On the discrete logarithm problem for plane curves
نویسنده
چکیده
In this article the discrete logarithm problem in degree 0 class groups of curves over finite fields given by plane models is studied. It is proven that the discrete logarithm problem in degree 0 class groups of non-hyperelliptic curves of genus 3 (given by plane models of degree 4) can be solved in an expected time of Õ(q), where q is the cardinality of the ground field. Moreover, it is proven that for every fixed natural number d ≥ 4 such that d or d − 1 is prime, the discrete logarithm problem for curves given by reflexive plane models of degree d can be solved in an expected time of Õ(q 2 d−2 ).
منابع مشابه
Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves
Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
متن کاملAn efficient blind signature scheme based on the elliptic curve discrete logarithm problem
Elliptic Curve Cryptosystems (ECC) have recently received significant attention by researchers due to their high performance such as low computational cost and small key size. In this paper a novel untraceable blind signature scheme is presented. Since the security of proposed method is based on difficulty of solving discrete logarithm over an elliptic curve, performance of the proposed scheme ...
متن کاملAn Efficient Threshold Verifiable Multi-Secret Sharing Scheme Using Generalized Jacobian of Elliptic Curves
In a (t,n)-threshold secret sharing scheme, a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together, but no group of fewer than t participants can do. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao, and the intractability of the elliptic curve discrete logar...
متن کاملThe new protocol blind digital signature based on the discrete logarithm problem on elliptic curve
In recent years it has been trying that with regard to the question of computational complexity of discrete logarithm more strength and less in the elliptic curve than other hard issues, applications such as elliptic curve cryptography, a blind digital signature method, other methods such as encryption replacement DLP. In this paper, a new blind digital signature scheme based on elliptic curve...
متن کاملOrdinary plane models and completely split divisors
Let C be a smooth, non-hyperelliptic curve over an algebraically closed field of genus g ≥ 4. We show that the projection from the canonical model of C through (g−3) generic points on C is a birational morphism to a plane curve which has only finitely many non-ordinary tangents, that is, flexor bitangents. For smooth, non-hyperelliptic curves of a fixed genus g ≥ 4 over finite fields, we show t...
متن کامل