Abstract
In this paper we describe some countermeasures against differential side-channel attacks on hyperelliptic curve cryptosystems. The techniques are modelled on the corresponding ones for elliptic curves. The first method consists in picking a random group isomorphic to the one where we are supposed to compute, transferring the computation to the random group and then pulling the result back. The second method consists in altering the internal representation of the divisors on the curve in a random way. The impact of the recent attack of L. Goubin is assessed and ways to avoid it are proposed.
Chapter PDF
Similar content being viewed by others
Keywords
References
Agnew, G.B., Mullin, R.C., Vanstone, S.A.: An Implementation of Elliptic Curve Cryptosystems over \( F_{2^{155} } \). IEEE Journal on Selected Areas in Communications 11(2), 804–813 (1993)
Bellezza, A.: Countermeasures against Side-Channel Attacks for Elliptic Curve Cryptosystems. Cryptology ePrint Archive, Report 2001/103, Available from http://eprint.iacr.org/
Brier, E., Joye, M.: Weierstrass Elliptic Curves and Side-Channel Attacks. In: Naccache, D., Paillier, P. (eds.) PKC 2002. LNCS, vol. 2274, pp. 335–345. Springer, Heidelberg (2002)
Cantor, D.: Computing in the jacobian of a hyperelliptic curve. Mathematics of Computation 48, 95–101 (1987)
Chudnovsky, D.V., Chudnovsky, G.V.: Sequences of numbers generated by addition in formal groups and new primality and factoring tests. Advances in Applied Mathematics 7, 385–434 (1987)
Clavier, C., Joye, M.: Universal exponentiation algorithm - a first step towards provable SPA-resistance. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 300–308. Springer, Heidelberg (2001)
Coron, J.-S.: Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 292–302. Springer, Heidelberg (1999)
Fischer, W., Giraud, C., Knudsen, E.W., Seifert, J.-P.: Parallel Scalar Multiplication on General Elliptic Curves over Fp hedged against Differential Side Channel Attacks. Cryptology ePrint Archive, Report 2002/007 (2002), Available from http://eprint.iacr.org/
Frey, G.: How to disguise an elliptic curve (Weil descent). Talk at ECC 1998, Waterloo (1998), Slides available from http://www.cacr.math.uwaterloo.ca/conferences/1998/ecc98/slides.html
Frey, G.: Applications of arithmetical geometry to cryptographic constructions. In: Finite fields and applications (Augsburg, 1999), pp. 128–161. Springer, Heidelberg (2001)
Galbraith, S.D.: Supersingular curves in cryptography. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 495–513. Springer, Heidelberg (2001)
Gaudry, P.: An algorithm for solving the discrete log problem on hyperelliptic curves. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 19–34. Springer, Heidelberg (2000)
Goubin, L.: A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 199–211. Springer, Heidelberg (2002)
Izu, T., Takagi, T.: Exceptional procedure attackon elliptic curve cryptosystems. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 224–239. Springer, Heidelberg (2002)
Joye, M., Quisquater, J.-J.: Hessian Elliptic Curves and Side-Channel Attacks. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 412–420. Springer, Heidelberg (2001)
Joye, M., Tymen, C.: Protections against Differential Analysis for Elliptic Curve Cryptography – An Algebraic Approach. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 377–390. Springer, Heidelberg (2001)
Koblitz, N.: A family of Jacobians suitable for discrete log cryptosystems. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 94–99. Springer, Heidelberg (1990)
Koblitz, N.: Hyperelliptic Cryptosystems. Journal of Cryptology 1, 139–150 (1989)
Koblitz, N.: Algebraic aspects of cryptography. Springer, Heidelberg (1998)
Kocher, P.C.: Timing attacks on implementations of Diffie-Hellman, RSA, DSS and other systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)
Kocher, P., Jaffe, J., Jun, B.: Introduction to Differential Power Analysis and Related Attacks (1998), Available from http://www.cryptography.com/dpa/technical
Kocher, P., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
Kuroki, J., Gonda, M., Matsuo, K., Chao, J., Tsujii, S.: Fast Genus Three Hyperelliptic Curve Cryptosystems. In: The 2002 Symposium on Cryptography and Information Security, Japan - SCIS 2002, January 29–Feruary 1 (2002)
Lange, T.: Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae. Cryptology ePrint Archive, Report 2002/121, Available from http://eprint.iacr.org/ – See also [27]
Lange, T.: Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves. Cryptology ePrint Archive, Report 2002/147, Available from http://eprint.iacr.org/ – See also [27]
Lange, T.: Weighted Coordinates on Genus 2 Hyperelliptic Curves. Cryptology ePrint Archive, Report 2002/153, Available from http://eprint.iacr.org/ – See also [27]
Lange, T.: Formulae for Arithmetic on Genus 2 Hyperelliptic Curves, It partially contains and extends the material of the previous three papers [24, 25,26], Available from http://www.ruhr-uni-bochum.de/itsc/tanja/ (Preprint)
Liardet, P.-Y., Smart, N.P.: Preventing SPA/DPA in ECC system using the Jacobi Form. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 401–411. Springer, Heidelberg (2001)
Lockhart, P.: On the discriminant of a hyperelliptic curve. Trans. Amer. Math. Soc. 342(2), 729–752 (1994)
López, J., Dahab, R.: Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 316–327. Springer, Heidelberg (1999)
Menezes, A., Wu, Y.-H., Zuccherato, R.: An Elementary Introduction to Hyperelliptic Curves. In: [19]
Miyamoto, Y., Doi, H., Matsuo, K., Chao, J., Tsuji, S.: A fast addition algorithm of genus two hyperelliptic curve. In: Proceedings of SCIS 2002, pp. 497–502. IEICE, Japan (2002) (in Japanese)
Montgomery, P.L.: Speeding the Pollard and Elliptic Curve Methods for Factorizations. Mathematics of Computation 48, 243–264 (1987)
Möller, B.: Securing Elliptic Curve Point Multiplication against Side-Channel Attacks. In: Davida, G.I., Frankel, Y. (eds.) ISC 2001. LNCS, vol. 2200, pp. 324–334. Springer, Heidelberg (2001)
Mumford, D.: Tata Lectures on Theta II. Birkhäuser, Basel (1984)
Okeya, K., Sakurai, K.: Power analysis breaks elliptic curve cryptosystems even secure against the timing attack. In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol. 1977, pp. 178–190. Springer, Heidelberg (2000)
Okeya, K., Kurumatani, H., Sakurai, K.: Elliptic curves with the Montgomery–form and their cryptographic applications. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 238–257. Springer, Heidelberg (2000)
Pelzl, J., Wollinger, T., Guajardo, J., Paar, C.: Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 351–365. Springer, Heidelberg (2003)
Scholten, J., Zhu, H.J.: Hyperelliptic curves in characteristic 2. Inter. Math. Research Notices 17, 905–917 (2002)
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)
Walter, C.D.: MIST: An Efficient, Randomized Exponentiation Algorithm for Resisting Power Analysis. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 53–66. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Avanzi, R.M. (2003). Countermeasures against Differential Power Analysis for Hyperelliptic Curve Cryptosystems. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds) Cryptographic Hardware and Embedded Systems - CHES 2003. CHES 2003. Lecture Notes in Computer Science, vol 2779. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45238-6_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-45238-6_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40833-8
Online ISBN: 978-3-540-45238-6
eBook Packages: Springer Book Archive