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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, ...
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.
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 ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 10 3, the logarithm base of 1000 is 3, or log 10 (1000) = 3.
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
The implementation used 2000 CPU cores and took about 6 months to solve the problem. [ 40 ] On 16 June 2020, Aleksander Zieniewicz (zielar) and Jean Luc Pons ( JeanLucPons ) announced the solution of a 114-bit interval elliptic curve discrete logarithm problem on the secp256k1 curve by solving a 114-bit private key in Bitcoin Puzzle ...