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For example, log 10 10000 = 4, and log 10 0.001 = −3. These are instances of the discrete logarithm problem. Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents. For example, the equation log 10 53 = 1.724276… means that 10 1.724276… = 53.
Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation = given elements g and h of a finite cyclic group G.
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.
The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollard's rho algorithm for solving the same problem. [ 1 ] [ 2 ] Although Pollard described the application of his algorithm to the discrete logarithm problem in the multiplicative group of units modulo a prime p , it is in fact a ...
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.
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.
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