Faster PMNS Multi-precision Multiplications Using Truncated Montgomery Technique
A truncated Montgomery-style internal reduction speeds PMNS modular multiplication by up to 15% on AVX-512.
The paper improves Polynomial Modular Number System arithmetic for large-characteristic fields and rings. A schoolbook PMNS implementation for 4096-bit moduli reduces element size by 11% and runs 20% faster than a Toeplitz baseline while using a smaller n. Applying a truncated Montgomery-style technique to the internal reduction yields up to 15% faster modular multiplication in AVX-512 software for moduli up to 8192 bits versus conventional approaches.
- Schoolbook PMNS is 20% faster and 11% smaller at 4096 bits.
- Truncated Montgomery-style internal reduction adds up to 15% speed.
- Results cover AVX-512 software and moduli up to 8192 bits.
From the original article
1 min read at arxiv.orgThe Polynomial Modular Number Systems (PMNS) aim to represent elements of fields or rings of large characteristics using polynomials satisfying bounds on some parameters (degree, absolute values of the coefficients). Those PMNS, while some conditions are fulfilled, using convenient parameters and implementation features, allow some speed-ups in cryptographic computations. Recent works (Meloni \emph{et al.
By Laurent-Stéphane Didier · arxiv.org
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