Abstract
We obtain a black-box construction of non-interactive CCA commitments against non-uniform adversaries. This makes black-box use of an appropriate base commitment scheme for small tag spaces, variants of sub-exponential hinting PRG (Koppula and Waters, Crypto 2019) and variants of keyless sub-exponentially collision-resistant hash function with security against non-uniform adversaries (Bitansky, Kalai and Paneth, STOC 2018 and Bitansky and Lin, TCC 2018).
All prior works on non-interactive non-malleable or CCA commitments without setup first construct a “base” scheme for a relatively small identity/tag space, and then build a tag amplification compiler to obtain commitments for an exponential-sized space of identities. Prior black-box constructions either add multiple rounds of interaction (Goyal, Lee, Ostrovsky and Visconti, FOCS 2012) or only achieve security against uniform adversaries (Garg, Khurana, Lu and Waters, Eurocrypt 2021).
Our key technical contribution is a novel tag amplification compiler for CCA commitments that replaces the non-interactive proof of consistency required in prior work. Our construction satisfies the strongest known definition of non-malleability, i.e., CCA2 (chosen commitment attack) security. In addition to only making black-box use of the base scheme, our construction replaces sub-exponential NIWIs with sub-exponential hinting PRGs, which can be obtained based on assumptions such as (sub-exponential) CDH or LWE.
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Notes
- 1.
The assumption that the commitment takes input a \(\textsf{tag}\) is without loss of generality when the tag space is exponential. As is standard with non-malleable commitments, tags can be generically removed by setting the tag as the verification key of a signature scheme, and signing the commitment string using the signing key.
- 2.
- 3.
Technically, they rely on a more general notion of incompressible problems, which is a collection of efficiently recognizable and sufficiently dense sets, one for each security parameter, for which no adversary with non-uniform description of polynomial size in S can find more than K(S) elements in the set.
- 4.
For example, any sub-exponentially secure injective one-way function will suffice for our purposes.
- 5.
In order for the scheme to be secure, the runtime of the \(\mathsf {CCA.Val}\) oracle should be bigger than the runtime of the subexponential adversary. We will imagine runtime of the \(\mathsf {CCA.Val}\) oracle to be \(2^{{\kappa }^v}\) where \(v>1\).
- 6.
Recall from Definition 3.3 that a \(2^{{\kappa }^v}\)-efficient scheme with \(v\ge 1\) implies that the runtime of \(\mathsf {Small.Val}\) is polynomial in \(2^{{\kappa }^v}\).
- 7.
The variables \(\delta \) and \(\gamma \) are known from the security guarantees of \(\textsf{AuxEquiv},\textsf{HPRG}\) respectively.
- 8.
The notation \(\textsf{ilog}(0,{\kappa })\) is defined as \({\kappa }\).
- 9.
The length of the decommitment string can depend on \(\textsf{aux}\), but since \(\textsf{aux}\) is also called with a polynomial function in \({\kappa }\) based on the hinting PRG construction, we simplify the notation. In our specific construction for \(\textsf{AuxEquiv}\) in Sect. 4, the decommitment string length doesn’t depend on \(\textsf{aux}\).
- 10.
Recall from Definition 3.3 that a \(2^{{\kappa }^v}\)-efficient scheme with \(v\ge 1\) implies that the runtime of \(\mathsf {Small.Val}\) is polynomial in \(2^{{\kappa }^v}\).
References
Ananth, P., Choudhuri, A.R., Jain, A.: A new approach to round-optimal secure multiparty computation. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 468–499. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_16
Badrinarayanan, S., Goyal, V., Jain, A., Kalai, Y.T., Khurana, D., Sahai, A.: Promise zero knowledge and its applications to round optimal MPC. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 459–487. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_16
Badrinarayanan, S., Goyal, V., Jain, A., Khurana, D., Sahai, A.: Round optimal concurrent MPC via strong simulation. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 743–775. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_25
Barak, B.: Constant-round coin-tossing with a man in the middle or realizing the shared random string model. In: FOCS (2002)
Barak, B., Ong, S.J., Vadhan, S.P.: Derandomization in cryptography. SIAM J. Comput. 37, 380–400 (2007)
Benhamouda, F., Lin, H.: k-round multiparty computation from k-round oblivious transfer via garbled interactive circuits. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 500–532. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_17
Bitansky, N., Kalai, Y.T., Paneth, O.: Multi-collision resistance: a paradigm for keyless hash functions. In: STOC (2018)
Bitansky, N., Lin, H.: One-message zero knowledge and non-malleable commitments. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11239, pp. 209–234. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03807-6_8
Bitansky, N., Paneth, O.: ZAPs and non-interactive witness indistinguishability from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 401–427. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_16
Brakerski, Z., Halevi, S., Polychroniadou, A.: Four round secure computation without setup. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 645–677. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70500-2_22
Broadnax, B., Fetzer, V., Müller-Quade, J., Rupp, A.: Non-malleability vs. cca-security: the case of commitments. In: IACR International Workshop on Public Key Cryptography (2018)
Canetti, R., Lin, H., Pass, R.: Adaptive hardness and composable security in the plain model from standard assumptions. In: FOCS (2010)
Choudhuri, A.R., Ciampi, M., Goyal, V., Jain, A., Ostrovsky, R.: Round optimal secure multiparty computation from minimal assumptions. Cryptology ePrint Archive, Report 2019/216 (2019)
