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The Multiple Number Field Sieve for Medium and High Characteristic > Finite Fields
public-key cryptography discrete logarithm problem
2016/1/25
In this paper, we study the discrete logarithm problem in medium and high characteristic finite fields. We propose a variant of the Number Field Sieve (NFS) based on numerous number fields. Our improv...
Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms - Simplified Setting for Small Characteristic Finite Fields
discrete logarithm problem finite fields
2016/1/6
In this paper, we revisit the recent small characteristic discrete logarithm algorithms. We show that a simplified description of the algorithm, together with some additional ideas, permits to obtain ...
Computing Discrete Logarithms in the Jacobian of High-Genus Hyperelliptic Curves over Even Characteristic Finite Fields
Computing Discrete Logarithms High-Genus Hyperelliptic Curves Characteristic Finite Fields
2011/3/10
We describe improved versions of index-calculus algorithms for
solving discrete logarithm problems in Jacobians of high-genus hyperelliptic
curves de ned over even characteristic elds. Our rst imp...
Computing Discrete Logarithms in the Jacobian of High-Genus Hyperelliptic Curves over Even Characteristic Finite Fields
foundations / hyperelliptic curves discrete logarithm problem sieving, Weil descent
2012/3/29
We describe improved versions of index-calculus algorithms for solving discrete logarithm problems in Jacobians of high-genus hyperelliptic curves defi ned over even characteristic fields. Our first i...
Generating genus two hyperelliptic curves over large characteristic finite fields
hyperelliptic curve point counting
2009/6/9
In hyperelliptic curve cryptography, finding a suitable hyperelliptic
curve is an important fundamental problem. One of necessary
conditions is that the order of its Jacobian is a product of a large...