Discrete logarithm

Problem of inverting exponentiation in groups

In mathematics, for given real numbers a {\displaystyle a} and b {\displaystyle b} , the logarithm log b ⁡ ( a) {\displaystyle \log _{b}(a)} is a number x {\displaystyle x} such that b x = a {\displaystyle b^{x}=a} . The discrete logarithm is an analogous concept in group theory. In any group G {\displaystyle G} , powers b k {\displaystyle b^{k}} can be defined for all integers k {\displaystyle k} , and the discrete logarithm log b ⁡ ( a) {\displaystyle \log _{b}(a)} is an integer k {\displaystyle k} such that b k = a {\displaystyle b^{k}=a} .

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