Abstract
We propose modes for weakly-secure block ciphers that take one block input to provide output of arbitrary length. Damgård and Nielsen proposed such a mode called the Pseudorandom Tree (PRT) mode, and demonstrated that PRT could be used to establish a communication channel that is secure against Chosen-Plaintext Attacks, if the underlying block cipher is secure against any Known-Plaintext Attacks. We present a mode that reduces the key size of PRT to about 60% without any additional computation. We call this the Extended PRT (ERT) mode and prove its security. One drawback of PRT and ERT is that their key sizes are not much small under small expansion, since functions with small expansion are important from practical point of view. We also present a mode that greatly reduces the key size under small expansion.
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References
Aiello, W., Rajagopalan, S., Venkatesan, R.: High-speed Pseudorandom Number Generation with Small Memory. In: Knudsen, L.R. (ed.) FSE 1999. LNCS, vol. 1636, pp. 290–304. Springer, Heidelberg (1999)
Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A Concrete Security Treatment of Symmetric Encryption. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science, FOCS 1997, pp. 394–403 (1997)
Bellare, M., Kilian, J., Rogaway, P.: The Security of Cipher Block Chaining. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 341–358. Springer, Heidelberg (1994)
Damgård, I., Nielsen, J.: Expanding Pseudorandom Functions; or: From Known-Plaintext Security to Chosen-Plaintext Security. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 449–464. Springer, Heidelberg (2002)
Gilbert, H.: The Security of “One-Block-to-Many” Modes of Operation. In: Johansson, T. (ed.) FSE 2003. LNCS, vol. 2887, pp. 377–395. Springer, Heidelberg (2003)
Goldreich, O., Goldwasser, S., Micali, S.: How to Construct Random Functions. Journal of the ACM 33(4), 792–807 (1986)
Klemm, A., Lindemann, C., Lohmann, M.: Traffic Modeling of IP Networks Using the Batch Markovian Arrival Process. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 92–110. Springer, Heidelberg (2002)
Luby, M., Rackoff, C.: How to Construct Pseudo-random Permutations from Pseudo-random functions. SIAM J. Computing 17(2), 373–386 (1988)
Maurer, U., Massey, J.L.: Cascade Ciphers: The Importance of Being First. J. Cryptology 6(1), 55–61 (1993)
Maurer, U.: Indistinguishability of Random Systems. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 110–132. Springer, Heidelberg (2002)
Maurer, U., Pietrzak, K.: Composition of Random Systems: When Two Weak Make One Strong. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 410–427. Springer, Heidelberg (2004)
Naor, M., Reingold, O.: Number-theoretic Constructions of Efficient Pseudo-random Functions. In: 38th Annual Symposium on Foundations of Computer Science, FOCS 1997, pp. 458–467 (1997)
Naor, M., Reingold, O.: From Unpredictability to Indistinguishability: A Simple Construction of Pseudo-Random Functions from MACs (extended abstract). In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 267–282. Springer, Heidelberg (1998)
Naor, M., Reingold, O.: On the Construction of Pseudorandom Permutations: Luby-Rackoff Revisited. Journal of Cryptology 12(1), 29–66 (1999)
Naor, M., Reingold, O.: Synthesizers and their application to the parallel construction of pseudo-random functions. J. of Computer and Systems Sciences 58(2), 336–375 (1999)
3rd Generation Partnership Project, http://www.3gpp.org
Vaudenay, S.: Feistel Ciphers with L 2-Decorrelation. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 1–14. Springer, Heidelberg (1999)
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Minematsu, K., Tsunoo, Y. (2006). Expanding Weak PRF with Small Key Size. In: Won, D.H., Kim, S. (eds) Information Security and Cryptology - ICISC 2005. ICISC 2005. Lecture Notes in Computer Science, vol 3935. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734727_24
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DOI: https://doi.org/10.1007/11734727_24
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