Towards scalable threshold cryptosystems

Alin Tomescu, Robert Chen, Yiming Zheng, Ittai Abraham, Benny Pinkas, Guy Golan Gueta, Srinivas Devadas

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

30 Scopus citations

Abstract

The resurging interest in Byzantine fault tolerant systems will demand more scalable threshold cryptosystems. Unfortunately, current systems scale poorly, requiring time quadratic in the number of participants. In this paper, we present techniques that help scale threshold signature schemes (TSS), verifiable secret sharing (VSS) and distributed key generation (DKG) protocols to hundreds of thousands of participants and beyond. First, we use efficient algorithms for evaluating polynomials at multiple points to speed up computing Lagrange coefficients when aggregating threshold signatures. As a result, we can aggregate a 130,000 out of 260,000 BLS threshold signature in just 6 seconds (down from 30 minutes). Second, we show how "authenticating"such multipoint evaluations can speed up proving polynomial evaluations, a key step in communication-efficient VSS and DKG protocols. As a result, we reduce the asymptotic (and concrete) computational complexity of VSS and DKG protocols from quadratic time to quasilinear time, at a small increase in communication complexity. For example, using our DKG protocol, we can securely generate a key for the BLS scheme above in 2.3 hours (down from 8 days). Our techniques improve performance for thresholds as small as 255 and generalize to any Lagrange-based threshold scheme, not just threshold signatures. Our work has certain limitations: we require a trusted setup, we focus on synchronous VSS and DKG protocols and we do not address the worst-case complaint overhead in DKGs. Nonetheless, we hope it will spark new interest in designing large-scale distributed systems.

Original languageEnglish
Title of host publicationProceedings - 2020 IEEE Symposium on Security and Privacy, SP 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages877-893
Number of pages17
ISBN (Electronic)9781728134970
DOIs
StatePublished - May 2020
Event41st IEEE Symposium on Security and Privacy, SP 2020 - San Francisco, United States
Duration: 18 May 202021 May 2020

Publication series

NameProceedings - IEEE Symposium on Security and Privacy
Volume2020-May
ISSN (Print)1081-6011

Conference

Conference41st IEEE Symposium on Security and Privacy, SP 2020
Country/TerritoryUnited States
CitySan Francisco
Period18/05/2021/05/20

Bibliographical note

Publisher Copyright:
© 2020 IEEE.

Keywords

  • BLS
  • Distributed key generation
  • Polynomial commitments
  • Polynomial multi-point evaluation
  • Threshold signatures
  • Verifiable secret sharing

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