Cryptology ePrint Archive: Report 2022/067

Parallel Operations over TFHE-Encrypted Multi-Digit Integers

Jakub Klemsa and Melek Önen

Abstract: Recent advances in Fully Homomorphic Encryption (FHE) allow for a practical evaluation of non-trivial functions over encrypted data. In particular, novel approaches for combining ciphertexts broadened the scope of prospective applications. However, for arithmetic circuits, the overall complexity grows with the desired precision and there is only a limited space for parallelization.

In this paper, we put forward several methods for fully parallel addition of multi-digit integers encrypted with the TFHE scheme. Since these methods handle integers in a special representation, we also revisit the signum function, firstly addressed by Bourse et al., and we propose a method for the maximum of two numbers; both with particular respect to parallelization. On top of that, we outline an approach for multiplication by a known integer.

According to our experiments, the fastest approach for parallel addition of 31-bit encrypted integers in an idealized setting with 32 threads is estimated to be more than 6x faster than the fastest sequential approach. Finally, we demonstrate our algorithms on an evaluation of a practical neural network.

Category / Keywords: implementation / fully homomorphic encryption; TFHE scheme; parallelization; parallel addition

Original Publication (with minor differences): Proceedings of the Twelveth ACM Conference on Data and Application Security and Privacy (CODASPY ’22)

Date: received 18 Jan 2022, last revised 23 Feb 2022

Contact author: jakub klemsa at gmail com

Available format(s): PDF | BibTeX Citation

Note: Errata: corrected equation (16). Text description was correct, other stuff not affected.

Version: 20220223:192318 (All versions of this report)

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