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Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm ... Solutions to this equation are easily ...
Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. [1] They were rapidly adopted by navigators, scientists, engineers, surveyors, and others to perform high-accuracy computations more easily. Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler ...
The logarithm in the table, however, is of that sine value divided by 10,000,000. [1]: p. 19 The logarithm is again presented as an integer with an implied denominator of 10,000,000. The table consists of 45 pairs of facing pages. Each pair is labeled at the top with an angle, from 0 to 44 degrees, and at the bottom from 90 to 45 degrees.
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.
In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm 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 ...
Analogously, in any group G, powers b k can be defined for all integers k, and the discrete logarithm log b a is an integer k such that b k = a. In arithmetic modulo an integer m , the more commonly used term is index : One can write k = ind b a (mod m ) (read "the index of a to the base b modulo m ") for b k ≡ a (mod m ) if k is a primitive ...