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2 Example. 3 Complexity. 4 References. ... Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm ...
"On the Efficiency of Pollard's Rho Method for Discrete Logarithms". Conferences in Research and Practice in Information Technology, Vol. 77. The Australasian Theory Symposium (CATS2008). Wollongong. pp. 125– 131. Describes the improvements available from different iteration functions and cycle-finding algorithms.
In computer science, lg * is often used to indicate the binary iterated logarithm, which iterates the binary logarithm (with base ) instead of the natural logarithm (with base e). Mathematically, the iterated logarithm is well defined for any base greater than e 1 / e ≈ 1.444667 {\displaystyle e^{1/e}\approx 1.444667} , not only for base 2 ...
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.
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.
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 collects relations among the discrete logarithms of small primes, computes them by a linear algebra procedure and finally expresses the desired discrete ...
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.
Alternatively one can use Pollard's rho algorithm for logarithms, which has about the same running time as the baby-step giant-step algorithm, but only a small memory requirement. While this algorithm is credited to Daniel Shanks, who published the 1971 paper in which it first appears, a 1994 paper by Nechaev [ 3 ] states that it was known to ...