Paper 2021/1131 Original: eprint.iacr.org/2021/1131 ↗

Multi-key Fully Homomorphic Encryption Scheme with Compact Ciphertexts

Abstract

Multi-Key fully homomorphic encryption (MKFHE) allows computations on data encrypted by different parties. One disadvantage of previous MKFHE schemes is that the ciphertext size increases linearly or squarely with respect to the number of parties. It incurs a heavy communication and computation burden for the homomorphic evaluation, especially when the number of involved parties is large. In this paper, we propose the first method to construct MKFHE scheme while keeping the size of the ciphertext and corresponding evaluation key to be independent of the number of parties during the homomorphic evaluation. Specifically, we construct efficient compact MKFHE schemes with various advantages. On the one hand, we show how to construct compact MKFHE schemes which support the homomorphic encryption of ring elements and are friendly to floating point numbers. On the other hand, we give a compact MKFHE scheme that supports high efficient bootstrapping. In our paper, we show a novel method to reduce the cost of generating these evaluation keys from a quadratic time to a linear time with respect to the number of parties.