Question: 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 log_bcolon G ightarrow mathbb{Z}_n (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 log_c (g) = log_c (b) cdot log_b (g).
Posted on: Fri, 19 Jul 2013 22:04:13 +0000
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