This paper investigates a novel RSA-like cryptosystem proposed by Murru-Saettone. This cryptosystem is constructed from a cubic field connected to the cubic Pell equation and Redei rational functions. The scheme is claimed to be secure against the Wiener-type attack. However, in this paper, we show a Wiener-type attack that can recover the secret key from the continued fraction constructed from public information.

中文翻译：

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对由三次佩尔方程构造的类 RSA 密码系统的 Wiener 型攻击

本文研究了 Murru-Saettone 提出的一种新颖的类 RSA 密码系统。该密码系统由连接到三次佩尔方程和 Redei 有理函数的三次场构成。据称该方案对维纳式攻击是安全的。然而，在本文中，我们展示了一种维纳式攻击，它可以从公共信息构建的连分数中恢复密钥。