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In this paper, we present a new small private exponent attack on RSA by combining continued fractions and Coppersmith’s techniques. Our results improve upon previous bounds, including Herrmann-May’s attack, by leveraging a crucial relation derived from continued fraction. Additionally, we extend the range of vulnerable small private exponents by considering the partial leakage of prime factors or their sum. The validity of our proposed main attack is confirmed through numerical experiments, demonstrating its improved performance over existing attacks.

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Improving RSA Cryptanalysis: Combining Continued Fractions and Coppersmith’s Techniques

  • 会议论文

  • 发表日期：

    2025年

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  • Mengce Zheng,
  • Yansong Feng,
  • Abderrahmane Nitaj,
  • Yanbin Pan

摘要

In this paper, we present a new small private exponent attack on RSA by combining continued fractions and Coppersmith’s techniques. Our results improve upon previous bounds, including Herrmann-May’s attack, by leveraging a crucial relation derived from continued fraction. Additionally, we extend the range of vulnerable small private exponents by considering the partial leakage of prime factors or their sum. The validity of our proposed main attack is confirmed through numerical experiments, demonstrating its improved performance over existing attacks.