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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2025.56

Boosting SNARKs and Rate-1 Barrier in Arguments of Knowledge

Authors: Jiaqi Cheng and Rishab Goyal

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract

We design a generic compiler to boost any non-trivial succinct non-interactive argument of knowledge (SNARK) to full succinctness. Our results come in two flavors: 1) For any constant ε > 0, any SNARK with proof size |π| < |ω|/(λ^ε) + poly(λ, |x|) can be upgraded to a fully succinct SNARK, where all system parameters (such as proof/CRS sizes and setup/verifier run-times) grow as fixed polynomials in λ, independent of witness size. 2) Under an additional assumption that the underlying SNARK has as an efficient knowledge extractor, we further improve our result to upgrade any non-trivial SNARK. For example, we show how to design fully succinct SNARKs from SNARKs with proofs of length |ω| - Ω(λ), or |ω|/(1+ε) + poly(λ, |x|), any constant ε > 0. Our result reduces the long-standing challenge of designing fully succinct SNARKs to designing arguments of knowledge that beat the trivial construction. It also establishes optimality of rate-1 arguments of knowledge (such as NIZKs [Gentry-Groth-Ishai-Peikert-Sahai-Smith; JoC'15] and BARGs [Devadas-Goyal-Kalai-Vaikuntanathan, Paneth-Pass; FOCS'22]), and suggests any further improvement is tantamount to designing fully succinct SNARKs, thus requires bypassing established black-box barriers [Gentry-Wichs; STOC'11].

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Jiaqi Cheng and Rishab Goyal. Boosting SNARKs and Rate-1 Barrier in Arguments of Knowledge. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 56:1-56:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cheng_et_al:LIPIcs.ICALP.2025.56,
  author =	{Cheng, Jiaqi and Goyal, Rishab},
  title =	{{Boosting SNARKs and Rate-1 Barrier in Arguments of Knowledge}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{56:1--56:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.56},
  URN =		{urn:nbn:de:0030-drops-234339},
  doi =		{10.4230/LIPIcs.ICALP.2025.56},
  annote =	{Keywords: SNARGs, RAM Delegation}
}

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DOI: 10.4230/LIPIcs.ITCS.2025.56

Incompressible Functional Encryption

Authors: Rishab Goyal, Venkata Koppula, Mahesh Sreekumar Rajasree, and Aman Verma

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

Incompressible encryption (Dziembowski, Crypto'06; Guan, Wichs, Zhandry, Eurocrypt'22) protects from attackers that learn the entire decryption key, but cannot store the full ciphertext. In incompressible encryption, the attacker must try to compress a ciphertext within pre-specified memory bound S before receiving the secret key. In this work, we generalize the notion of incompressibility to functional encryption. In incompressible functional encryption, the adversary can corrupt non-distinguishing keys at any point, but receives the distinguishing keys only after compressing the ciphertext to within S bits. An important efficiency measure for incompressible encryption is the ciphertext-rate (i.e., rate = |m|/|ct|). We give many new results for incompressible functional encryption for circuits, from minimal assumption of (non-incompressible) functional encryption, with 1) ct-rate-1/2 and short secret keys, 2) ct-rate-1 and large secret keys. Along the way, we also give a new incompressible attribute-based encryption for circuits from standard assumptions, with ct-rate-1/2 and short secret keys. Our results achieve optimal efficiency, as incompressible attribute-based/functional encryption with ct-rate-1 as well as short secret keys has strong barriers for provable security from standard assumptions. Moreover, our assumptions are minimal as incompressible attribute-based/functional encryption are strictly stronger than their non-incompressible counterparts.

Cite as

Rishab Goyal, Venkata Koppula, Mahesh Sreekumar Rajasree, and Aman Verma. Incompressible Functional Encryption. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 56:1-56:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goyal_et_al:LIPIcs.ITCS.2025.56,
  author =	{Goyal, Rishab and Koppula, Venkata and Rajasree, Mahesh Sreekumar and Verma, Aman},
  title =	{{Incompressible Functional Encryption}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{56:1--56:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.56},
  URN =		{urn:nbn:de:0030-drops-226849},
  doi =		{10.4230/LIPIcs.ITCS.2025.56},
  annote =	{Keywords: functional encryption, attribute-based encryption, incompressible encryption}
}

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Boosting SNARKs and Rate-1 Barrier in Arguments of Knowledge

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Incompressible Functional Encryption

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