Ciampi, M., Ostrovsky, R., Siniscalchi, L., Visconti, I.: Concurrent non-malleable commitments (and more) in 3 rounds. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9816, pp. 270–299. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53015-3_10
Ciampi, M., Ostrovsky, R., Siniscalchi, L., Visconti, I.: Four-round concurrent non-malleable commitments from one-way functions. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 127–157. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63715-0_5
Crescenzo, G.D., Ishai, Y., Ostrovsky, R.: Non-interactive and non-malleable commitment. In: Vitter, J.S. (ed.) STOC (1998)
Damgård, I.B., Pedersen, T.P., Pfitzmann, B.: On the existence of statistically hiding bit commitment schemes and fail-stop signatures. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 250–265. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_22
Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: STOC (1991)
Garg, R., Khurana, D., Lu, G., Waters, B.: Black-box non-interactive non-malleable commitments. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12698, pp. 159–185. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77883-5_6
Goyal, R., Vusirikala, S., Waters, B.: New constructions of hinting prgs, owfs with encryption, and more. IACR Cryptology ePrint Archive (2019)
Goyal, V.: Constant round non-malleable protocols using one-way functions. In: STOC (2011)
Goyal, V., Lee, C.K., Ostrovsky, R., Visconti, I.: Constructing non-malleable commitments: a black-box approach. In: FOCS (2012)
Goyal, V., Pandey, O., Richelson, S.: Textbook non-malleable commitments. In: STOC (2016)
Goyal, V., Richelson, S.: Non-malleable commitments using goldreich-levin list decoding. In: FOCS (2019)
Goyal, V., Richelson, S., Rosen, A., Vald, M.: An algebraic approach to non-malleability. In: FOCS (2014)
Groth, J., Ostrovsky, R., Sahai, A.: New techniques for noninteractive zero-knowledge. J. ACM 59, 1–35 (2012)
Halevi, S., Hazay, C., Polychroniadou, A., Venkitasubramaniam, M.: Round-optimal secure multi-party computation. J. Cryptol. 34(3), 1–63 (2021). https://doi.org/10.1007/s00145-021-09382-3
Halevi, S., Micali, S.: Practical and provably-secure commitment schemes from collision-free hashing. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 201–215. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68697-5_16
Kalai, Y.T., Khurana, D.: Non-interactive non-malleability from quantum supremacy. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 552–582. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26954-8_18
Khurana, D.: Round optimal concurrent non-malleability from polynomial hardness. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 139–171. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_5
Khurana, D.: Non-interactive distributional indistinguishability (NIDI) and non-malleable commitments. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12698, pp. 186–215. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77883-5_7
Khurana, D., Sahai, A.: How to achieve non-malleability in one or two rounds. In: FOCS (2017)
Koppula, V., Waters, B.: Realizing chosen ciphertext security generically in attribute-based encryption and predicate encryption. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 671–700. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_23
Lin, H., Pass, R.: Non-malleability Amplification. In: STOC (2009)
Lin, H., Pass, R.: Constant-round Non-malleable Commitments from Any One-way Function. In: STOC (2011)
Lin, H., Pass, R., Soni, P.: Two-round and non-interactive concurrent non-malleable commitments from time-lock puzzles. In: FOCS (2017)
Lin, H., Pass, R., Venkitasubramaniam, M.: Concurrent non-malleable commitments from any one-way function. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 571–588. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78524-8_31
Pandey, O., Pass, R., Vaikuntanathan, V.: Adaptive one-way functions and applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 57–74. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_4
Pass, R.: Unprovable security of perfect NIZK and non-interactive non-malleable commitments. Comput. Complex. 25(3), 607–666 (2016). https://doi.org/10.1007/s00037-016-0122-2
Pass, R., Rosen, A.: Concurrent non-malleable commitments. In: FOCS (2005)
Pass, R., Rosen, A.: New and improved constructions of nonmalleable cryptographic protocols. SIAM J. Comput. (2008)
Pass, R., Wee, H.: Constant-round non-malleable commitments from sub-exponential one-way functions. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 638–655. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_32
Unruh, D.: Random oracles and auxiliary input. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 205–223. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_12
Wee, H.: Black-box, round-efficient secure computation via non-malleability amplification. In: FOCS (2010)
Acknowledgments
We thank Daniel Wichs for a useful discussion about the construction of our new Hinting PRGs, anonymous reviewers for helpful feedback on a preliminary version of this work, and Nir Bitansky and Rachel Lin for answering our questions about keyless collision-resistant hash functions.
D. Khurana was supported in part by NSF CNS - 2238718, DARPA SIEVE and a gift from Visa Research. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024. Brent Waters was supported by NSF CNS-1908611, Simons Investigator award and Packard Foundation Fellowship.
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Garg, R., Khurana, D., Lu, G., Waters, B. (2023). On Non-uniform Security for Black-Box Non-interactive CCA Commitments. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14004. Springer, Cham. https://doi.org/10.1007/978-3-031-30545-0_7
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