Time-Memory Tradeoff is a probabilistic method for quickly inverting one-way functions (e.g. Hash functions) using pre-computed tables. Using this method, one can trades time against memory which results in a more reasonable attack cost. In this thesis we studied some well-known tradeoffmethods including “Hellman” and “Rainbow” algorithms as well as their multi-target variants. The performance of each tradeoff algorithm was studied in the terms of time and memory complexities. We specially studied an existing analysis of the “Fuzzy Rainbow” tradeoff. Unfortunately, all of the previously mentioned analyses were done in the RAM model of computation, which is not a realistic model to represent the storage model of a modern computer in most practical implementations of tradeoff algorithms. As a result, the time complexity estimated by those analyses may not properly reflect the real performance of tradeoff algorithms. Since we were interested in examining the real performance of tradeoff algorithms inpractical implementations, we attempted to provide an accurate time analysis for the fuzzy rainbow tradeoff based on external memory model, hence, the issue of practical relevance is taken into account.As a result, we were able to find explicit formulas for calculating the wall-clock time for the whole password recovery process. Finally, our theoretical findings were validated through simulation. Keywords: Time-Memory Tradeoff, External Memory Model, Fuzzy Rainbow Tradeoff