Using number fields to compute logarithms in finite fields

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by Oliver Schirokauer
Venue:Math. Comp
Citations:13 - 2 self

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24 Discrete Logarithms: the Effectiveness of the Index Calculus Method – Oliver Schirokauer, Damian Weber, Thomas Denny - 1996
Cryptographic Primitives – Paul Garrett - 2007
Algorithmic Number Theory MSRI Publications – Oliver Schirokauer
40 Algorithms in algebraic number theory – H. W. Lenstra - 1992
6 Cover and Decomposition Index Calculus on Elliptic Curves made practical. Application to a seemingly secure curve over Fp6. Cryptology ePrint Archive, Report 2011/020, 2011. http: //eprint.iacr.org – Antoine Joux, Vanessa Vitse
26 Open Problems in Number Theoretic Complexity, II – Leonard M. Adleman, Kevin S. Mccurley
4 Discrete logarithms in curves over finite fields – Andreas Enge - 2007
On class group computations using the number field sieve – Mark L. Bauer, Safuat Hamdy - 2003
4 An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves, 2009, http://hal.inria.fr/inria-00383941/en/, Accepted for publication in Journal of Cryptology – Andreas Enge, Pierrick Gaudry, Emmanuel Thomé
1 On taking square roots and constructing quadratic nonresidues over finite fields – Tsz-Wo Sze - 2007
6 Mathematical Background of Public Key Cryptography – Gerhard Frey, Tanja Lange - 2005
Algorithms 63 11.8 Discrete logarithms over finite fields – unknown authors
1 On Taking Square Roots without Quadratic Nonresidues over Finite Fields – Tsz-wo Sze - 2009
1 Approximate Constructions In Finite Fields – Igor Shparlinski
Algorithms 61 11.6 Discrete logarithms over finite fields – Andrew Odlyzko
4 On Solving Univariate Polynomial Equations over Finite Fields and Some Related Problems – Tsz-wo Sze - 2007
Abelian Groups, Gauß Periods, and Normal Bases – Shuhong Gao
A New Special-Purpose Factorization Algorithm – Qi Cheng
3 COMPRESSION IN FINITE FIELDS AND TORUS-BASED CRYPTOGRAPHY – K. Rubin, A. Silverberg