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The GGM function family is a weakly one-way family of functions. (English) Zbl 1369.94527
Hirt, Martin (ed.) et al., Theory of cryptography. 14th international conference, TCC 2016-B, Beijing, China, October 31 – November 3, 2016. Proceedings. Part I. Berlin: Springer (ISBN 978-3-662-53640-7/pbk; 978-3-662-53641-4/ebook). Lecture Notes in Computer Science 9985, 84-107 (2016).
Summary: We give the first demonstration of the cryptographic hardness of the Goldreich-Goldwasser-Micali (GGM) function family when the secret key is exposed. We prove that for any constant \(\epsilon >0\), the GGM family is a \(1/n^{2+\varepsilon}\)-weakly one-way family of functions, when the lengths of secret key, inputs, and outputs are equal. Namely, any efficient algorithm fails to invert GGM with probability at least \(1/n^{2+\epsilon}\) – even when given the secret key.{
} Additionally, we state natural conditions under which the GGM family is strongly one-way.
For the entire collection see [Zbl 1347.94003].
94A60 Cryptography
Full Text: DOI
[1] Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 501–519. Springer, Heidelberg (2014). doi: 10.1007/978-3-642-54631-0_29 · Zbl 1290.94145
[2] Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 337–367. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-46803-6_12 · Zbl 1371.94664
[3] Bai, S., Langlois, A., Lepoint, T., Stehlé, D., Steinfeld, R.: Improved security proofs in lattice-based cryptography: using the Rényi divergence rather than the statistical distance. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 3–24. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48797-6_1 · Zbl 1337.94021
[4] Boneh, D., Waters, B.: Constrained pseudorandom functions and their applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8270, pp. 280–300. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-42045-0_15 · Zbl 1314.94057
[5] Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM (JACM) 51(4), 557–594 (2004) · Zbl 1204.94063
[6] Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994). doi: 10.1007/3-540-48329-2_40 · Zbl 0870.94026
[7] Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM (JACM) 33(4), 792–807 (1986) · Zbl 0596.65002
[8] Goldreich, O.: The GGM construction does not yield correlation intractable function ensembles (2002) · Zbl 1343.94052
[9] Goldreich, O.: Foundations of Cryptography: Basic Applications, vol. 2. Cambridge University Press, Cambridge (2004) · Zbl 1068.94011
[10] Kiayias, A., Papadopoulos, S., Triandopoulos, N., Zacharias, T.: Delegatable pseudorandom functions and applications. In: 2013 ACM SIGSAC Conference on Computer and Communications Security, CCS 2013, Berlin, Germany, 4–8 November 2013, pp. 669–684 (2013)
[11] Luby, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM J. Comput. 17(2), 373–386 (1988) · Zbl 0644.94018
[12] Razborov, A.A., Rudich, S.: Natural proofs. J. Comput. Syst. Sci. 55(1), 24–35 (1997) · Zbl 0884.68055
[13] Sahai, A., Waters, B.: How to use indistinguishability obfuscation, deniable encryption, and more. In: Symposium on Theory of Computing, STOC 2014, 31 May–3 June 2014, pp. 475–484. ACM, New York (2014) · Zbl 1315.94102
[14] Valiant, L.G.: A theory of the learnable. Commun. ACM 27(11), 1134–1142 (1984) · Zbl 0587.68077
[15] Zhandry, M.: How to construct quantum random functions. In: 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science (FOCS), pp. 679–687. IEEE (2012)
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