Optimizing homomorphic evaluation circuits by program synthesis and term rewriting

Dong Kwon Lee, Woosuk Lee, Hakjoo Oh, Kwangkeun Yi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present a new and general method for optimizing homomorphic evaluation circuits. Although fully homomorphic encryption (FHE) holds the promise of enabling safe and secure third party computation, building FHE applications has been challenging due to their high computational costs. Domain-specific optimizations require a great deal of expertise on the underlying FHE schemes, and FHE compilers that aims to lower the hurdle, generate outcomes that are typically sub-optimal as they rely on manually-developed optimization rules. In this paper, based on the prior work of FHE compilers, we propose a method for automatically learning and using optimization rules for FHE circuits. Our method focuses on reducing the maximum multiplicative depth, the decisive performance bottleneck, of FHE circuits by combining program synthesis and term rewriting. It first uses program synthesis to learn equivalences of small circuits as rewrite rules from a set of training circuits. Then, we perform term rewriting on the input circuit to obtain a new circuit that has lower multiplicative depth. Our rewriting method maximally generalizes the learned rules based on the equational matching and its soundness and termination properties are formally proven. Experimental results show that our method generates circuits that can be homomorphically evaluated 1.18x - 3.71x faster (with the geometric mean of 2.05x) than the state-of-the-art method. Our method is also orthogonal to existing domain-specific optimizations.

Original languageEnglish
Title of host publicationPLDI 2020 - Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation
EditorsAlastair F. Donaldson, Emina Torlak
PublisherAssociation for Computing Machinery
Pages503-518
Number of pages16
ISBN (Electronic)9781450376136
DOIs
Publication statusPublished - 2020 Jun 11
Event41st ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2020 - London, United Kingdom
Duration: 2020 Jun 152020 Jun 20

Publication series

NameProceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI)

Conference

Conference41st ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2020
CountryUnited Kingdom
CityLondon
Period20/6/1520/6/20

Keywords

  • Homomorphic Encryption Circuit
  • Program Synthesis
  • Term Rewriting

ASJC Scopus subject areas

  • Software

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  • Cite this

    Lee, D. K., Lee, W., Oh, H., & Yi, K. (2020). Optimizing homomorphic evaluation circuits by program synthesis and term rewriting. In A. F. Donaldson, & E. Torlak (Eds.), PLDI 2020 - Proceedings of the 41st ACM SIGPLAN Conference on Programming Language Design and Implementation (pp. 503-518). (Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI)). Association for Computing Machinery. https://doi.org/10.1145/3385412.3385996