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Let \(N=pq\) be the product of two balanced prime numbers p and q. In 2015, Roman’kov introduced an interesting RSA-like cryptosystem that, unlike the classical RSA key equation \(ed - k (p-1)(q-1) = 1\) , uses the key equation \(ed - k r = 1\) , where \(r | p-1\) and is a large prime number. In this paper, we study if small private key attacks based on lattices can be applied to Roman’kov’s cryptosystem. More precisely, we argue that such attacks do not appear to be applicable to this scheme without substantial adaptations.

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Another Lattice Attack Against an RSA-Like Cryptosystem

  • 会议论文

  • 发表日期：

    2025年

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  • George Teşeleanu

摘要

Let \(N=pq\) be the product of two balanced prime numbers p and q. In 2015, Roman’kov introduced an interesting RSA-like cryptosystem that, unlike the classical RSA key equation \(ed - k (p-1)(q-1) = 1\) , uses the key equation \(ed - k r = 1\) , where \(r | p-1\) and is a large prime number. In this paper, we study if small private key attacks based on lattices can be applied to Roman’kov’s cryptosystem. More precisely, we argue that such attacks do not appear to be applicable to this scheme without substantial adaptations.