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Friendly primes for efficient modular arithmetic using the Polynomial Modular Number System
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DOI：10.1007/s13389-025-00382-8.png)
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Abstract
En 中文
The Polynomial Modular Number System (PMNS) is a non-positional number system designed for modular arithmetic. Its efficiency, both in software and hardware, has been demonstrated for integers commonly used in Elliptic Curve Cryptography [1, 2]. In [3, 4], the authors introduce specific prime forms that are particularly well-suited for PMNS arithmetic. In this work, we extend their results to a broader class of prime numbers. In practice, our approach yields performance that is competitive with, and in some cases superior to, Pseudo-Mersenne arithmetic. As a result, we expand the set of prime numbers that are well-suited for modular arithmetic. Furthermore, we contribute a database of proof of concept Elliptic Curves constructed with those primes that verify the Brainpool Standard.
Keywords:
Modular arithmetic
Polynomial modular number system
Internal reduction
Mersenne primes
Pseudo-Mersenne primes
Fermat primes
Journal
J
IF:
1.4
Papers:
18
Citations:
649