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<p>This article proposes a&#xa0;novel high-speed reverse converter from the Residue Number System (RNS) to a&#xa0;positional number system. The proposed method is designed for arbitrary RNS moduli sets that include a&#xa0;power-of-two modulus and is based on a&#xa0;Chinese Remainder Theorem with fractional values conversion technique. Hardware simulations demonstrate that our converter outperforms the state-of-the-art designs by 34.70% to 86.11% in terms of speed, at the cost of increased silicon area and power consumption, making it particularly suitable for latency-critical applications. This performance gain makes it directly applicable to demanding RNS-based domains such as cryptography, digital signal processing, and image processing for neural networks. Furthermore, the proposed conversion method provides a&#xa0;foundation for efficiently implementing other complex RNS operations, including division, sign detection, and magnitude comparison.</p>

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High-speed residue number system reverse converter based on new Chinese remainder theorem with fractional values

  • 期刊论文

  • 发表日期：

    2026年5月26日

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  • Pavel Lyakhov,
  • Maxim Bergerman,
  • Ruslan Abdulkadirov,
  • Nikolay Nagornov,
  • Diana Kalita,
  • Ekaterina Kopets,
  • Denis Butusov

摘要

This article proposes a novel high-speed reverse converter from the Residue Number System (RNS) to a positional number system. The proposed method is designed for arbitrary RNS moduli sets that include a power-of-two modulus and is based on a Chinese Remainder Theorem with fractional values conversion technique. Hardware simulations demonstrate that our converter outperforms the state-of-the-art designs by 34.70% to 86.11% in terms of speed, at the cost of increased silicon area and power consumption, making it particularly suitable for latency-critical applications. This performance gain makes it directly applicable to demanding RNS-based domains such as cryptography, digital signal processing, and image processing for neural networks. Furthermore, the proposed conversion method provides a foundation for efficiently implementing other complex RNS operations, including division, sign detection, and magnitude comparison.