Plantard Arithmetic for NTT, STARKS & Lattices#491

Plantard arithmetic, introduced in https://thomas-plantard.github.io/pdf/Plantard21.pdf significantly improve modular arithmetic for single word fields. Those fields are popular for lattices and Starks based on small fields. In particular, quoting section 4.2.4 > 4.2.4 Comparison with Pseudo-Mersenne > Pseudo-Mersenne numbers offer enough moduli for them > to be used in each application we are proposing. However, > table 6 clearly shows that even without correction, pseudo- > Mersenne based arithmetic is slower than our by at lease > 17% and up to 38% depending of applications, and up to > 52% when redundancy is not available.  This should allow the BabyBear and KoalaBear field to be very competitive with M31. Further research - Efficient Word Size Modular Multiplication over Signed Integers\ Aoki, Minematsu Okamura, Takagi\ ARITH 2022 (IEEE)\ http://crypto.mist.i.u-tokyo.ac.jp/publications/782700a094.pdf - Improved Plantard AArithmetic for Lattice-based Cryptography\ Huang, Zhang, Zhao, Liu, Cheung, Koç, Chen,\ TCHES 2022\ https://eprint.iacr.org/2022/956