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Parallelizable Delegation from LWE

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13748))

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Abstract

We present the first non-interactive delegation scheme for \(\textsf{P} \) with time-tight parallel prover efficiency based on standard hardness assumptions. More precisely, in a time-tight delegation scheme—which we refer to as a SPARG (succinct parallelizable argument)—the prover’s parallel running time is \(t + \textrm{polylog} (t)\), while using only \(\textrm{polylog} (t)\) processors and where t is the length of the computation. (In other words, the proof is computed essentially in parallel with the computation, with only some minimal additive overhead in terms of time).

Our main results show the existence of a publicly-verifiable, non-interactive, SPARG for \(\textsf{P} \) assuming polynomial hardness of LWE. Our SPARG construction relies on the elegant recent delegation construction of Choudhuri, Jain, and Jin (FOCS’21) and combines it with techniques from Ephraim et al. (EuroCrypt’20).

We next demonstrate how to make our SPARG time-independent—where the prover and verifier do not need to known the running-time t in advance; as far as we know, this yields the first construction of a time-tight delegation scheme with time-independence based on any hardness assumption.

We finally present applications of SPARGs to the constructions of VDFs (Boneh et al., Crypto’18), resulting in the first VDF construction from standard polynomial hardness assumptions (namely LWE and the minimal assumption of a sequentially hard function).

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Notes

  1. 1.

    An iteratively sequential function f has the property that the t-wise composition \(f^{(t)}\) of f cannot be computed faster than computing f sequentially t times, even with \(\textrm{poly} (t)\) processors.

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Acknowledgements

This work was supported in part by NSF CNS-2149305, CNS-2128519, NSF Award SATC-1704788, NSF Award RI-1703846, AFOSR Award FA9550-18-1-0267, DARPA Award HR00110C0086, and a JP Morgan Faculty Award. Rafael Pass’s work was done partially while visiting Tel-Aviv University. Cody Freitag’s work was done partially during an internship at NTT Research, and he is also supported in part by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-2139899. Naomi Sirkin was also supported in part by a JP Morgan AI Research PhD Fellowship. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of NSF, DARPA or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.

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Authors and Affiliations

  1. Cornell Tech, New York, NY, 10044, USA

    Cody Freitag, Rafael Pass & Naomi Sirkin

  2. Tel Aviv University, Tel Aviv, Israel

    Rafael Pass

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  1. Cody Freitag
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Correspondence to Cody Freitag .

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  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Freitag, C., Pass, R., Sirkin, N. (2022). Parallelizable Delegation from LWE. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13748. Springer, Cham. https://doi.org/10.1007/978-3-031-22365-5_22

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