Abstract
In this paper we use the Hessian form of an elliptic curve and show that it offers some performance advantages over the standard representation. In particular when a processor allows the evaluation of a number of field multiplications in parallel (either via separate ALU’s, a SIMD type operation or a pipelined multiplication unit) one can obtain a performance advantage of around forty percent.
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
J.W.S. Cassels. Lectures on Elliptic Curves. LMS Student Texts, Cambridge University Press, 1991.
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.
C. Clapp. Instruction level parallelism in AES Candidates. Second Advanced Encryption Standard Candidate Conference, Rome March 1999.
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.
M. Desboves. Résolution en nombres entiers et sous sa forme la plus générale, de l’équation cubique, homogéne, á trois inconnues. Nouvelles Ann. de Math., 45, 545–579, 1886.
C.K. Koc, T. Acer and B.S. Kaliski Jnr. Analyzing and comparing Montgomery multiplication algorithm. IEEE Micro, 16, 26–33, June 1996.
J. López and R. Dahab. Improved algorithms for elliptic curve arithmetic in GF(2n) In Selected Areas in Cryptography-SAC’ 98, Springer-Verlag, LNCS 1556, 201–212, 1999.
G. Orlando and C. Paar. A high-performance reconfigurable elliptic curve processor for GF(2m). In Cryptographic Hardware and Embedded Systems (CHES) 2000, Springer-Verlag, LNCS 1965, 41–56, 2000.
A.D. Woodbury, D.V. Bailey and C. Paar. Elliptic curve cryptography on smart cards without coprocessors. In Smart Card and Advanced Applications, CARDIS 2000, 71–92, Kluwer, 2000.
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
Smart, N.P. (2001). The Hessian Form of an Elliptic Curve. 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_11
Download citation
DOI: https://doi.org/10.1007/3-540-44709-1_11
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