论文信息 - Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic

Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic

We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality $p^n$ in expected time $(pn)^{2\log_2(n) + O(1)}$.

Thorsten Kleinjung | Benjamin Wesolowski | B. Wesolowski | T. Kleinjung

[1] Thorsten Kleinjung,et al. On the discrete logarithm problem in finite fields of fixed characteristic , 2015, IACR Cryptol. ePrint Arch..

[2] Benjamin Wesolowski. Arithmetic and geometric structures in cryptography , 2018 .

[3] Giacomo Micheli. On the Selection of Polynomials for the DLP Quasi-Polynomial Time Algorithm for Finite Fields of Small Characteristic , 2019, SIAM J. Appl. Algebra Geom..

[4] C. Diem. On the discrete logarithm problem in elliptic curves , 2010, Compositio Mathematica.

[5] W. Waterhouse,et al. Abelian varieties over finite fields , 1969 .

[6] P. Gaudry,et al. A general framework for subexponential discrete logarithm algorithms , 2002 .

[7] Michael Rosen,et al. Number Theory in Function Fields , 2002 .

[8] Villa Salvador,et al. Topics in the Theory of Algebraic Function Fields , 2006 .

[9] Joseph H. Silverman,et al. The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[10] Antoine Joux,et al. A Heuristic Quasi-Polynomial Algorithm for Discrete Logarithm in Finite Fields of Small Characteristic , 2014, EUROCRYPT.

[11] Thorsten Kleinjung,et al. A new perspective on the powers of two descent for discrete logarithms in finite fields , 2018, IACR Cryptol. ePrint Arch..

[12] Eric Bach,et al. Weil bounds for singular curves , 1996, Applicable Algebra in Engineering, Communication and Computing.

[13] C. Pomerance. Fast, Rigorous Factorization and Discrete Logarithm Algorithms , 1987 .