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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.
The discrete logarithm is the integer n solving the equation =, where x is an element of the group. Carrying out the exponentiation can be done efficiently, but the discrete logarithm is believed to be very hard to calculate in some groups.
The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science.The framework captures problems such as factoring, discrete logarithm, graph isomorphism, and the shortest vector problem.
Computing the discrete logarithm is the only known method for solving the CDH problem. But there is no proof that it is, in fact, the only method. It is an open problem to determine whether the discrete log assumption is equivalent to the CDH assumption, though in certain special cases this can be shown to be the case. [3] [4]
For example, a logarithm of base 2 8 = 256 will produce a measurement in bytes per symbol, and a logarithm of base 10 will produce a measurement in decimal digits (or hartleys) per symbol. Intuitively, the entropy H X of a discrete random variable X is a measure of the amount of uncertainty associated with the value of X when only its ...
An equivalent definition of entropy is the expected value of the self-information of a variable. [1] Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes — with two coins there are four possible outcomes, and two bits of entropy. Generally ...
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 ...
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 ...