Abstract
For making elliptic curve point multiplication secure against side-channel attacks, various methods have been proposed using special point representations for specifically chosen elliptic curves. We show that the same goal can be achieved based on conventional elliptic curve arithmetic implementations. Our point multiplication method is much more general than the proposals requiring non-standard point representations; in particular, it can be used with the curves recommended by NIST and SECG. It also provides efficiency advantages over most earlier proposals.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Blake, I. F., Seroussi, G., AND Smart, N. P. Elliptic Curves in Cryptography, vol. 265 of London Mathematical Society Lecture Note Series. Cambridge University Press, 1999.
Brown, M., Hankerson, D., López, J., AND Menezes, A. Software implementation of the NIST elliptic curves over prime fields. In Progress in Cryptology-CT-RSA 2001 (2001), D. Naccache, Ed., vol. 2020 of Lecture Notes in Computer Science, pp. 250–265.
Certicom Research. Standards for efficient cryptography-SEC 1: Elliptic curve cryptography. Version 1.0, 2000. Available from http://www.secg.org/.
Certicom Research. Standards for efficient cryptography-SEC 2: Recommended elliptic curve cryptography domain parameters. Version 1.0, 2000. Available http://www.secg.org/.
Cohen, H., Ono, T., AND Miyaji, A. Efficient elliptic curve exponentiation using mixed coordinates. In Advances in Cryptology-ASIACRYPT ’98 (1998), K. Ohta and D. Pei, Eds., vol. 1514 of Lecture Notes in Computer Science, pp. 51–65.
Coron, J.-S. Resistance against differential power analysis for elliptic curve cryptosystems. In Cryptographic Hardware and Embedded Systems-CHES ’99 (1999), C. K. Koç and C. Paar, Eds., vol. 1717 of Lecture Notes in Computer Science, pp. 292–302.
Institute of Electrical and Electronics Engineers (IEEE). IEEE standard specifications for public-key cryptography. IEEE Std 1363-2000, 2000.
Joye, M., AND Quisquater, J.-J. Hessian elliptic curves and side-channel attacks. In Cryptographic Hardware and Embedded Systems-CHES 2001 [Pre-]Proceedings (2001), C. K. Koç, D. Naccache, and C. Paar, Eds., pp. 412–420.
Kocher, P. C. Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In Advances in Cryptology-CRYPTO ’96 (1996), N. Koblitz, Ed., vol. 1109 of Lecture Notes in Computer Science, pp. 104–113.
Kocher, P. C., Jaffe, J., AND Jun, B. Differential power analysis. In Advances in Cryptology-CRYPTO ’99 (1999), M. Wiener, Ed., vol. 1666 of Lecture Notes in Computer Science, pp. 388–397.
Liardet, P.-Y., AND Smart, N. P. Preventing SPA/DPA in ECC systems using the Jacobi form. In Cryptographic Hardware and Embedded Systems-CHES 2001 [Pre-]Proceedings (2001), C. K. Koç, D. Naccache, and C. Paar, Eds., pp. 401–411.
Miyaji, A., Ono, T., AND Cohen, H. Efficient elliptic curve exponentiation. In International Conference on Information and Communications Security-ICICS ’97 (1997), Y. Han, T. Okamoto, and S. Qing, Eds., vol. 1334 of Lecture Notes in Computer Science, pp. 282–290.
Montgomery, P. L. Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation 48 (1987), 243–264.
National Institute of Standards and Technology (NIST). Digital Signature Standard (DSS). FIPS PUB 186-2, 2000.
Okeya, K., Kurumatani, H., AND Sakurai, K. Elliptic curves with the Montgomery-form and their cryptographic applications. In Public Key Cryptography-PKC 2000 (2000), H. Imai and Y. Zheng, Eds., vol. 1751 of Lecture Notes in Computer Science, pp. 238–257.
Okeya, K., AND Sakurai, K. Power analysis breaks elliptic curve cryptosystems even secure against the timing attack. In Progress in Cryptology-INDOCRYPT 2000 (2000), B. K. Roy and E. Okamoto, Eds., vol. 1977 of Lecture Notes in Computer Science, pp. 178–190.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Möller, B. (2001). Securing Elliptic Curve Point Multiplication against Side-Channel Attacks. In: Davida, G.I., Frankel, Y. (eds) Information Security. ISC 2001. Lecture Notes in Computer Science, vol 2200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45439-X_22
Download citation
DOI: https://doi.org/10.1007/3-540-45439-X_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42662-2
Online ISBN: 978-3-540-45439-7
eBook Packages: Springer Book Archive