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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 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.
ECC2K-108, involving taking a discrete logarithm on a Koblitz curve over a field of 2 108 elements. The prize was awarded on 4 April 2000 to a group of about 1300 people represented by Robert Harley. They used a parallelized Pollard rho method with speedup. ECC2-109, involving taking a discrete logarithm on a curve over a field of 2 109 ...
The algorithm is performed in three stages. The first two stages depend only on the generator g and prime modulus q, and find the discrete logarithms of a factor base of r small primes. The third stage finds the discrete log of the desired number h in terms of the discrete logs of the factor base.
The errors are believed to make the problem intractable (for appropriate parameters); in particular, there are known worst-case to average-case reductions from variants of SVP. [12] For quantum computers, Factoring and Discrete Log problems are easy, but lattice problems are conjectured to be hard. [13]
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 ...
The development of MOOSE at Idaho National Laboratory (INL) since May 2008, has resulted in a unique approach to computational engineering that combines computer science with a strong underlying mathematical description in a unique way that allows scientists and engineers to develop engineering simulation tools in a fraction of the time previously required. [2]
Tracing in software engineering refers to the process of capturing and recording information about the execution of a software program. This information is typically used by programmers for debugging purposes, and additionally, depending on the type and detail of information contained in a trace log, by experienced system administrators or technical-support personnel and by software monitoring ...