High Quality Content by WIKIPEDIA articles! In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga(b) is a solution of the equation ax = b over the real or complex numbers. Similarly, if g and h are elements of a finite cyclic group G then a solution x of the equation gx = h is called a discrete logarithm to the base g of h in the group G. Discrete logarithms are perhaps simplest to understand in the group (Zp)x. This is the set {1, …, p ? 1} of congruence classes under multiplication modulo the prime p. If we want to find the kth power of one of the numbers in this group, we can do so by finding its kth power as an integer and then finding the remainder after division by p. This process is called discrete exponentiation. For example, consider (Z17)x. To compute 34 in this group, we first compute 34 = 81, and then we divide 81 by 17, obtaining a remainder of 13. Thus 34 = 13 in the group (Z17)x.

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