Abstract
In this work, we study the Time-Lock Encryption (TLE) cryptographic primitive. The concept of TLE involves a party initiating the encryption of a message that one can only decrypt after a certain amount of time has elapsed. Following the Universal Composability (UC) paradigm introduced by Canetti [IEEE FOCS 2001], we formally abstract the concept of TLE into an ideal functionality. In addition, we provide a standalone definition for secure TLE schemes in a game-based style and we devise a hybrid protocol that relies on such a secure TLE scheme. We show that if the underlying TLE scheme satisfies the standalone game-based security definition, then our hybrid protocol UC realises the TLE functionality in the random oracle model. Finally, we present Astrolabous, a TLE construction that satisfies our security definition, leading to the first UC realization of the TLE functionality.
Interestingly, it is hard to prove UC secure any of the TLE construction proposed in the literature. The reason behind this difficulty relates to the UC framework itself. Intuitively, to capture semantic security, no information should be leaked regarding the plaintext in the ideal world, thus the ciphertext should not contain any information relating to the message. On the other hand, all ciphertexts will eventually open, resulting in a trivial distinction of the real from the ideal world in the standard model. We overcome this limitation by extending any secure TLE construction adopting the techniques of Nielsen [CRYPTO 2002] in the random oracle model. Specifically, the description of the extended TLE algorithms includes calls to the random oracle, allowing our simulator to equivocate. This extension can be applied to any TLE algorithm that satisfies our standalone game-based security definition, and in particular to Astrolabous.
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Notes
- 1.
Recall that in the ideal world, to capture semantic security, ciphertexts do not contain any information about the actual message except its length.
- 2.
The simulator gives back the ciphertext as this is the case in most encryption functionalities [11, 12]. Now, because we allow the simulator to delay the delivery of messages, the simulator needs a handle for updating the functionality’s database. Here the tag comes into play and works as a receipt for that call.
- 3.
Note that this time difficulty is relative, that means that it specifies the duration for solving the puzzle rather than the specific date at which the puzzle should be solved.
- 4.
To do this efficiently all the hash queries can be performed simultaneously as \(k_{\mathsf {E}}\) and \(r_{0}||r_{1}||\ldots ||r_{q\tau _{\mathsf {dec}}-1}\) are known. In the UC setting, the party sends \((\mathsf {sid},\textsc {Evaluate},\tau _{\mathsf {dec}})\) to \(\mathcal {W}_{q}\) and receives back \((\mathsf {sid},\textsc {Evaluate},\tau _{\mathsf {dec}},\{(r_{j},y_{j})\}_{j=0}^{q\tau _{\mathsf {dec}}-1})\).
References
Arapinis, M., Lamprou, N., Zacharias, T.: E-cclesia: universally composable self-tallying elections. Cryptology ePrint Archive, Report 2020/513 (2020)
Arapinis, M., Lamprou, N., Zacharias, T.: A universally composable time-lock encryption scheme. Cryptology ePrint Archive, Astrolabous (2021)
Christian, B., et al.: A composable treatment. In: CRYPTO, Bitcoin as a Transaction Ledger (2017)
Baum, C., et al.: Craft: composable randomness and almost fairness from time. Cryptology ePrint Archive, Report 2020/784 (2020)
Baum, C. et al.: A foundation of time-lock puzzles in uc. Advances in Cryptology - EUROCRYPT (2021)
Biryukov, A., Dinu, D., Khovratovich, D.: Argon2: new generation of memory-hard functions for password hashing and other applications. In: 2016 IEEE European Symposium on Security and Privacy (EuroS P) (2016)
Bitansky, N., et al.: Time-lock puzzles from randomized encodings. In: ITCS (2016)
Boneh, D., Naor, M.: Timed commitments. In: CRYPTO (2000)
Boneh, D., Bonneau, J., Bunz, B., Fisch, B.: Verifiable delay functions. In: CRYPTO 2018 (2018)
Bellare, M.: Timed commitments. In: Bellare, Mihir (ed.) Advances in Cryptology – CRYPTO 2000. Springer, Berlin Heidelberg (2000)
Camenisch, J., Lehmann, A., Neven, G., Samelin, K.: Uc-secure non-interactive public-key encryption. In: CSF 2017 (2017)
Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: FOCS (2001)
Canetti, R., Dodis, Y., Pass, R., Walfish, S.: Universally composable security with global setup. In: TCC (2007)
Cheon, J.H., Hopper, N., Kim, Y., Osipkov, I.: Timed-release and key-insulated public key encryption. In: Di Crescenzo, G., Rubin, A. (eds.) Financial Cryptography and Data Security. FC 2006. LNCS, vol. 4107. Springer, Heidelberg (2006). https://doi.org/10.1007/11889663_17
Cheon, J.H., Hopper, N., Kim, Y., Osipkov, I.: Provably secure timed-release public key encryption. ACM Trans. Inf. Syst. Secur., 11(2), (2008)
