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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.
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 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 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 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.
Steps of the Pohlig–Hellman algorithm. In group theory, the Pohlig–Hellman algorithm, sometimes credited as the Silver–Pohlig–Hellman algorithm, [1] is a special-purpose algorithm for computing discrete logarithms in a finite abelian group whose order is a smooth integer.
For example, logarithms appear in the analysis of algorithms that solve a problem by dividing it into two similar smaller problems and patching their solutions. [56] The dimensions of self-similar geometric shapes, that is, shapes whose parts resemble the overall picture are also based on logarithms.
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.
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