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In the context of fully-homomorphic-encryption, we consider the representation of large integers by their decomposition over a product of rings (through the Chinese Remainder Theorem) and introduce a new algorithm for the determination of the sign solely through the knowledge of ring-components. Our implementation with 128 bits of security delivers a correct result with a probability higher than \(1-10^{-12}\) in less than 140 ms for 32-bit integers on a laptop.

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Homomorphic Sign Evaluation with a RNS Representation of Integers

  • 会议论文

  • 发表日期：

    2025年

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  • Philippe Chartier,
  • Michel Koskas,
  • Mohammed Lemou,
  • Florian Méhats

摘要

In the context of fully-homomorphic-encryption, we consider the representation of large integers by their decomposition over a product of rings (through the Chinese Remainder Theorem) and introduce a new algorithm for the determination of the sign solely through the knowledge of ring-components. Our implementation with 128 bits of security delivers a correct result with a probability higher than \(1-10^{-12}\) in less than 140 ms for 32-bit integers on a laptop.