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.

翻译：本文提出GRAFHEN——一种无需自举（即无噪声）的新型全同态加密方案。基于Nuida等人的研究，我们通过群编码实现该方案。在计算机中采用重写系统表示群结构，使得攻击者破解方案所需解决的子群成员判定问题达到最大难度，同时保持计算性能。我们提供的简易基准测试表明，该实现比现有标准方案快数个数量级。文中系统分析了可能针对本协议的攻击方式，并逐一说明相应的防护机制。