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A cryptographic application of Weil descent
 CODES AND CRYPTOGRAPHY, LNCS 1746
, 1999
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On the performance of hyperelliptic cryptosystems
, 1999
"... In this paper we discuss various aspects of cryptosystems based on hyperelliptic curves. In particular we cover the implementation of the group law on such curves and how to generate suitable curves for use in cryptography. This paper presents a practical comparison between the performance of ellip ..."
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In this paper we discuss various aspects of cryptosystems based on hyperelliptic curves. In particular we cover the implementation of the group law on such curves and how to generate suitable curves for use in cryptography. This paper presents a practical comparison between the performance of elliptic curve based digital signature schemes and schemes based on hyperelliptic curves. We conclude that, at present, hyperelliptic curves offer no performance advantage over elliptic curves.
Fast Scalar Multiplication on the Jacobian of aFamily of Hyperelliptic Curves?
"... Abstract. Hyperelliptic curve cryptosystems (HCC for short) is a generalization of ECC. It has been drawing the attention of more and more researchers in recent years. The problem of how to decrease the amount of addition and scalar multiplication on the Jacobians of hyperelliptic curves so that the ..."
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Abstract. Hyperelliptic curve cryptosystems (HCC for short) is a generalization of ECC. It has been drawing the attention of more and more researchers in recent years. The problem of how to decrease the amount of addition and scalar multiplication on the Jacobians of hyperelliptic curves so that the implementation speed can be improved is very important for the practical use of HCC. In this paper, Using Frobenius endomorphism as a tool, we discuss the problem of faster scalar multiplication. A faster algorithm on Jacobian's scalar multiplication of a family of speci c hyperelliptic curves is proposed with its computational cost analyzed. Analysis reveals that our algorithms's computational cost is less than that of Signed Binary Method. 1
Internal Accession Date Only
, 1998
"... function fields, divisor class group, reduced ideals, cryptography Let F denote a function field of transcendence degree one over a finite field k. We assume that the field is tamely ramified at infinity, that the valuations at infinity of a set of fundamental units are known and we have gcd(f 1, … ..."
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function fields, divisor class group, reduced ideals, cryptography Let F denote a function field of transcendence degree one over a finite field k. We assume that the field is tamely ramified at infinity, that the valuations at infinity of a set of fundamental units are known and we have gcd(f 1, … , f s) = 1, where f i denotes the degree of a place at infinity. In such a situation we describe a simple arithmetic in the divisor class group. One draw back of this arithmetic is that we do not obtain a unique representative for each divisor class. The method makes use of multiplication and reduction of reduced fractional ideals.
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, 2011
"... ter verkrijging van de graad van do�or aan de Technische Universiteit Eindhoven, op gezag van de re�or magni�cus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 14 juli 2011 om 14.00 uur door ..."
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ter verkrijging van de graad van do�or aan de Technische Universiteit Eindhoven, op gezag van de re�or magni�cus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties in het openbaar te verdedigen op donderdag 14 juli 2011 om 14.00 uur door