Abstract
We show how to construct, from any weak pseudorandom function, a 3-round symmetric-key authentication protocol that is secure against man-in-the-middle attacks. The construction is very efficient, requiring both the secret key and communication size to be only 3n bits long and involving only one call to the weak-PRF. Our techniques also extend to certain classes of randomized weak-PRFs, chiefly among which are those based on the classical LPN problem and its more efficient variants such as Toeplitz-LPN and Ring-LPN. Building an efficient man-in-the-middle secure authentication scheme from any weak-PRF resolves a problem left open by Dodis et al. (Eurocrypt 2012), while building a man-in-the-middle secure scheme based on any variant of the LPN problem solves the main open question in a long line of research aimed at constructing a practical light-weight authentication scheme based on learning problems, which began with the work of Hopper and Blum (Asiacrypt 2001).
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Banerjee, A., Peikert, C., Rosen, A.: Pseudorandom functions and lattices. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 719–737. Springer, Heidelberg (2012)
Bellare, M., Palacio, A.: Gq and schnorr identification schemes: Proofs of security against impersonation under active and concurrent attacks. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 162–177. Springer, Heidelberg (2002)
Blum, A., Furst, M., Kearns, M., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. CRYPTO, pp. 278–291. Springer, Heidelberg (1994)
Bogdanov, A., Knudsen, L.R., Leander, G., Paar, C., Poschmann, A., Robshaw, M., Seurin, Y., Vikkelsoe, C.: Present: An ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007)
Damgård, I.B., Nielsen, J.B.: 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)
Dodis, Y., Kiltz, E., Pietrzak, K., Wichs, D.: Message authentication, revisited. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 355–374. Springer, Heidelberg (2012)
Gilbert, H., Robshaw, M., Sibert, H.: An active attack against HB + - a provably secure lightweight authentication protocol. Cryptology ePrint Archive, Report 2005/237 (2005)
Gilbert, H., Robshaw, M.J.B., Seurin, Y.: Good variants of HB + are hard to find. In: Tsudik, G. (ed.) FC 2008. LNCS, vol. 5143, pp. 156–170. Springer, Heidelberg (2008)
Gilbert, H., Robshaw, M.J.B., Seurin, Y.: HB#: Increasing the security and efficiency of HB + . In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 361–378. Springer, Heidelberg (2008)
Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792–807 (1986)
Goldreich, O., Krawczyk, H., Luby, M.: On the existence of pseudorandom generators. SIAM J. Comput. 22(6), 1163–1175 (1993)
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)
Heyse, S., Kiltz, E., Lyubashevsky, V., Paar, C., Pietrzak, K.: Lapin: An efficient authentication protocol based on ring-lpn. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 346–365. Springer, Heidelberg (2012)
Hopper, N.J., Blum, M.: Secure human identification protocols. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 52–66. Springer, Heidelberg (2001)
Juels, A., Weis, S.A.: Authenticating pervasive devices with human protocols. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 293–308. Springer, Heidelberg (2005)
Katz, J., Shin, J.S.: Parallel and concurrent security of the HB and HB + protocols. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 73–87. Springer, Heidelberg (2006)
Katz, J., Shin, J.S., Smith, A.: Parallel and concurrent security of the HB and HB + protocols. J. Cryptology 23(3), 402–421 (2010)
Kiltz, E., Pietrzak, K., Cash, D., Jain, A., Venturi, D.: Efficient authentication from hard learning problems. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 7–26. Springer, Heidelberg (2011)
Leander, G., Paar, C., Poschmann, A., Schramm, K.: New lightweight des variants. In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 196–210. Springer, Heidelberg (2007)
Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010)
Maurer, U.M., Sjödin, J.: A fast and key-efficient reduction of chosen-ciphertext to known-plaintext security. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 498–516. Springer, Heidelberg (2007)
Naor, M., Reingold, O.: Number-theoretic constructions of efficient pseudo-random functions. In: FOCS, pp. 458–467 (1997)
Naor, M., Reingold, O., Rosen, A.: Pseudorandom functions and factoring. SIAM J. Comput. 31(5), 1383–1404 (2002)
Ouafi, K., Overbeck, R., Vaudenay, S.: On the security of HB# against a man-in-the-middle attack. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 108–124. Springer, Heidelberg (2008)
Pietrzak, K.: A leakage-resilient mode of operation. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 462–482. Springer, Heidelberg (2009)
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6) (2009)
Schnorr, C.-P.: Efficient signature generation by smart cards. J. Cryptology 4(3), 161–174 (1991)
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Lyubashevsky, V., Masny, D. (2013). Man-in-the-Middle Secure Authentication Schemes from LPN and Weak PRFs. In: Canetti, R., Garay, J.A. (eds) Advances in Cryptology – CRYPTO 2013. CRYPTO 2013. Lecture Notes in Computer Science, vol 8043. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40084-1_18
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