f5883286e3 Add a fuzz test for Num3072 multiplication and inversion (Pieter Wuille)
a26ce62894 Safegcd based modular inverse for Num3072 (Pieter Wuille)
91ce8cef2d Add benchmark for MuHash finalization (Pieter Wuille)
Pull request description:
This implements a safegcd-based modular inverse for MuHash3072. It is a fairly straightforward translation of [the libsecp256k1 implementation](https://github.com/bitcoin-core/secp256k1/pull/831), with the following changes:
* Generic for 32-bit and 64-bit
* Specialized for the specific MuHash3072 modulus (2^3072 - 1103717).
* A bit more C++ish
* Far fewer sanity checks
A benchmark is also included for MuHash3072::Finalize. The new implementation is around 100x faster on x86_64 for me (from 5.8 ms to 57 μs); for 32-bit code the factor is likely even larger.
For more information:
* [Original paper](https://gcd.cr.yp.to/papers.html) by Daniel J. Bernstein and Bo-Yin Yang
* [Implementation](https://github.com/bitcoin-core/secp256k1/pull/767) for libsecp256k1 by Peter Dettman; and the [final](https://github.com/bitcoin-core/secp256k1/pull/831) version
* [Explanation](https://github.com/bitcoin-core/secp256k1/blob/master/doc/safegcd_implementation.md) of the algorithm using Python snippets
* [Analysis](https://github.com/sipa/safegcd-bounds) of the maximum number of iterations the algorithm needs
* [Formal proof in Coq](https://medium.com/blockstream/a-formal-proof-of-safegcd-bounds-695e1735a348) by Russell O'Connor (for the 256-bit version of the algorithm; here we use a 3072-bit one).
ACKs for top commit:
achow101:
ACK f5883286e3
TheCharlatan:
Re-ACK f5883286e3
dergoegge:
tACK f5883286e3
Tree-SHA512: 275872c61d30817a82901dee93fc7153afca55c32b72a95b8768f3fd464da1b09b36f952f30e70225e766b580751cfb9b874b2feaeb73ffaa6943c8062aee19a
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