Abstract
We formally study iterated block ciphers that alternate between two sequences of independent and identically distributed (i.i.d.) rounds. It is demonstrated that, in some cases the effect of alternating increases security, while in other cases the effect may strictly decrease security relative to the corresponding product of one of its component sequences. As this would appear to contradict conventional wisdom based on the ideal cipher approximation, we introduce new machinery for provable security comparisons. The comparisons made here simultaneously establish a coherent ordering of security metrics ranging from key-recovery cost to computational indistinguishability.
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References
Black, J.A.: The ideal-cipher model, revisited: An uninstantiable blockcipher-based hash function. In: Robshaw, M. (ed.) FSE 2006. LNCS, vol. 4047, pp. 328–340. Springer, Heidelberg (2006)
Bonneau, J.: Guessing human-chosen secrets. PhD thesis, University of Cambridge (May 2012)
Campbell, K.W., Wiener, M.: DES is not a group. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 512–520. Springer, Heidelberg (1993)
Cicalese, F., Vaccaro, U.: Supermodularity and subadditivity properties of the entropy on the majorization lattice. IEEE Transactions on Information Theory 48(4), 933–938 (2002)
Diaconis, P.: Group Representations in Probability and Statistics. Institute of Mathematical Statistics, Hayward, CA (1988)
Gaži, P., Maurer, U.: Cascade encryption revisited. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 37–51. Springer, Heidelberg (2009)
Kaliski, B., Rivest, R., Sherman, A.: Is the Data Encryption Standard a group (results of cycling experiments on DES). Journal of Cryptology 1(1), 1–36 (1988)
Knudsen, L.R., Robshaw, M.J.B.: The block cipher companion. Springer-Verlag, New York (2011)
Marshall, A.W., Olkin, I., Arnold, B.C.: Inequalities: Theory of Majorization and Its Applications, 2nd edn. Springer, New York (2011)
Massey, J.L.: Guessing and entropy. In: Proc. 1994 IEEE Int’l Symp. on Information Theory, p. 204 (1994)
Morris, B., Rogaway, P., Stegers, T.: How to encipher messages on a small domain: Deterministic encryption and the Thorp shuffle. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 286–302. Springer, Heidelberg (2009)
Pliam, J.O.: On the Incomparability of Entropy and Marginal Guesswork in Brute-Force Attacks. In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol. 1977, pp. 67–79. Springer, Heidelberg (2000)
Pliam, J.O.: A Polynomial-Time Universal Security Amplifier in the Class of Block Ciphers. Communications in Information and Systems 1(2), 181–204 (2001)
Pliam, J.O.: Alternating Product Ciphers: A Case for Provable Security Comparisons. arXiv preprint arXiv:1307.4107, Full version of this paper (2013)
Rotman, J.J.: An Introduction to the Theory of Groups, 4th edn. Springer (1995)
Shannon, C.E.: Communication theory of secrecy systems. Bell System Tech. Jour. 28, 656–715 (1949)
Vaudenay, S.: Decorrelation: a theory for block cipher security. Journal of Cryptology 16(4), 249–286 (2003)
Wernsdorf, R.: The one-round functions of the DES generate the alternating group. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 99–112. Springer, Heidelberg (1993)
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Pliam, J.O. (2013). Alternating Product Ciphers: A Case for Provable Security Comparisons. In: Paul, G., Vaudenay, S. (eds) Progress in Cryptology – INDOCRYPT 2013. INDOCRYPT 2013. Lecture Notes in Computer Science, vol 8250. Springer, Cham. https://doi.org/10.1007/978-3-319-03515-4_3
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DOI: https://doi.org/10.1007/978-3-319-03515-4_3
Publisher Name: Springer, Cham
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