Sparks: Succinct parallelizable arguments of knowledge

Naomi Ephraim; Cody Freitag; Ilan Komargodski; Rafael Pass

doi:10.1007/978-3-030-45721-1_25

Sparks: Succinct parallelizable arguments of knowledge

Naomi Ephraim^*, Cody Freitag, Ilan Komargodski, Rafael Pass

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

8 Scopus citations

Abstract

We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument system with the following three properties for computing and proving a time T (non-deterministic) computation:The prover’s (parallel) running time is T + polylog T. (In other words, the prover’s running time is essentially T for large computation times!)The prover uses at most T processors.The communication complexity and verifier complexity are both polylogT. While the third property is standard in succinct arguments, the combination of all three is desirable as it gives a way to leverage moderate parallelism in favor of near-optimal running time. We emphasize that even a factor two overhead in the prover’s parallel running time is not allowed. Our main results are the following, all for non-deterministic polynomial-time RAM computation. We construct (1) an (interactive) SPARK based solely on the existence of collision-resistant hash functions, and (2) a non-interactive SPARK based on any collision-resistant hash function and any SNARK with quasi-linear overhead (as satisfied by recent SNARK constructions).

Original language	English
Title of host publication	Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
Editors	Anne Canteaut, Yuval Ishai
Publisher	Springer
Pages	707-737
Number of pages	31
ISBN (Print)	9783030457204
DOIs	https://doi.org/10.1007/978-3-030-45721-1_25
State	Published - 2020
Externally published	Yes
Event	39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 - Zagreb, Croatia Duration: 10 May 2020 → 14 May 2020

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12105 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020
Country/Territory	Croatia
City	Zagreb
Period	10/05/20 → 14/05/20

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2020.

Access to Document

10.1007/978-3-030-45721-1_25

Cite this

Ephraim, N., Freitag, C., Komargodski, I., & Pass, R. (2020). Sparks: Succinct parallelizable arguments of knowledge. In A. Canteaut, & Y. Ishai (Eds.), Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings (pp. 707-737). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12105 LNCS). Springer. https://doi.org/10.1007/978-3-030-45721-1_25

Ephraim, Naomi ; Freitag, Cody ; Komargodski, Ilan et al. / Sparks : Succinct parallelizable arguments of knowledge. Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. editor / Anne Canteaut ; Yuval Ishai. Springer, 2020. pp. 707-737 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument system with the following three properties for computing and proving a time T (non-deterministic) computation:The prover{\textquoteright}s (parallel) running time is T + polylog T. (In other words, the prover{\textquoteright}s running time is essentially T for large computation times!)The prover uses at most T processors.The communication complexity and verifier complexity are both polylogT. While the third property is standard in succinct arguments, the combination of all three is desirable as it gives a way to leverage moderate parallelism in favor of near-optimal running time. We emphasize that even a factor two overhead in the prover{\textquoteright}s parallel running time is not allowed. Our main results are the following, all for non-deterministic polynomial-time RAM computation. We construct (1) an (interactive) SPARK based solely on the existence of collision-resistant hash functions, and (2) a non-interactive SPARK based on any collision-resistant hash function and any SNARK with quasi-linear overhead (as satisfied by recent SNARK constructions).",

author = "Naomi Ephraim and Cody Freitag and Ilan Komargodski and Rafael Pass",

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doi = "10.1007/978-3-030-45721-1_25",

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Ephraim, N, Freitag, C, Komargodski, I & Pass, R 2020, Sparks: Succinct parallelizable arguments of knowledge. in A Canteaut & Y Ishai (eds), Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12105 LNCS, Springer, pp. 707-737, 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020, Zagreb, Croatia, 10/05/20. https://doi.org/10.1007/978-3-030-45721-1_25

Sparks: Succinct parallelizable arguments of knowledge. / Ephraim, Naomi; Freitag, Cody; Komargodski, Ilan et al.
Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. ed. / Anne Canteaut; Yuval Ishai. Springer, 2020. p. 707-737 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12105 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument system with the following three properties for computing and proving a time T (non-deterministic) computation:The prover’s (parallel) running time is T + polylog T. (In other words, the prover’s running time is essentially T for large computation times!)The prover uses at most T processors.The communication complexity and verifier complexity are both polylogT. While the third property is standard in succinct arguments, the combination of all three is desirable as it gives a way to leverage moderate parallelism in favor of near-optimal running time. We emphasize that even a factor two overhead in the prover’s parallel running time is not allowed. Our main results are the following, all for non-deterministic polynomial-time RAM computation. We construct (1) an (interactive) SPARK based solely on the existence of collision-resistant hash functions, and (2) a non-interactive SPARK based on any collision-resistant hash function and any SNARK with quasi-linear overhead (as satisfied by recent SNARK constructions).

AB - We introduce the notion of a Succinct Parallelizable Argument of Knowledge (SPARK). This is an argument system with the following three properties for computing and proving a time T (non-deterministic) computation:The prover’s (parallel) running time is T + polylog T. (In other words, the prover’s running time is essentially T for large computation times!)The prover uses at most T processors.The communication complexity and verifier complexity are both polylogT. While the third property is standard in succinct arguments, the combination of all three is desirable as it gives a way to leverage moderate parallelism in favor of near-optimal running time. We emphasize that even a factor two overhead in the prover’s parallel running time is not allowed. Our main results are the following, all for non-deterministic polynomial-time RAM computation. We construct (1) an (interactive) SPARK based solely on the existence of collision-resistant hash functions, and (2) a non-interactive SPARK based on any collision-resistant hash function and any SNARK with quasi-linear overhead (as satisfied by recent SNARK constructions).

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Ephraim N, Freitag C, Komargodski I, Pass R. Sparks: Succinct parallelizable arguments of knowledge. In Canteaut A, Ishai Y, editors, Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings. Springer. 2020. p. 707-737. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-45721-1_25

Sparks: Succinct parallelizable arguments of knowledge

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