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Nowadays, elliptic curve cryptosystems receive attention and much effort is being dedicated to make it more and more practical. It is worthwhile to construct discrete logarithm based cryptosystems using more general algebraic curves, because it supplies more security sources for public key cryptosystems. The presented paper introduces Cab curves. Roughly(More)
This paper shows that many of elliptic curve cryptosystems over quartic extension fields of odd characteristics are reduced to genus two hyperelliptic curve cryptosystems over quadratic extension fields. Moreover, it shows that almost all of the genus two hyperelliptic curve cryptosystems over quadratic extension fields of odd characteristics come under(More)
This paper proposes a heuristic algorithm which, given a basis of a subspace of the space of cuspforms of weight 2 for Γ0(N) which is invariant for the action of the Hecke operators, tests whether the subspace corresponds to a quotient A of the jacobian of the modular curve X0(N) such that A is the jacobian of a curve C. Moreover, equations for such a curve(More)
We have designed and experimentally implemented a tool for developing a natural language systems tha t can accept extra-grammatical expressions, keyword sequences, and linguistic fragments, as well as ordi nary na tura l language queries. The key to this tool 's efficiency is its effective use of a simple keyword analyzer in combination with a conventional(More)
Gaudry has described a new algorithm (Gaudry’s variant) for the discrete logarithm problem (DLP) in hyperelliptic curves. For a hyperelliptic curve of a small genus on a finite field GF(q), Gaudry’s variant solves for the DLP in time O(q2+2). This paper shows that Cab curves can be attacked with a modified form of Gaudry’s variant and presents the timing(More)
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