Scalable zero knowledge via cycles of elliptic curves

Eli Ben-Sasson, Alessandro Chiesa, Eran Tromer, Madars Virza

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

Abstract

Non-interactive zero-knowledge proofs of knowledge for general NP statements are a powerful cryptographic primitive, both in theory and in practical applications. Recently, much research has focused on achieving an additional property, succinctness, requiring the proof to be very short and easy to verify. Such proof systems are known as zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs), and are desired when communication is expensive, or the verifier is computationally weak. Existing zk-SNARK implementations have severe scalability limitations, in terms of space complexity as a function of the size of the computation being proved (e.g., running time of the NP statement's decision program). First, the size of the proving key is quasilinear in the upper bound on the computation size. Second, producing a proof requires "writing down" all intermediate values of the entire computation, and then conducting global operations such as FFTs. The bootstrapping technique of Bitansky et al. (STOC '13), following Valiant (TCC '08), offers an approach to scalability, by recursively composing proofs: proving statements about acceptance of the proof system's own verifier (and correctness of the program's latest step). Alas, recursive composition of known zk-SNARKs has never been realized in practice, due to enormous computational cost. Using new elliptic-curve cryptographic techniques, and methods for exploiting the proof systems' field structure and nondeterminism, we achieve the first zk-SNARK implementation that practically achieves recursive proof composition. Our zk-SNARK implementation runs random-access machine programs and produces proofs of their correct execution, on today's hardware, for any program running time. It takes constant time to generate the keys that support all computation sizes. Subsequently, the proving process only incurs a constant multiplicative overhead compared to the original computation's time, and an essentially-constant additive overhead in memory. Thus, our zk-SNARK implementation is the first to have a well-defined, albeit low, clock rate of "verified instructions per second".

Original languageEnglish
Title of host publicationAdvances in Cryptology, CRYPTO 2014 - 34th Annual Cryptology Conference, Proceedings
PublisherSpringer Verlag
Pages276-294
Number of pages19
EditionPART 2
ISBN (Print)9783662443804
DOIs
StatePublished - 2014
Event34rd Annual International Cryptology Conference, CRYPTO 2014 - Santa Barbara, CA, United States
Duration: 17 Aug 201421 Aug 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume8617 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference34rd Annual International Cryptology Conference, CRYPTO 2014
Country/TerritoryUnited States
CitySanta Barbara, CA
Period17/08/1421/08/14

Keywords

  • computationally-sound proofs
  • elliptic curves
  • proof-carrying data
  • zero-knowledge

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