$$\mathsf {Rubato}$$: Noisy Ciphers for Approximate Homomorphic Encryption

A transciphering framework converts a symmetric ciphertext into a homomorphic ciphertext on the server-side, reducing computational and communication overload on the client-side. In Asiacrypt 2021, Cho et al. proposed the RtF framework that supports approximate computation. In this paper, we propose a family of noisy ciphers, dubbed Rubato, with a novel design strategy of introducing noise to a symmetric cipher of a low algebraic degree. With this strategy, the multiplicative complexity of the cipher is significantly reduced, compared to existing HE-friendly ciphers, without degrading the overall security. More precisely, given a moderate block size (16 to 64), Rubato enjoys a low multiplicative depth (2 to 5) and a small number of multiplications per encrypted word (2.1 to 6.25) at the cost of slightly larger ciphertext expansion (1.26 to 1.31). The security of Rubato is supported by comprehensive analysis including symmetric and LWE cryptanalysis. Compared to HERA within the RtF framework, client-side and server-side throughput is improved by 22.9% and 32.2%, respectively, at the cost of only 1.6% larger ciphertext expansion.