Search results
Results from the WOW.Com Content Network
The discrete logarithm problem is considered to be computationally intractable. That is, no efficient classical algorithm is known for computing discrete logarithms in general. A general algorithm for computing log b a in finite groups G is to raise b to larger and larger powers k until the desired a is found.
In April 2014, Erich Wenger and Paul Wolfger from Graz University of Technology solved the discrete logarithm of a 113-bit Koblitz curve in extrapolated [note 1] 24 days using an 18-core Virtex-6 FPGA cluster. [36] In January 2015, the same researchers solved the discrete logarithm of an elliptic curve defined over a 113-bit binary field.
There are two other well known algorithms that solve the discrete logarithm problem in sub-exponential time: the index calculus algorithm and a version of the Number Field Sieve. [5] In their easiest forms both solve the DLP in a finite field of prime order but they can be expanded to solve the DLP in as well.
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in (/) where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves. The algorithm collects relations among the ...
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorization problem.
In group theory, a branch of mathematics, the baby-step giant-step is a meet-in-the-middle algorithm for computing the discrete logarithm or order of an element in a finite abelian group by Daniel Shanks. [1] The discrete log problem is of fundamental importance to the area of public key cryptography.
As of 2006, the most efficient means known to solve the DHP is to solve the discrete logarithm problem (DLP), which is to find x given g and g x. In fact, significant progress (by den Boer, Maurer, Wolf, Boneh and Lipton) has been made towards showing that over many groups the DHP is almost as hard as the DLP. There is no proof to date that ...
The discrete logarithm algorithm and the factoring algorithm are instances of the period-finding algorithm, and all three are instances of the hidden subgroup problem. On a quantum computer, to factor an integer N {\displaystyle N} , Shor's algorithm runs in polynomial time , meaning the time taken is polynomial in log N {\displaystyle \log ...