Abstract
Fischlin’s transformation is an alternative to the standard Fiat-Shamir transform to turn a certain class of public key identification schemes into digital signatures (in the random oracle model).
We show that signatures obtained via Fischlin’s transformation are existentially unforgeable even if the adversary can get arbitrary (yet bounded) information on the full state of the signer (including the signing key and the random coins used to generate signatures). A similar fact was already known for the Fiat-Shamir transform, however, Fischlin’s transformation allows for a significantly higher leakage parameter than Fiat-Shamir.
Moreover, in contrast to signatures obtained via Fiat-Shamir, signatures obtained via Fischlin enjoy a tight reduction to the underlying hard problem. We use this observation to show (via simulations) that Fischlin’s transformation, usually considered less efficient, outperforms the Fiat-Shamir transform in verification time for a reasonable choice of parameters. In terms of signing Fiat-Shamir is faster for equal signature sizes. Nonetheless, our experiments show that the signing time of Fischlin’s transformation becomes, e.g., 22% of the one via Fiat-Shamir if one allows the signature size to be doubled.
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References
Agrawal, S., Dodis, Y., Vaikuntanathan, V., Wichs, D.: On continual leakage of discrete log representations. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 401–420. Springer, Heidelberg (2013)
Akinyele, J.A., Garman, C., Miers, I., Pagano, M.W., Rushanan, M., Green, M., Rubin, A.D.: Charm: A framework for rapidly prototyping cryptosystems. Journal of Cryptographic Engineering 3(2), 111–128 (2013), http://dx.doi.org/10.1007/s13389-013-0057-3
Alwen, J., Dodis, Y., Wichs, D.: Leakage-resilient public-key cryptography in the bounded-retrieval model. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 36–54. Springer, Heidelberg (2009)
Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security, pp. 62–73 (1993)
blog, K.: Mostly on computers and mathematics. Website Blog, http://kenta.blogspot.de/2011/01/cvogqzhd-some-large-safe-primes.html (last acess: Januaury 31, 2013)
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)
Boyle, E., Segev, G., Wichs, D.: Fully leakage-resilient signatures. J. Cryptology 26(3), 513–558 (2013)
Brakerski, Z., Kalai, Y.T., Katz, J., Vaikuntanathan, V.: Overcoming the hole in the bucket: Public-key cryptography resilient to continual memory leakage. In: FOCS, pp. 501–510 (2010)
Chatterjee, S., Menezes, A., Sarkar, P.: Another look at tightness. IACR Cryptology ePrint Archive 2011, 442 (2011)
Dagdelen, Ö., Fischlin, M., Gagliardoni, T.: The fiat–shamir transformation in a quantum world. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 62–81. Springer, Heidelberg (2013)
Damgård, I.: On Σ-protocols. Tech. rep., Aarhus University (2013), http://www.daimi.au.dk/~ivan/Sigma.pdf
Damgård, I., Faust, S., Mukherjee, P., Venturi, D.: Bounded tamper resilience: How to go beyond the algebraic barrier. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 140–160. Springer, Heidelberg (2013)
Davì, F., Dziembowski, S., Venturi, D.: Leakage-resilient storage. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 121–137. Springer, Heidelberg (2010)
Dodis, Y., Haralambiev, K., López-Alt, A., Wichs, D.: Cryptography against continuous memory attacks. In: FOCS, pp. 511–520 (2010)
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)
Dodis, Y., Ostrovsky, R., Reyzin, L., Smith, A.: Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. SIAM J. Comput. 38(1), 97–139 (2008)
Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: FOCS, pp. 293–302 (2008)
Dziembowski, S., Pietrzak, K., Wichs, D.: Non-malleable codes. In: ICS, pp. 434–452 (2010)
Faust, S., Kiltz, E., Pietrzak, K., Rothblum, G.N.: Leakage-resilient signatures. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 343–360. Springer, Heidelberg (2010)
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)
Faust, S., Mukherjee, P., Nielsen, J.B., Venturi, D.: Continuous non-malleable codes. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 465–488. Springer, Heidelberg (2014)
