functions use the self/left-hand side argument as the overflow width.

The mul_wide operation widens to as many limbs as are in the sum of the number of limbs in the operands (though should perhaps be renamed to just BoxedUint::mul for consistency with Uint::mul, which is also a widening multiply.

This seems like a reasonable enough approach, but whatever one we take should be thoroughly documented, both as an overall policy and on the individual functions.

We should also ensure it's consistent with how Uint performs widening, where applicable.

tarcieri commented 1 year ago

I should probably add some context that these semantics are necessarily different from your typical num-bigint-style arbitrary precision library.

Notably in cryptographic cases we want all of the values to be the same precision, or if not that, then known/fixed precisions at every point in the program. In the case of an algorithm like RSA, that would be the number of bits of precision in the RSA modulus. This means preserving leading zero limbs in such cases, so that we don't wind up with value-dependent timing variability with respect to the number of limbs.

xuganyu96 commented 11 months ago

Automatic widening when instantiating BoxedMontyForm should also be considered here. BoxedMontyForm::new currently panics if integer and params have different precision, but I think it makes sense to automatically widen the integer if it is less precise than the params. I am not sure if we should consider widening the params since it has more moving parts.