Fully Homomorphic Encryption Scheme Based on Decomposition Ring

SUMMARY In this paper, we propose the decomposition ring homomorphic encryption scheme, that is a homomorphic encryption scheme built on the decomposition ring, which is a subring of cyclotomic ring. By using the decomposition ring the structure of plaintext slot becomes Z p l , instead of GF( p d ) in conventional schemes on the cyclotomic ring. For homomorphic multiplication of integers, one can use the full of Z p l slots using the proposed scheme, although in conventional schemes one can use only one-dimensional subspace GF( p ) in each GF( p d ) slot. This allows us to realize fast and compact homomorphic encryption for integer plaintexts. In fact, our benchmark results indicate that our decomposition ring homomorphic encryption schemes are several times faster than HElib for integer plaintexts due to its higher parallel computation.

**摘要** 在本文中，我们提出了分解环同态加密方案，它是一种基于分解环构建的同态加密方案，分解环是分圆环的一个子环。通过使用分解环，明文槽的结构变为\(Z_{p^l}\)，而不是分圆环上常规方案中的\(GF(p^d)\)。对于整数的同态乘法，使用所提出的方案可以利用\(Z_{p^l}\)的所有槽，然而在常规方案中，在每个\(GF(p^d)\)槽中只能使用一维子空间\(GF(p)\)。这使我们能够实现对整数明文的快速且紧凑的同态加密。实际上，我们的基准测试结果表明，由于其更高的并行计算能力，我们的分解环同态加密方案对于整数明文比HElib快几倍。