ASIACRYPT
2000
Springer
13 years 9 months ago
2000
Springer
Abstract. Construction of secure hyperelliptic curves is of most important yet most difficult problem in design of cryptosystems based on the discrete logarithm problems on hyperel...
ASIACRYPT
2001
Springer
13 years 9 months ago
2001
Springer
We present an algorithm for counting points on superelliptic curves yr = f(x) over a finite field Fq of small characteristic different from r. This is an extension of an algorit...
ASIACRYPT
2003
Springer
13 years 9 months ago
2003
Springer
We present a variation of the index calculus attack by Gaudry which can be used to solve the discrete logarithm problem in the Jacobian of hyperelliptic curves. The new algorithm h...
WISA
2004
Springer
13 years 10 months ago
2004
Springer
Abstract. Cryptographic algorithms are used in a large variety of different applications to ensure security services. It is, thus, very interesting to investigate various implement...
CHES
2004
Springer
13 years 10 months ago
2004
Springer
We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3 over prime fields. To achieve a fair comparison between the different types of groups,...
ANTS
2004
Springer
13 years 10 months ago
2004
Springer
Using powerful tools on genus 2 curves like the Kummer variety, we generalize the Montgomery method for scalar multiplication to the jacobian of these curves. Previously this metho...
ITCC
2005
IEEE
13 years 10 months ago
2005
IEEE
Recently, a lot of effort has been done to investigate all kinds of explicit formulae for speeding up group operation of hyperelliptic curve cryptosystem (HECC). In this paper, ex...
PAIRING
2007
Springer
13 years 10 months ago
2007
Springer
We assemble and reorganize the recent work in the area of hyperelliptic pairings: We survey the research on constructing hyperelliptic curves suitable for pairing-based cryptograph...
EUROCRYPT
2007
Springer
13 years 10 months ago
2007
Springer
Abstract. In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has...
DCC
2005
IEEE
14 years 4 months ago
2005
IEEE
We present a family of hyperelliptic curves whose Jacobians are suitable for cryptographic use, and whose parameters can be specified in a highly efficient way. This is done via co...