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Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. In cryptography, the computational complexity of the discrete logarithm problem, along with its application, was first proposed in the Diffie–Hellman problem.
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.
He give specific logarithm quantities to be added or subtracted in different cases: 23025842 + 0 or 46051684 + 00, or 69077527 + 000, or 92103369 + 0000, or 115129211 + 00000; These correspond to 10,000,000*ln(10), 10,000,000*ln(100), etc. Chapter 5 presents four problems in proportionality and their solution using Napier's logarithms.
The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems such as factoring , discrete logarithm , graph isomorphism , and the shortest vector problem .
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.
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 ...
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