Abstract
Since their introduction in 1985, by Goldwasser, Micali and Rackoff, followed by Feige, Fiat and Shamir, zero-knowledge proofs have played a significant role in modern cryptography: they allow a party to convince another party of the validity of a statement (proof of membership) or of its knowledge of a secret (proof of knowledge). Cryptographers frequently use them as building blocks in complex protocols since they offer quite useful soundness features, which exclude cheating players. In most of modern telecommunication services, the execution of these protocols involves a prover on a portable device, with limited capacities, and namely distinct trusted part and more powerful part. The former thus has to delegate some computations to the latter. However, since the latter is not fully trusted, it should not learn any secret information.
This paper focuses on proofs of knowledge of discrete logarithm relations sets (DLRS), and the delegation of some prover’s computations, without leaking any critical information to the delegatee. We will achieve various efficient improvements ensuring perfect zero-knowledge against the verifier and partial zero-knowledge, but still reasonable in many contexts, against the delegatee.
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References
Bellare, M., Micciancio, D., Warinschi, B.: Foundations of group signatures: Formal definitions, simplified requirements, and a construction based on general assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 614–629. Springer, Heidelberg (2003)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993: 1st Conference on Computer and Communications Security, pp. 62–73. ACM Press (November 1993)
Bernhard, D., Fuchsbauer, G., Ghadafi, E., Smart, N.P., Warinschi, B.: Anonymous attestation with user-controlled linkability. Int. J. Inf. Sec. 12(3), 219–249 (2013)
Bichsel, P., Camenisch, J., Neven, G., Smart, N.P., Warinschi, B.: Get shorty via group signatures without encryption. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 381–398. Springer, Heidelberg (2010)
Brickell, E.F., Camenisch, J., Chen, L.: Direct anonymous attestation. In: Atluri, V., Pfitzmann, B., McDaniel, P. (eds.) ACM CCS 2004: 11th Conference on Computer and Communications Security, pp. 132–145. ACM Press (October 2004)
Brickell, E., Chen, L., Li, J.: Simplified security notions of direct anonymous attestation and a concrete scheme from pairings. Int. J. Inf. Sec. 8(5), 315–330 (2009)
Canard, S., Coisel, I., De Meulenaer, G., Pereira, O.: Group signatures are suitable for constrained devices. In: Rhee, K.-H., Nyang, D. (eds.) ICISC 2010. LNCS, vol. 6829, pp. 133–150. Springer, Heidelberg (2011)
Canard, S., Coisel, I., Devigne, J., Gallais, C., Peters, T., Sanders, O.: Toward generic method for server-aided cryptography. In: Qing, S., Zhou, J., Liu, D. (eds.) ICICS 2013. LNCS, vol. 8233, pp. 373–392. Springer, Heidelberg (2013)
Cathalo, J., Libert, B., Yung, M.: Group encryption: Non-interactive realization in the standard model. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 179–196. Springer, Heidelberg (2009)
Chen, L., Page, D., Smart, N.P.: On the design and implementation of an efficient daa scheme. In: Gollmann, D., Lanet, J.-L., Iguchi-Cartigny, J. (eds.) CARDIS 2010. LNCS, vol. 6035, pp. 223–237. Springer, Heidelberg (2010)
Delerablée, C., Pointcheval, D.: Dynamic fully anonymous short group signatures. In: Nguyên, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol. 4341, pp. 193–210. Springer, Heidelberg (2006)
Feige, U., Fiat, A., Shamir, A.: Zero knowledge proofs of identity. In: Aho, A.V. (ed.) STOC, pp. 210–217. ACM (1987)
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)
Girault, M.: An identity-based identification scheme based on discrete logarithms modulo a composite number (rump session). In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 481–486. Springer, Heidelberg (1991)
Girault, M., Poupard, G., Stern, J.: On the fly authentication and signature schemes based on groups of unknown order. Journal of Cryptology 19(4), 463–487 (2006)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems (extended abstract). In: Sedgewick, R. (ed.) STOC, pp. 291–304. ACM (1985)
Groth, J.: Fully anonymous group signatures without random oracles. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 164–180. Springer, Heidelberg (2007)
Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008)
Hofheinz, D., Kiltz, E.: Secure hybrid encryption from weakened key encapsulation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 553–571. Springer, Heidelberg (2007)
Kiayias, A., Tsiounis, Y., Yung, M.: Traceable signatures. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 571–589. Springer, Heidelberg (2004)
Libert, B., Peters, T., Yung, M.: Group signatures with almost-for-free revocation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 571–589. Springer, Heidelberg (2012)
Nakanishi, T., Fujii, H., Hira, Y., Funabiki, N.: Revocable group signature schemes with constant costs for signing and verifying. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 463–480. Springer, Heidelberg (2009)
Ohara, K., Sakai, Y., Emura, K., Hanaoka, G.: A group signature scheme with unbounded message-dependent opening. In: Kefei, C., Qi, X., Weidong, Q., Ninghui, L., Wen-Guey, T. (eds.) ASIACCS, pp. 517–522. ACM (2013)
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. Journal of Cryptology 13(3), 361–396 (2000)
Schnorr, C.-P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)
Shacham, H.: A cramer-shoup encryption scheme from the linear assumption and from progressively weaker linear variants. IACR Cryptology ePrint Archive 2007:74 (2007)
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Canard, S., Pointcheval, D., Sanders, O. (2014). Efficient Delegation of Zero-Knowledge Proofs of Knowledge in a Pairing-Friendly Setting. In: Krawczyk, H. (eds) Public-Key Cryptography – PKC 2014. PKC 2014. Lecture Notes in Computer Science, vol 8383. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54631-0_10
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