Abstract
In recent years, fault attacks have been developed to be very powerful tools in the field of attack against crypto-algorithm. The basic idea of fault attacks is through provoking disturbances, then an adversary is able to recover some secret data from a carelessly implemented crypto-algorithm. As we known the Miller’s algorithm is the critical step for bilinear pairing calculation. Since the Miller’s algorithm is usually embedded in identity aware devices such as smart card, a lot of attentions are attracted to analyze these devices. In this paper, we investigate a new approach based on the resolution of a nonlinear system, and this approach has an advantage that the pairing based cryptography in Hessian coordinates is vulnerable to a fault attack.
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References
Anderson, R., Kuhn, M.: Tamper Resistance-a Cautionary Note. In: The Second USENIX Workshop on Electronic Commerce Proceedings, Okland, California, pp. 1–11 (1996)
Bajard, J.C., El Mrabet, N.: Pairing in cryptography: an arithmetic point de view. In: Advanced Signal Processing Algorithms, Architectures, and Implementations XVI, part of SPIE (August 2007)
Boneh, D., Franklin, M.: Identity-Based Encryption from the Weil Pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)
Chudnovsky, D.V., Chudnovsky, G.V.: Sequences of numbers generated by addition in formal groups and new primality and factorisation tests. Adv. in Appl. Math. 7, 385–434 (1987)
Dan, P., Frederik, V.: Fault and Side Channel Attacks on Pairing based Cryptography. IEEE Transactions on Computers 55(9), 1075–1080 (2006)
El Mrabet, N.: What about Vulnerability to a Fault Attack of the Miller’s Algorithm During an Identity Based Protocol? In: Park, J.H., Chen, H.-H., Atiquzzaman, M., Lee, C., Kim, T.-H., Yeo, S.-S. (eds.) ISA 2009. LNCS, vol. 5576, pp. 122–134. Springer, Heidelberg (2009)
Habing, D.H.: The Use of Lasers to Simulate Radiation-Induced Transients in Semiconductor Devices and Circuits. IEEE Transactions on Nuclear Science 39, 1647–1653 (1992)
Miller, V.: The Weil pairing and its efficient calculation. Journal of Cryptology 17, 235–261 (2004)
Smart, N.P.: The Hessian Form of an Elliptic Curve. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 118–125. Springer, Heidelberg (2001)
PARI/GP, version2.1.7, Bordeaux 2005 (2005), http://pari.math.u-bordeaux.fr/
Shamir, A.: Identity-Based Cryptosystems and Signature Schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)
Whelan, C., Scott, M.: Side Channel Analysis of Practical Pairing Implementations: Which Path Is More Secure? In: Nguyên, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol. 4341, pp. 99–114. Springer, Heidelberg (2006)
Whelan, C., Scott, M.: The Importance of the Final Exponentiation in Pairings When Considering Fault Attacks. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 225–246. Springer, Heidelberg (2007)
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Weng, J., Dou, Y., Ma, C. (2012). Fault Attacks against the Miller Algorithm in Hessian Coordinates. In: Wu, CK., Yung, M., Lin, D. (eds) Information Security and Cryptology. Inscrypt 2011. Lecture Notes in Computer Science, vol 7537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34704-7_9
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DOI: https://doi.org/10.1007/978-3-642-34704-7_9
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