Abstract
In this paper we show how using a representation of an ellip-tic curve as the intersection of two quadrics in ℙ3 can provide a defence against Simple and Differental Power Analysis (SPA/DPA) style attacks. We combine this with a ‘random window’ method of point multiplication and point blinding. The proposed method offers considerable advantages over standard algorithmic techniques of preventing SPA and DPA which usually require a significant increased computational cost, usually more than double. Our method requires roughly a seventy percent increase in computational cost of the basic cryptographic operation, although we give some indication as to how this can be reduced. In addition we show that the Jacobi form is also more efficient than the standard Weierstrass form for elliptic curves in the situation where SPA and DPA are not a concern.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
I.F. Blake, G. Seroussi and N.P. Smart. Elliptic curves in cryptography. Cambridge University Press, 1999.
J.W.S. Cassels. Lectures on Elliptic Curves. LMS Student Texts, Cambridge University Press, 1991.
J.W.S. Cassels and E.V. Flynn. Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2. Cambridge University Press, 1996.
D.V. Chudnovsky and G.V. Chudnovsky. Sequences of numbers generated by addition in formal groups and new primality and factorisation tests. Adv. in Appl. Math., 7, 385–434, 1987.
H. Cohen, A. Miyaji and T. Ono. Efficient elliptic curve exponentiation using mixed coordinates. In Advances in Cryptology, ASIACRYPT 98. Springer-Verlag, LNCS 1514, 51–65, 1998.
N.A. Howgrave-Graham and N.P. Smart. Lattice attacks on digital signature schemes. To appear Designs, Codes and Cryptography.
P. Kocher, J. Jaffe and B. Jun. Differential power analysis. In Advances in Cryptology, CRYPTO’ 99, Springer LNCS 1666, pp 388–397, 1999.
J.R. Merriman, S. Siksek, and N.P. Smart. Explicit 4-descents on an elliptic curve. Acta. Arith., 77, 385–404, 1996.
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
Liardet, P.Y., Smart, N.P. (2001). Preventing SPA/DPA in ECC Systems Using the Jacobi Form. In: Koç, Ç.K., Naccache, D., Paar, C. (eds) Cryptographic Hardware and Embedded Systems — CHES 2001. CHES 2001. Lecture Notes in Computer Science, vol 2162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44709-1_32
Download citation
DOI: https://doi.org/10.1007/3-540-44709-1_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42521-2
Online ISBN: 978-3-540-44709-2
eBook Packages: Springer Book Archive