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Let \(N = pq\) be the product of two balanced primes. Cotan and Teşeleanu (2023) introduced a family of RSA-like cryptosystems defined by \(ed - k(p^n - 1)(q^n - 1) = 1\) , where \(n \ge 1\) , encompassing classical RSA ( \(n=1\) ) and the Elkamchouchi–Elshenawy–Shaban variant ( \(n=2\) ). We present a new attack for \(n=3\) that integrates continued fractions with lattice-based methods, naturally extending previous results for \(n = 1, 2, 4, 6\) .

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Attacking an RSA-Like Cryptosystem Using Continued Fractions and Lattices

  • 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 primes. Cotan and Teşeleanu (2023) introduced a family of RSA-like cryptosystems defined by \(ed - k(p^n - 1)(q^n - 1) = 1\) , where \(n \ge 1\) , encompassing classical RSA ( \(n=1\) ) and the Elkamchouchi–Elshenawy–Shaban variant ( \(n=2\) ). We present a new attack for \(n=3\) that integrates continued fractions with lattice-based methods, naturally extending previous results for \(n = 1, 2, 4, 6\) .