Index calculus algorithm

In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in

Roughly speaking, the discrete log problem asks us to find an x such that g, modulus {−1,2,3,5,7,11,…,pr}, of length gx=hmodq.

• relations ← empty_list
• for ei's such that ei's as a vector −1 and the second element is the discrete log of gshmodq=(−1)f02f13f2⋯prfr over the factor base
• When a factorization is found:
  • Output p, the state-of-art algorithms are the Number Field Sieve for Discrete Logarithms, q, the function field sieve, c>0, when Lq[1/3,c] for 0"}}'>c>0 when c>0, but the general case remains exponential.

    External links

    edit
    • Discrete logarithms in finite fields and their cryptographic significance, by Andrew Odlyzko
    • Discrete Logarithm Problem, by Chris Studholme, including the June 21, 2002 paper "The Discrete Log Problem".
    • A. Menezes; P. van Oorschot; S. Vanstone (1997). Handbook of Applied Cryptography. CRC Press. pp. 107–109. ISBN 0-8493-8523-7.

    Notes

    edit
  • ↑ L(1/4 + o(1))</math> in very small characteristic"},"editor-last1":{"wt":"Lange"},"editor-first1":{"wt":"Tanja"},"editor-link1":{"wt":"Tanja Lange"},"editor-last2":{"wt":"Lauter"},"editor-first2":{"wt":"Kristin"},"editor-link2":{"wt":"Kristin Lauter"},"editor-last3":{"wt":"Lisoněk"},"editor-first3":{"wt":"Petr"},"conference":{"wt":"Selected Areas in Cryptography&mdash;SAC 2013"},"date":{"wt":"August 2013"},"conference-url":{"wt":"https://link.springer.com/book/10.1007/978-3-662-43414-7"},"volume":{"wt":"8282"},"series":{"wt":"Lecture Notes in Computer Science"},"publisher":{"wt":"Springer"},"location":{"wt":"Burnaby, BC, Canada"},"isbn":{"wt":"978-3-662-43414-7"},"pages":{"wt":"355&ndash;379"},"doi":{"wt":"10.1007/978-3-662-43414-7_18"},"doi-access":{"wt":"free"}},"i":0}}]}'/>Joux, Antoine (August 2013). Lange, Tanja; Lauter, Kristin; Lisoněk, Petr (eds.). A new index calculus algorithm with complexity