Dachman-Soled, D., Mahmoody, M., Malkin, T.: Can optimally-fair coin tossing be based on one-way functions?. In: Lindell, Y. (eds.) Theory of Cryptography. TCC 2014. LNCS, vol. 8349. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_10
Daemen, J., Rijmen, V.: The design of Rijndael. Springer-Verlag (2002). https://doi.org/10.1007/978-3-662-60769-5
ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_2
Ephraim, N., Freitag, C., Komargodski, I., Pass, R.: Non-malleable time-lock puzzles and applications. Cryptology ePrint Archive, Report 2020/779 (2020)
Garay, J., Kiayias, A., Panagiotakos, G.: Proofs of work for blockchain protocols. IACR Cryptol. ePrint Arch., 2017 (2017)
Juan, A.: Garay, Aggelos Kiayias, and Nikos Leonardos. analysis and applications. In: EUROCRYPT, The Bitcoin Backbone Protocol (2015)
Garg, S., Gentry, C., Sahai, A., Waters, B.: Witness encryption and its applications. In: STOC (2013)
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. J. Cryptol. 20 (2007)
Gilbert, H., Handschuh, H.: Security analysis of SHA-256 and sisters. In: Matsui, M., Zuccherato, R.J. (eds.) Selected Areas in Cryptography. SAC 2003. LNCS, vol. 3006. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24654-1_13
Goldreich, O.: The foundations of modern cryptography. In: Modern Cryptography, Probabilistic Proofs and Pseudorandomness. Algorithms and Combinatorics, vol. 17. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-662-12521-2_1
Goldreich, O.: Foundations of cryptography:, vol. 1. Cambridge University Press, USA (2006)
Gordon, D., Ishai, Y., Moran, T., Ostrovsky, R., Sahai, A.: On complete primitives for fairness. In: Micciancio, D. (eds.) Theory of Cryptography. TCC 2010. LNCS, vol. 5978. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_7
Groth, J.: Evaluating security of voting schemes in the universal composability framework. In: Jakobsson, M., Yung, M., Zhou, J. (eds) Applied Cryptography and Network Security. ACNS 2004. LNCS, vol. 3089. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24852-1_4
Hirt, M., Zikas, V.: Adaptively secure broadcast. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 466–485. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_24
Katz, J., Loss, J., Xu, J.: On the security of time-lock puzzles and timed commitments. In: Pass, R., Pietrzak, K. (eds.) Theory of Cryptography. TCC 2020. Lecture Notes in Computer Science, vol. 12552. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64381-2_14
Katz, J., Maurer, U., Tackmann, B., Zikas, V.: Universally composable synchronous computation. In: TCC (2013)
Khisti, A., Tchamkerten, A., Wornell, G. W.: Secure broadcasting over fading channels. IEEE Trans. Inf. Theory, 54(6) (2008)
Kiayias, A., Yung, M.: Self-tallying elections and perfect ballot secrecy. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 141–158. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45664-3_10
Kościelny, C., Kurkowski, M., Srebrny, M.: Foundations of symmetric cryptography. In: Modern Cryptography Primer, pp. 77–118. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41386-5_3
Lindell, Y.: Highly-efficient universally-composable commitments based on the DDH assumption. In: EUROCRYPT 2011 (2011)
Liu, J., Jager, T., Kakvi, S.A., Warinschi, B.: How to build time-lock encryption. Designs, Codes and Cryptography (2018)
Mahmoody, M., Moran, T., Vadhan, S.: Time-lock puzzles in the random oracle model. In: Rogaway, P. (eds.) Advances in Cryptology. LNCS, vol. 6841. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_3
Timothy, C.: May. Timed-release crypto (1993)
Nielsen, J.B.: Separating random oracle proofs from complexity theoretic proofs: the non-committing encryption case. In: CRYPTO (2002)
Okamoto, T.: Receipt-free electronic voting schemes for large scale elections. In: Security Protocols (1998)
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) Advances in Cryptology. LNCS, vol. 576. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_9
Pietrzak, K.: Simple verifiable delay functions. In: Blum, A., (ed.) 10th Innovations in Theoretical Computer Science Conference (ITCS 2019), of Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, vol. 124 (2018)
Rivest, R.L., Shamir, A., Wagner, D.A.: Time-lock puzzles and timed-release crypto. Technical report (1996)
Szepieniec, A., Preneel, B.: New techniques for electronic voting. USENIX Association (2015)
Toponce, A.: Further investigation into scrypt and argon2 password hashing (2016)
Wesolowski, B.: Efficient verifiable delay functions. In: Ishai, Y., Rijmen, V. (eds.) Advances in Cryptology. LNCS, vol. 11478. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_13
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Arapinis, M., Lamprou, N., Zacharias, T. (2021). Astrolabous: A Universally Composable Time-Lock Encryption Scheme. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13091. Springer, Cham. https://doi.org/10.1007/978-3-030-92075-3_14
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