Attacks on multi-prime RSA with small prime difference

Hui Zhang, Tsuyoshi Takagi

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

8 被引用数 (Scopus)


We consider some attacks on multi-prime RSA (MPRSA) with a modulus N = p1 (r ≥ 3). It is believed that the small private exponent attack on the MPRSA is less effective than that on RSA (see Hinek et al.'s work at SAC 2003), which means that one can use a smaller private exponent in the MPRSA than that in the original RSA. However, our attacks show that private exponents which are significantly beyond Hinek's bound may be insecure when the prime difference Δ (Δ = pr - p1 = Nγ, 0 < γ < 1/r, suppose p 1 < p2 <⋯< pr) is small. By exploring the relation between φ(N) and its upper bound, our proposed small private exponent attack can make full use of the benefit brought by small prime difference. It is shown that the MPRSA is insecure when δ < 1-√1+γ-2/r, where δ is the exponential of the private exponent d with base N, i.e., d = Nδ. This result is a perfect extension of the best known small private exponent attack. We also present a Fermat-like factoring attack on the MPRSA which can directly factor the modulus N when Δ < N1/r2. These results surpass those of Bahig et al. (ICICS 2012) and the attacks are experimentally proved effective in practice.

ホスト出版物のタイトルInformation Security and Privacy - 18th Australasian Conference, ACISP 2013, Proceedings
出版ステータス出版済み - 2013
イベント18th Australasian Conference on Information Security and Privacy, ACISP 2013 - Brisbane, QLD, オーストラリア
継続期間: 7 1 20137 3 2013


名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7959 LNCS


その他18th Australasian Conference on Information Security and Privacy, ACISP 2013
CityBrisbane, QLD

All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)


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