Abstract
Asymmetric bilinear maps using Type-3 pairings are known to be advantageous in several points (e.g., the speed and the size of a group element) to symmetric bilinear maps using Type-1 pairings. Kremer and Mazaré introduce a symbolic model to analyze protocols based on bilinear maps, and show that the symbolic model is computationally sound. However, their model only covers symmetric bilinear maps. In this paper, we propose a new symbolic model to capture asymmetric bilinear maps. Our model allows us to analyze security of various protocols based on asymmetric bilinear maps (e.g., Scott’s client-server ID-based key exchange). Also, we show computational soundness of our symbolic model under the decisional bilinear Diffie-Hellman assumption.
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References
Dolev, D., Yao, A.C.C.: On the Security of Public Key Protocols. In: FOCS 1981, pp. 350–357. IEEE (1981)
Abadi, M., Rogaway, P.: Reconciling Two Views of Cryptography (The Computational Soundness of Formal Encryption). In: Watanabe, O., Hagiya, M., Ito, T., van Leeuwen, J., Mosses, P.D. (eds.) IFIP TCS 2000. LNCS, vol. 1872, pp. 3–22. Springer, Heidelberg (2000)
Granger, R., Kleinjung, T., Zumbrägel, J.: Breaking e128-bit Securef Supersingular Binary Curves (or how to solve discrete logarithms in \(\mathbb{F}_{2^{4 \cdot 1223}}\) and \(\mathbb{F}_{2^{12 \cdot 367}}\)). In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 126–145. Springer, Heidelberg (2014)
Kremer, S., Mazaré, L.: Computationally sound analysis of protocols using bilinear pairings. Journal of Computer Security 18(6), 999–1033 (2010)
Bresson, E., Lakhnech, Y., Mazaré, L., Warinschi, B.: A Generalization of DDH with Applications to Protocol Analysis and Computational Soundness. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 482–499. Springer, Heidelberg (2007)
Scott, M.: Authenticated ID-based Key Exchange and remote log-in with simple token and PIN number. In: Cryptology ePrint Archive: 2002/164 (2002)
Shoup, V.: Sequences of games: A tool for taming complexity in security proofs. In: Cryptology ePrint Archive: 2004/332 (2004)
Black, J., Rogaway, P., Shrimpton, T.: Encryption-Scheme Security in the Presence of Key-Dependent Messages. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 62–75. Springer, Heidelberg (2003)
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Yoneyama, K. (2014). Computational Soundness of Asymmetric Bilinear Pairing-Based Protocols. In: Chow, S.S.M., Liu, J.K., Hui, L.C.K., Yiu, S.M. (eds) Provable Security. ProvSec 2014. Lecture Notes in Computer Science, vol 8782. Springer, Cham. https://doi.org/10.1007/978-3-319-12475-9_23
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DOI: https://doi.org/10.1007/978-3-319-12475-9_23
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12474-2
Online ISBN: 978-3-319-12475-9
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