Mathematical preliminaries of crypto Discrete Logarithm

is the exponentiation operation. Moreover, if h = gx then we say that x is the discrete logarithm of h on basis g, and write x = logg h. The discrete logarithm assumption in a cyclic finite group G of order p is that given a generator g of G and a randomly generated element h of G, it is computationally infeasible to find logg h. To formalize this, we need to define infeasibility. Thus, more formally, the discrete logarithm assumption in G is (τ, σ, ε)-hard, if for any probabilistic polynomial-time adversary A that runs in time τ and requires at most σ space (in some fixed machine model), the probability that the next experiment returns 1 is at most ε: