Abstract
Chameleon-hashes are collision-resistant hash-functions parametrized by a public key. If the corresponding secret key is known, arbitrary collisions for the hash can be found. Recently, Derler et al. (PKC ’20) introduced the notion of fully collision-resistant chameleon-hashes. Full collision-resistance requires the intractability of finding collisions, even with full-adaptive access to a collision-finding oracle. Their construction combines simulation-sound extractable (SSE) NIZKs with perfectly correct IND-CPA secure public-key encryption (PKE) schemes. We show that, instead of perfectly correct PKE, non-interactive commitment schemes are sufficient. For the first time, this gives rise to efficient instantiations from plausible post-quantum assumptions and thus candidates of chameleon-hashes with strong collision-resistance guarantees and long-term security guarantees. On the more theoretical side, our results relax the requirement to not being dependent on public-key encryption.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
We note that the randomness r is also sometimes called “check value” [3].
- 2.
We note that replacing LPN by learning with errors (LWE) and using the commitment scheme and zero-knowledge proofs of Benhamouda et al. [10] gives an immediate post-quantum instantiation that does not require parallel repetitions, yet requiring assumptions that give rise to public-key encryption.
References
Abe, M., David, B., Kohlweiss, M., Nishimaki, R., Ohkubo, M.: Tagged one-time signatures: tight security and optimal tag size. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 312–331. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_20
Ateniese, G., Chou, D.H., de Medeiros, B., Tsudik, G.: Sanitizable signatures. In: di Vimercati, S.C., Syverson, P., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 159–177. Springer, Heidelberg (2005). https://doi.org/10.1007/11555827_10
Ateniese, G., Magri, B., Venturi, D., Andrade, E.R.: Redactable blockchain - or - rewriting history in bitcoin and friends. In: EuroS&P, pp. 111–126 (2017)
Ateniese, G., de Medeiros, B.: Identity-based Chameleon Hash and applications. In: Juels, A. (ed.) FC 2004. LNCS, vol. 3110, pp. 164–180. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27809-2_19
Ateniese, G., de Medeiros, B.: On the key exposure problem in Chameleon Hashes. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 165–179. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30598-9_12
Bao, F., Deng, R.H., Ding, X., Lai, J., Zhao, Y.: Hierarchical identity-based Chameleon Hash and its applications. In: Lopez, J., Tsudik, G. (eds.) ACNS 2011. LNCS, vol. 6715, pp. 201–219. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21554-4_12
Beck, M.T., et al.: Practical strongly invisible and strongly accountable sanitizable signatures. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017. LNCS, vol. 10342, pp. 437–452. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60055-0_23
Bellare, M., Ristov, T.: Hash functions from sigma protocols and improvements to VSH. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 125–142. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89255-7_9
Bellare, M., Ristov, T.: A characterization of Chameleon Hash functions and new, efficient designs. J. Cryptol. 27(4), 799–823 (2014)
Benhamouda, F., Krenn, S., Lyubashevsky, V., Pietrzak, K.: Efficient zero-knowledge proofs for commitments from learning with errors over rings. In: Pernul, G., Ryan, P.Y.A., Weippl, E. (eds.) ESORICS 2015. LNCS, vol. 9326, pp. 305–325. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24174-6_16
Blazy, O., Kakvi, S.A., Kiltz, E., Pan, J.: Tightly-secure signatures from Chameleon Hash functions. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 256–279. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_12
Blum, M.: Coin flipping by telephone. In: Crypto, pp. 11–15 (1981)
Boneh, D., Dagdelen, Ö., Fischlin, M., Lehmann, A., Schaffner, C., Zhandry, M.: Random Oracles in a quantum world. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 41–69. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_3
Brassard, G., Chaum, D., Crépeau, C.: Minimum disclosure proofs of knowledge. J. Comput. Syst. Sci. 37(2), 156–189 (1988)
Brzuska, C., et al.: Security of sanitizable signatures revisited. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 317–336. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00468-1_18
Beck, M.T., et al.: Practical strongly invisible and strongly accountable sanitizable signatures. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017. LNCS, vol. 10342, pp. 437–452. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60055-0_23
Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_27
Chen, X., Zhang, F., Susilo, W., Mu, Y.: Efficient generic on-line/off-line signatures without key exposure. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 18–30. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72738-5_2
Cramer, R., Damgård, I., Schoenmakers, B.: Proofs of partial knowledge and simplified design of witness hiding protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48658-5_19
Derler, D., Samelin, K., Slamanig, D.: Bringing order to chaos: the case of collision-resistant Chameleon-Hashes. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12110, pp. 462–492. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45374-9_16
