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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.
In mathematics, for given real numbers a and b, the logarithm log b a is a number x such that b x = a.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.
ECC2K-108, involving taking a discrete logarithm on a Koblitz curve over a field of 2 108 elements. The prize was awarded on 4 April 2000 to a group of about 1300 people represented by Robert Harley. They used a parallelized Pollard rho method with speedup. ECC2-109, involving taking a discrete logarithm on a curve over a field of 2 109 ...
Here’s another problem that’s very easy to write, but hard to solve. All you need to recall is the definition of rational numbers. Rational numbers can be written in the form p/q, where p and ...
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.
He then called the logarithm, with this number as base, the natural logarithm. As noted by Howard Eves, "One of the anomalies in the history of mathematics is the fact that logarithms were discovered before exponents were in use." [16] Carl B. Boyer wrote, "Euler was among the first to treat logarithms as exponents, in the manner now so ...
The second stage solves the system of linear equations to compute the discrete logs of the factor base. A system of hundreds of thousands or millions of equations is a significant computation requiring large amounts of memory, and it is not embarrassingly parallel, so a supercomputer is typically used. This was considered a minor step compared ...
The U.S. is struggling to solve its homelessness crisis. The number of Americans living on the streets and in shelters is growing. In 2020 nearly 600,000 Americans were left without a home ...