Abstract
Time-lock puzzles allow one to encrypt messages for the future, by efficiently generating a puzzle with a solution s that remains hidden until time \(\mathcal {T}\) has elapsed. The solution is required to be concealed from the eyes of any algorithm running in (parallel) time less than \(\mathcal {T}\). We put forth the concept of homomorphic time-lock puzzles, where one can evaluate functions over puzzles without solving them, i.e., one can manipulate a set of puzzles with solutions \((s_1, \dots , s_n)\) to obtain a puzzle that solves to \(f(s_1, \ldots , s_n)\), for any function f. We propose candidate constructions under concrete cryptographic assumptions for different classes of functions. Then we show how homomorphic time-lock puzzles overcome the limitations of classical time-lock puzzles by proposing new protocols for applications of interest, such as e-voting, multi-party coin flipping, and fair contract signing.
G. Malavolta—Part of the work done while at Friedrich-Alexander-Universität Erlangen-Nürnberg.
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- 1.
We implicitly assume that all puzzles are honestly generated, which can be enforced with standard cryptographic tools.
- 2.
In [20] the signing algorithm requires an additional timing parameter, which we fix to be the round number and omit for the sake of clarity.
References
Bitansky, N., Garg, S., Lin, H., Pass, R., Telang, S.: Succinct randomized encodings and their applications. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, pp. 439–448. ACM Press, June 2015
Bitansky, N., Goldwasser, S., Jain, A., Paneth, O., Vaikuntanathan, V., Waters, B.: Time-lock puzzles from randomized encodings. In: Sudan, M. (ed.) ITCS 2016, pp. 345–356. ACM, Cambridge (2016)
Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo random bits. In: 23rd FOCS, pp. 112–117. IEEE Computer Society Press, November 1982
Boneh, D., Bonneau, J., Bünz, B., Fisch, B.: Verifiable delay functions. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 757–788. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_25
Boneh, D., Bünz, B., Fisch, B.: A survey of two verifiable delay functions. Cryptology ePrint Archive, Report 2018/712 (2018). https://eprint.iacr.org/2018/712
Boneh, D., Naor, M.: Timed commitments. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 236–254. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_15
Brakerski, Z., Goldwasser, S.: Circular and leakage resilient public-key encryption under subgroup indistinguishability. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 1–20. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_1
Buchmann, J., Williams, H.C.: A key-exchange system based on imaginary quadratic fields. J. Cryptol. 1(2), 107–118 (1988)
Canetti, R., Lin, H., Tessaro, S., Vaikuntanathan, V.: Obfuscation of probabilistic circuits and applications. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 468–497. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_19
Couteau, G., Peters, T., Pointcheval, D.: Encryption switching protocols. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 308–338. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_12
Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44586-2_9
Dwork, C., Naor, M.: Zaps and their applications. In: 41st FOCS, pp. 283–293. IEEE Computer Society Press, November 2000
Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs based on a single random string (extended abstract). In: 31st FOCS, pp. 308–317. IEEE Computer Society Press, October 1990
Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th FOCS, pp. 40–49. IEEE Computer Society Press, October 2013
Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 467–476. ACM Press, June 2013
Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 169–178. ACM Press, May/June 2009
Gentry, C., Halevi, S., Vaikuntanathan, V.: i-Hop homomorphic encryption and rerandomizable yao circuits. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 155–172. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_9
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions (extended abstract). In: 25th FOCS, pp. 464–479. IEEE Computer Society Press, October 1984
Goldwasser, S., Micali, S.: Probabilistic encryption and how to play mental poker keeping secret all partial information. In: 14th ACM STOC, pp. 365–377. ACM Press, May 1982
Hohenberger, S., Waters, B.: Synchronized aggregate signatures from the RSA assumption. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 197–229. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_7
Ishai, Y., Paskin, A.: Evaluating branching programs on encrypted data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70936-7_31
Kiayias, A., Russell, A., David, B., Oliynykov, R.: Ouroboros: a provably secure proof-of-stake blockchain protocol. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 357–388. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63688-7_12
Lin, H., Pass, R., Soni, P.: Two-round and non-interactive concurrent non-malleable commitments from time-lock puzzles. In: 58th FOCS, pp. 576–587. IEEE Computer Society Press (2017)
Liu, J., Jager, T., Kakvi, S.A., Warinschi, B.: How to build time-lock encryption. Des. Codes Crypt. 86, 2549–2586 (2018)
Mahmoody, M., Moran, T., Vadhan, S.: Time-lock puzzles in the random Oracle model. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 39–50. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_3
Mahmoody, M., Moran, T., Vadhan, S.P.: Publicly verifiable proofs of sequential work. In: Kleinberg, R.D. (ed.) ITCS 2013, pp. 373–388. ACM, January 2013
Ostrovsky, R., Paskin-Cherniavsky, A., Paskin-Cherniavsky, B.: Maliciously circuit-private FHE. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 536–553. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_30
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_16
Pietrzak, K.: Simple verifiable delay functions. Cryptology ePrint Archive, Report 2018/627 (2018). https://eprint.iacr.org/2018/627
Rivest, R.L., Shamir, A., Wagner, D.A.: Time-lock puzzles and timed-release crypto. Technical report, Cambridge, MA, USA (1996)
Wesolowski, B.: Efficient verifiable delay functions. Cryptology ePrint Archive, Report 2018/623 (2018). https://eprint.iacr.org/2018/623
Acknowledgements
Research supported in part by a gift from Ripple, a gift from DoS Networks, a grant from Northrop Grumman, a Cylab seed funding award, and a JP Morgan Faculty Fellowship.
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Malavolta, G., Thyagarajan, S.A.K. (2019). Homomorphic Time-Lock Puzzles and Applications. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11692. Springer, Cham. https://doi.org/10.1007/978-3-030-26948-7_22
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