The Cramer-Shoup (CS) like cryptosystem based on index exchangeable family (IEF) construction is a novel scheme introduced in Asiaccs 2016 by Li et al. Its versatility was illustrated by building two public key encryption (PKE) schemes, a cramer-shoup encryption scheme based on IEFs, as well as an outsourcing technique based on non-abelian analog. However, the two schemes are not secure over the recommended linear group of Li et al. For them, we provide a new key-recovery attack by solving a linear equation respectively. Furthermore, we peel off complex encryption and decryption processes and propose more than three different attack methods. Finally, we give a corresponding example to illustrate the correctness of our attack methods. Our attack methods break an instance of claiming 80 bit security less than one minute under a personal computer.

中文翻译：

---

基于索引交换族的Cramer-Shoup状密码系统的密码分析

基于索引可交换族 (IEF) 构造的 Cramer-Shoup (CS) 类密码系统是 Li 等人在 Asiaccs 2016 中引入的一种新颖方案。通过构建两个公钥加密 (PKE) 方案、基于 IEF 的 cramer-shoup 加密方案以及基于非阿贝尔模拟的外包技术来说明其多功能性。然而，这两种方案在 Li 等人推荐的线性群上并不安全。对于他们，我们通过分别求解一个线性方程来提供一种新的密钥恢复攻击。此外，我们剥离了复杂的加密和解密过程，并提出了三种以上不同的攻击方法。最后，我们给出一个相应的例子来说明我们的攻击方法的正确性。我们的攻击方法在个人计算机下不到一分钟就破坏了一个声称 80 位安全性的实例。