Derler, D., Samelin, K., Slamanig, D., Striecks, C.: Fine-grained and controlled rewriting in blockchains: Chameleon-hashing gone attribute-based. In: NDSS (2019)
Derler, D., Slamanig, D.: Key-homomorphic signatures: definitions and applications to multiparty signatures and non-interactive zero-knowledge. Des. Codes Crypt. 87(6), 1373–1413 (2018). https://doi.org/10.1007/s10623-018-0535-9
Derler, D., Slamanig, D.: Highly-efficient fully-anonymous dynamic group signatures. In: AsiaCCS, pp. 551–565 (2018)
Dodis, Y., Haralambiev, K., López-Alt, A., Wichs, D.: Efficient public-key cryptography in the presence of key leakage. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 613–631. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_35
Don, J., Fehr, S., Majenz, C.: The measure-and-reprogram technique 2.0: Multi-round Fiat-Shamir and more. Cryptology ePrint Archive, Report 2020/282 (2020). https://eprint.iacr.org/2020/282
Don, J., Fehr, S., Majenz, C., Schaffner, C.: Security of the Fiat-Shamir transformation in the quantum random-oracle model. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 356–383. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_13
Even, S., Goldreich, O., Micali, S.: On-line/off-line digital signatures. J. Cryptol. 9(1), 35–67 (1996). https://doi.org/10.1007/BF02254791
Faust, S., Kohlweiss, M., Marson, G.A., Venturi, D.: On the non-malleability of the Fiat-Shamir transform. In: Galbraith, S., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 60–79. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34931-7_5
Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12
Groth, J.: Simulation-sound NIZK proofs for a practical language and constant size group signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006). https://doi.org/10.1007/11935230_29
Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_24
Hohenberger, S., Waters, B.: Short and stateless signatures from the RSA assumption. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 654–670. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_38
Huang, K., Zhang, X., Mu, Y., Rezaeibagha, F., Wang, X., Li, J., Xia, Q., Qin, J.: EVA: efficient versatile auditing scheme for iot-based datamarket in jointcloud. IEEE Internet Things J. 7(2), 882–892 (2020)
Jain, A., Krenn, S., Pietrzak, K., Tentes, A.: Commitments and efficient zero-knowledge proofs from learning parity with noise. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 663–680. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_40
Krawczyk, H., Rabin, T.: Chameleon signatures. In: NDSS, pp. 143–154 (2000)
Krenn, S., Pöhls, H.C., Samelin, K., Slamanig, D.: Chameleon-Hashes with dual long-term trapdoors and their applications. In: Joux, A., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2018. LNCS, vol. 10831, pp. 11–32. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89339-6_2
Liu, Q., Zhandry, M.: Revisiting post-quantum Fiat-Shamir. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 326–355. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_12
Mohassel, P.: One-time signatures and Chameleon Hash functions. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 302–319. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19574-7_21
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_9
Pietrzak, K.: Cryptography from learning parity with noise. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 99–114. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27660-6_9
Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: FOCS, pp. 543–553 (1999)
Samelin, K., Slamanig, D.: Policy-based sanitizable signatures. In: Jarecki, S. (ed.) CT-RSA 2020. LNCS, vol. 12006, pp. 538–563. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-40186-3_23
Shamir, A., Tauman, Y.: Improved online/offline signature schemes. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 355–367. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_21
Steinfeld, R., Bull, L., Wang, H., Pieprzyk, J.: Universal designated-verifier signatures. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 523–542. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-40061-5_33
Stern, J.: A new identification scheme based on syndrome decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_2
Zhang, R.: Tweaking TBE/IBE to PKE transforms with Chameleon Hash functions. In: Katz, J., Yung, M. (eds.) ACNS 2007. LNCS, vol. 4521, pp. 323–339. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72738-5_21
Acknowledgements
This work was supported by the European Union H2020 Programme under grant agreement n\(\circ \)830929 (CyberSec4Europe), the H2020 ECSEL Joint Undertaking under grant agreement n\(\circ \)783119 (SECREDAS), and by the Austrian Science Fund (FWF) and netidee SCIENCE under grant agreement P31621-N38 (PROFET).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Derler, D., Krenn, S., Samelin, K., Slamanig, D. (2020). Fully Collision-Resistant Chameleon-Hashes from Simpler and Post-quantum Assumptions. In: Galdi, C., Kolesnikov, V. (eds) Security and Cryptography for Networks. SCN 2020. Lecture Notes in Computer Science(), vol 12238. Springer, Cham. https://doi.org/10.1007/978-3-030-57990-6_21
Download citation
DOI: https://doi.org/10.1007/978-3-030-57990-6_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57989-0
Online ISBN: 978-3-030-57990-6
eBook Packages: Computer ScienceComputer Science (R0)