引入GRAFHEN：基于群的无噪声全同态加密
Introducing GRAFHEN: Group-based Fully Homomorphic Encryption without Noise
AI总结：
提出GRAFHEN，一种基于群编码的无噪声全同态加密方案，通过重写系统表示群使子群成员问题困难，性能比现有标准快几个数量级，并分析了防护攻击的方法。
AI中文摘要：
我们提出GRAFHEN，一种新的密码学方案，它提供了无需自举（或换句话说，无噪声）的全同态加密。基于Nuida等人的工作，我们利用群中的编码实现了这一点。这些群在机器上通过重写系统来表示。这样，攻击者为了破解该方案而必须解决的子群成员问题变得极其困难，同时性能得以保持。实际上，我们包含了一个简单的基准测试，表明我们的实现比现有标准快几个数量级。我们审查了针对我们协议的各种可能攻击，并解释了在每种情况下如何保护该方案。
英文摘要：
We present GRAFHEN, a new cryptographic scheme which offers Fully Homomorphic Encryption without the need for bootstrapping (or in other words, without noise). Building on the work of Nuida and others, we achieve this using encodings in groups. The groups are represented on a machine using rewriting systems. In this way the subgroup membership problem, which an attacker would have to solve in order to break the scheme, becomes maximally hard, while performance is preserved. In fact we include a simple benchmark demonstrating that our implementation runs several orders of magnitude faster than existing standards. We review many possible attacks against our protocol and explain how to protect the scheme in each case.
