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Let \(N = pq\) be the product of two balanced prime numbers p and q. In 2023, Cotan and Teşeleanu introduced a family of RSA-like cryptosystems based on the key equation \(ed - k(p^n - 1)(q^n - 1) = 1\) , where \(n \ge 1\) . Note that when \(n = 1\) , we obtain the classical RSA system, while \(n = 2\) yields the variant proposed by Elkamchouchi, Elshenawy, and Shaban. In this paper, we present a novel attack that combines continued fractions with lattice-based methods for the case \(n = 6\) . This represents a natural continuation of previous research, which successfully applied similar techniques for \(n = 1, 2, 4\) .

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A Generalized Wiener-Type Attack Against an RSA-Like Cryptosystem

  • 会议论文

  • 发表日期：

    2026年

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  • George Teşeleanu

摘要

Let \(N = pq\) be the product of two balanced prime numbers p and q. In 2023, Cotan and Teşeleanu introduced a family of RSA-like cryptosystems based on the key equation \(ed - k(p^n - 1)(q^n - 1) = 1\) , where \(n \ge 1\) . Note that when \(n = 1\) , we obtain the classical RSA system, while \(n = 2\) yields the variant proposed by Elkamchouchi, Elshenawy, and Shaban. In this paper, we present a novel attack that combines continued fractions with lattice-based methods for the case \(n = 6\) . This represents a natural continuation of previous research, which successfully applied similar techniques for \(n = 1, 2, 4\) .