Definition
In general, let G be a finite cyclic group with n elements. We assume that the group is written multiplicatively. Let b be a generator of G; then every element g of G can be written in the form g = bk for some integer k. Furthermore, any two such integers k1 and k2 representing g will be congruent modulo n. We can thus define a function
(where Zn denotes the ring of integers modulo n) by assigning to each g the congruence class of k modulo n. This function is a group isomorphism, called the discrete logarithm to base b.
The familiar base change formula for ordinary logarithms remains valid: If c is another generator of G, then we have
Read more about this topic: Discrete Logarithm
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