(An) HE-friendly cipher using modular arithmetic

Abstract

The Rasta cipher, proposed by Dobraunig et al. (CRYPTO 2018), is an HE-friendly cipher enjoying the fewest ANDs per bit and the lowest ANDdepth among the existing ciphers. A novel feature of Rasta is that its affine layers are freshly and randomly generated for every encryption. In this paper, we propose a new variant of Rasta, dubbed Masta. Similarly to Rasta, Masta takes as input a (master) secret key and a nonce, and generates a keystream block for each counter. On the other hand, Masta has two main differences from Rasta: Masta uses modular arithmetic to support HE schemes over a non-binary plaintext space, and it uses a smaller number of random bits in the affine layers by defining them with finite field multiplication. In this way, Masta outperforms Rasta in a transciphering framework with BGV/FV-style HE schemes. Our implementation shows that Masta is 505 to 592 times faster in terms of the throughput on the client-side, while 4792 to 6986 times faster on the server-side.