Abstract
In this paper we address two important topics in hyperelliptic cryptography. The first is how to construct in a verifiably random manner hyperelliptic curves for use in cryptography in generas two and three. The second topic is how to perform divisor compression in the hyperelliptic case. Hence, in both cases we generalise concepts used in the more familiar elliptic curve case to the hyperelliptic context.
References
X9.62 Public Key Cryptography For The Financial Services Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA). American National Standards Institute, 1999.
D.G. Cantor. Computing in the Jacobian of a hyperelliptic curve. Math. Comp., 48, 95–101, 1987.
M. Fouquet, P. Gaudry and R. Harley. An extension of Satoh’s algorithm and its implementation. J. Ramanujan Math. Soc., 15, 281–318, 2000.
G. Frey and H.-G. Rück. A remark concerning m-divisibility and the discrete logarithm problem in the divisor class group of curves. Math. Comp., 62, 865–874, 1994.
G. Frey, Applications of arithmetical geometry to cryptographic constructions, Preprint, 2000.
S.D. Galbraith. Limitations of constructive Weil descent. To appear Proceedings of a Conference on Cryptography and Computational Number Theory,Warsaw, Sept 2000.
P. Gaudry. An algorithm for solving the discrete log problem on hyperelliptic curves. Advances in Cryptology, EUROCRYPT 2000, Springer-Verlag LNCS 1807, 19–34, 2000.
P. Gaudry and R. Harley. Counting points on hyperelliptic curves over finite fields. ANTS-IV, Springer-Verlag LNCS 1838, 313–332, 2000.
P. Gaudry, F. Hess and N.P. Smart. Constructive and destructive facets of Weil descent on elliptic curves. To appear J. Cryptology.
K. Kedlaya. Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology. Preprint 2001.
N. Koblitz. Elliptic curve cryptosystems. Math. Comp., 48, 203–209, 1987.
N. Koblitz. Hyperelliptic cryptosystems. J. Cryptology, 1, 139–150, 1989.
V. Miller. Use of elliptic curves in cryptography. Advances in Cryptology, CRYPTO—’85, Springer-Verlag LNCS 218, 47–426, 1986.
T. Satoh. The canonical lift of an ordinary elliptic curve over a finite field and its point counting. J. Ramanujan Math. Soc., 15, 247–270, 2000.
B. Skjernaa. Satoh’s algorithm in characteristic two. Preprint 2000.
N.P. Smart. On the performance of hyperelliptic cryptosystems. Advances in Cryptology,EUROCRYPT’ 99, Springer-Verlag, LNCS 1592, 165–175, 1999.
A.-M. Spallek, Kurven vom Geschlecht 2 und ihre Anwendung in Public-Key-Kryptosystemen, PhD Thesis, IEM Essen, 1994.
F. Vercauteren, B. Preneel and J. Vandewalle. A memory e.cient version of Satoh’s algorithm. Advances in Cryptology,EUROCRYPT 2001, Springer-Verlag, LNCS 2045, 1–13, 2001.
A. Weng, Constructing hyperelliptic curves of genus 2 suitable for cryptography, Preprint, 2000.
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Hess, F., Seroussi, G., Smart, N.P. (2001). Two Topics in Hyperelliptic Cryptography. In: Vaudenay, S., Youssef, A.M. (eds) Selected Areas in Cryptography. SAC 2001. Lecture Notes in Computer Science, vol 2259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45537-X_14
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DOI: https://doi.org/10.1007/3-540-45537-X_14
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