The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent x belongs to a set known to the attacker. The complexity of generic algorithms f...
Abstract. Essentially all subexponential time algorithms for the discrete logarithm problem over nite elds are based on the index calculus idea. In proposing cryptosystems based on...
This paper extends the analysis of Pollard’s rho algorithm for solving a single instance of the discrete logarithm problem in a finite cyclic group G to the case of solving more...
At ISW’99, Nishioka, Hanaoka and Imai proposed a digital signature scheme on ID-based key-sharing infrastructures. That signature scheme is claimed to be secure if the discrete l...
Abstract. Frey and R¨uck gave a method to transform the discrete logarithm problem in the divisor class group of a curve over Fq into a discrete logarithm problem in some finite ...
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...
Abstract. Using a recent idea of Gaudry and exploiting rational representations of algebraic tori, we present an index calculus type algorithm for solving the discrete logarithm pr...
Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established prot...
Recently, the interest about the Tate pairing over binary fields has decreased due to the existence of efficient attacks to the discrete logarithm problem in the subgroups of su...