Titlebook: Coding Theory, Cryptography and Related Areas; Proceedings of an In Johannes Buchmann,Tom Høholdt,Horacio Tapia-Recill Conference proceedin

树木中

昏睡中

Efficient Reduction on the Jacobian Variety of Picard Curves,ric interpretation and provide us with an unifying environment to obtain an efficient algorithm for the reduction and addition of divisors. Exploiting the geometry of the Picard curves, a completely effective reduction algorithm is developed, which works for curves defined over any ground fieldk, wi

细查

Efficient Algorithms for the Jacobian Variety of Hyperelliptic Curves y,=x,-x+1 Over a Finite Fieldistic .. We first determine the zeta function of the curve which yields the order of the Jacobian. We also investigate the Frobenius operator and use it to show that, for field extensionsequation y.=x.-x+1 over a finite field ..., of degree . prime to ., the Jacobian has a cyclic group structure. We

不可救药

On Weierstrass Semigroups and One-point Algebraic Geometry Codes,plane model of the curve. The first one works in a quite general situation and it is founded on the Brill-Noether algorithm. The second method works in the case of . being the only point at infinity of the plane model, what is very usual in practice, and it is based on the Abhyankar-Moh theorem, the

Melanocytes

A Public Key Cryptosystem Based on Sparse Polynomials,d give some security analysis. Some preliminary timings are presented as well, which compare quite favourably with published optimized RSA timings. We believe that similar ideas can be used in some other settings as well.

倾听

ARC

谄媚于人

Zeta Functions of Curves over Finite Fields with Many Rational Points,n most cases come from the optimization of the explicit formulae method, which is detailed in [7] and [9]. In [4], we gave an example of a case where the best known bound could not be met. The purpose of this paper is to give another new example of this phenomenon, and to explain the method used to

incarcerate

Elliptic Curves, Pythagorean Triples and Applications,ways a multiple of eight. Moreover, a sub-family of them is also introduced: the curves which are associated with pythagorean triples, for which there exists a rational distinguished point. The number of such triples in ℤ., is given. Finally, a refinement on the Goldwasser-Kilian primality test is s

胡言乱语

Exponential Sums and Stationary Phase (I),especialy those arising from p-adic fields. The principal theme is the application of the classical method of stationary phase in a number theoretic context. After surveying the well known results of Kummer, Lamprecht, and Dwork, we indicate some generalizations which include and extend certain resu