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Index calculus algorithm
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#	Item
11	Discrete logarithm in GFwith FFS Razvan Barbulescu, Cyril Bouvier, Jérémie Detrey, Pierrick Gaudry, Hamza Jeljeli, Emmanuel Thomé, Marion Videau, and Paul Zimmermann CARAMEL project-team, LORIA, INRIA / CNRS / Add to Reading List Source URL: www.loria.fr Language: English - Date: 2014-01-09 15:35:58 Finite fields Logarithms Group theory Integer factorization algorithms Cryptography Index calculus algorithm XTR Polynomial Discrete logarithm Abstract algebra Mathematics Algebra
12	Imperfect Forward Secrecy: How Diffie-Hellman Fails in Practice David Adrian¶ Karthikeyan Bhargavan∗ Zakir Durumeric¶ Pierrick Gaudry† Matthew Green§ J. Alex Halderman¶ Nadia Heninger‡ Drew Springall¶ Emmanuel Add to Reading List Source URL: weakdh.org Language: English - Date: 2015-05-22 22:25:48 Finite fields Computational hardness assumptions Group theory Diffie–Hellman key exchange XTR Secure Shell Cipher suite Index calculus algorithm Elliptic curve Diffie–Hellman Cryptography Abstract algebra Cryptographic protocols
13	Motivation and Results Algebraic Tori Algorithm for T2 Algorithm for T6 Summary and Future Work Add to Reading List Source URL: www.iacr.org Language: English - Date: 2005-09-05 15:48:18 Index calculus algorithm Field Algorithm Group Algebraic structures Mathematics Group theory
14	Simplified Settings for Discrete Logarithms in Small Characteristic Finite Fields Antoine Joux CryptoExperts, Fondation UPMC, LIP6, INRIA/Ouragan Joint work with Cécile Pierrot Add to Reading List Source URL: www.iacr.org Language: English - Date: 2015-03-30 09:17:58 Logarithms Computational hardness assumptions Finite fields Modular arithmetic Discrete logarithm Index calculus algorithm Hyperelliptic curve Elliptic curve Pohlig–Hellman algorithm Abstract algebra Mathematics Group theory
15	A new index calculus algorithm with complexity L(1/4 + o(1)) in small characteristic Antoine Joux CryptoExperts and Universit´e de Versailles Saint-Quentin-en-Yvelines, Laboratoire PRISM, Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2013-07-24 03:29:23 Polynomials Finite field Irreducible polynomial XTR General number field sieve Field Monic polynomial Factorization of polynomials over a finite field and irreducibility tests Cantor–Zassenhaus algorithm Abstract algebra Algebra Mathematics
16	Some experiments investigating a possible L(1/4) algorithm for the discrete logarithm problem in algebraic curves Maike Massierer∗ LORIA, Campus Scientifique, BP 239, 54506 Vandœuvre-l`es-Nancy Cedex, France maike.mas Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2014-12-13 07:45:36 Polynomials Computer algebra Integer factorization algorithms Group theory General number field sieve Factorization of polynomials Logarithm Finite field Index calculus algorithm Abstract algebra Mathematics Algebra
17	Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Fields Jean-Charles Faug`ere1 Ludovic Perret1 Gu´ena¨el Renault1 Add to Reading List Source URL: www.iacr.org Language: English - Date: 2012-04-20 07:14:48 Group theory Cryptography Logarithms Computational hardness assumptions Index calculus algorithm Discrete logarithm Elliptic curve XTR Polynomial Abstract algebra Algebra Finite fields
18	Cover and Decomposition Index Calculus on Elliptic Curves made practical Application to a previously unreachable curve over Fp6 Vanessa VITSE – Antoine JOUX Universit´ Add to Reading List Source URL: www.iacr.org Language: English - Date: 2012-04-20 07:04:20 Finite fields Cryptography Logarithms Computational hardness assumptions Index calculus algorithm Elliptic curve cryptography Elliptic curve Discrete logarithm Calculus Abstract algebra Mathematics Group theory
19	ANOTHER LOOK AT NON-STANDARD DISCRETE LOG AND DIFFIE-HELLMAN PROBLEMS NEAL KOBLITZ AND ALFRED MENEZES Abstract. We examine several versions of the one-more-discrete-log and one-more-Diffie-Hellman problems. In attempting Add to Reading List Source URL: eprint.iacr.org Language: English - Date: 2008-09-21 19:02:16 Finite fields Computational hardness assumptions Cryptographic protocols Group theory Diffie–Hellman problem XTR Index calculus algorithm Diffie–Hellman key exchange Random oracle Cryptography Abstract algebra Mathematics
20	Index Calculus Attack for Hyperelliptic Curves of Small Genus Nicolas Th´eriault University of Toronto Abstract. We present a variation of the index calculus attack by Gaudry Add to Reading List Source URL: www.iacr.org Language: English - Date: 2008-09-15 00:54:54 Finite fields Integer sequences Field theory Computer algebra Divisor Ample line bundle Cantor–Zassenhaus algorithm Prime number Anatolii Alexeevitch Karatsuba Abstract algebra Mathematics Algebra