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The Polynomial Modular Number System (PMNS) is a non-positional number system that allows for fast modular arithmetic operations. It has shown its effectiveness in both hardware and software contexts, notably outperforming both GMP and OpenSSL from 256 to 8192 bits. Due to its non-positional nature however, equality tests become non-trivial and finding methods to perform them in an optimized fashion remains an open problem. In this work, we present several results, including a new coefficient reduction algorithm that allows for a faster than state of the art equality test without impacting the performance of the overall system.

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Equality Tests in the Polynomial Modular Number System

  • 会议论文

  • 发表日期：

    2026年

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  • Nicolas Méloni,
  • François Palma,
  • Pascal Véron

摘要

The Polynomial Modular Number System (PMNS) is a non-positional number system that allows for fast modular arithmetic operations. It has shown its effectiveness in both hardware and software contexts, notably outperforming both GMP and OpenSSL from 256 to 8192 bits. Due to its non-positional nature however, equality tests become non-trivial and finding methods to perform them in an optimized fashion remains an open problem. In this work, we present several results, including a new coefficient reduction algorithm that allows for a faster than state of the art equality test without impacting the performance of the overall system.