Ads
related to: online logarithm problem solver worksheet 3rd day of 2 college grade equivalent
Search results
Results From The WOW.Com Content Network
Let be a cyclic group of order , and given ,, and a partition =, let : be the map = {and define maps : and : by (,) = {() + (,) = {+ ()input: a: a generator of G b: an element of G output: An integer x such that a x = b, or failure Initialise i ← 0, a 0 ← 0, b 0 ← 0, x 0 ← 1 ∈ G loop i ← i + 1 x i ← f(x i−1), a i ← g(x i−1, a i−1), b i ← h(x i−1, b i−1) x 2i−1 ← ...
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 ...
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.
Finally, in an operation too simple to really be called a fourth stage, the results of the second and third stages can be rearranged by simple algebraic manipulation to work out the desired discrete logarithm x = f 0 log g (−1) + f 1 log g 2 + f 2 log g 3 + ··· + f r log g p r − s. The first and third stages are both embarrassingly ...
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
The zig-zagging entails starting from the point (n, 0) and iteratively moving to (n, log b (n) ), to (0, log b (n) ), to (log b (n), 0 ). In computer science , the iterated logarithm of n {\displaystyle n} , written log * n {\displaystyle n} (usually read " log star "), is the number of times the logarithm function must be iteratively applied ...
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]
There are two other well known algorithms that solve the discrete logarithm problem in sub-exponential time: the index calculus algorithm and a version of the Number Field Sieve. [5] In their easiest forms both solve the DLP in a finite field of prime order but they can be expanded to solve the DLP in F p n {\displaystyle \mathbb {F} _{p^{n ...