Faust, S., Mukherjee, P., Venturi, D., Wichs, D.: Efficient non-malleable codes and key-derivation for poly-size tampering circuits. In: Oswald, E. (ed.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 111–128. Springer, Heidelberg (2014)
Fiat, A., Shamir, A.: How to prove yourself: Practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) Advances in Cryptology - CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1986)
Fischlin, M.: Communication-efficient non-interactive proofs of knowledge with online extractors. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 152–168. Springer, Heidelberg (2005)
Fischlin, M., Fischlin, R.: The representation problem based on factoring. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 96–113. Springer, Heidelberg (2002)
Garg, S., Bhaskar, R., Lokam, S.V.: Improved bounds on security reductions for discrete log based signatures. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 93–107. Springer, Heidelberg (2008)
Goh, E.J., Jarecki, S., Katz, J., Wang, N.: Efficient signature schemes with tight reductions to the Diffie-Hellman problems. J. Cryptology 20(4), 493–514 (2007)
Goldreich, O.: On the foundations of modern cryptography. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 46–74. Springer, Heidelberg (1997)
Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)
Guillou, L.C., Quisquater, J.-J.: A “Paradoxical” identity-based signature scheme resulting from zero-knowledge. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 216–231. Springer, Heidelberg (1990)
Ishai, Y., Sahai, A., Wagner, D.: Private circuits: Securing hardware against probing attacks. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 463–481. Springer, Heidelberg (2003)
Katz, J., Vaikuntanathan, V.: Signature schemes with bounded leakage resilience. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 703–720. Springer, Heidelberg (2009)
Koblitz, N., Menezes, A.: Another look at “provable security”. J. Cryptology 20(1), 3–37 (2007)
Kocher, P.C.: Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In: Koblitz, N. (ed.) Advances in Cryptology - CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)
Kocher, P.C., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Lenstra, A.K., Verheul, E.R.: Selecting cryptographic key sizes. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 446–465. Springer, Heidelberg (2000)
Micali, S., Reyzin, L.: Physically observable cryptography. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 278–296. Springer, Heidelberg (2004)
Nielsen, J.B., Venturi, D., Zottarel, A.: Leakage-resilient signatures with graceful degradation. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 362–379. Springer, Heidelberg (2014)
Okamoto, T.: Provably secure and practical identification schemes and corresponding signature schemes. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 31–53. Springer, Heidelberg (1993)
Paillier, P., Vergnaud, D.: Discrete-log-based signatures may not be equivalent to discrete log. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 1–20. Springer, Heidelberg (2005)
Quisquater, J.-J., Samyde, D.: ElectroMagnetic analysis (EMA): Measures and counter-measures for smart cards. In: Attali, S., Jensen, T. (eds.) E-smart 2001. LNCS, vol. 2140, pp. 200–210. Springer, Heidelberg (2001)
Schäge, S.: Tight proofs for signature schemes without random oracles. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 189–206. Springer, Heidelberg (2011)
Schnorr, C.P.: Efficient identification and signatures for smart cards. In: Quisquater, J.-J., Vandewalle, J. (eds.) Advances in Cryptology - EUROCRYPT 1989. LNCS, vol. 434, pp. 688–689. Springer, Heidelberg (1990)
Schütze, T.: Automotive security: Cryptography for car2x communication. In: Embedded World Conference (2011)
Seurin, Y.: On the exact security of schnorr-type signatures in the random oracle model. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 554–571. Springer, Heidelberg (2012)
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Dagdelen, Ö., Venturi, D. (2014). A Second Look at Fischlin’s Transformation. In: Pointcheval, D., Vergnaud, D. (eds) Progress in Cryptology – AFRICACRYPT 2014. AFRICACRYPT 2014. Lecture Notes in Computer Science, vol 8469. Springer, Cham. https://doi.org/10.1007/978-3-319-06734-6_22
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