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Big integer multiplication currently performs immediate carry propagation from each step of the long multiplication, relying on the fact that the overall result has a known maximum value to minimise the number of carries performed without ever needing to explicitly check against the result buffer size. This is not a constant-time algorithm, since the number of carries performed will be a function of the input values. We could make it constant-time by always continuing to propagate the carry until reaching the end of the result buffer, but this would introduce a large number of redundant zero carries. Require callers of bigint_multiply() to provide a temporary carry storage buffer, of the same size as the result buffer. This allows the carry-out from the accumulation of each double-element product to be accumulated in the temporary carry space, and then added in via a single call to bigint_add() after the multiplication is complete. Since the structure of big integer multiplication is identical across all current CPU architectures, provide a single shared implementation of bigint_multiply(). The architecture-specific operation then becomes the multiplication of two big integer elements and the accumulation of the double-element product. Note that any intermediate carry arising from accumulating the lower half of the double-element product may be added to the upper half of the double-element product without risk of overflow, since the result of multiplying two n-bit integers can never have all n bits set in its upper half. This simplifies the carry calculations for architectures such as RISC-V and LoongArch64 that do not have a carry flag. Signed-off-by: Michael Brown <mcb30@ipxe.org>
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