Let G be a finite cyclic group (written multiplicatively). The discrete log prob

Question

Let G be a finite cyclic group (written multiplicatively). The discrete log problem in G requires finding x (mod |G|), given u & g as elements of G with g as a generator of G and u = g^x. Prove that the difficulty of the discrete log problem in G is independent of a generator of G. That is, if it is feasible to extract discrete logarithms with respect to one generator of G, show how one can extract discrete logarithms with respect to any generator of G. You may use the fact that computing the order |G| of G is a special instance of the discrete log problem in G.

Explanation / Answer

let x be in Zn, n>2. x generates Zn iff (x,n) = 1So we have to count the number of integers ^k be the prime factoization ofnthen E(n) = product(p-1)p^(k-1)each term in this product is even since prime p is either2 or odd. if it is odd (p-1) is evenif it is 2, then p^(k-1

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