The security of a symmetric cryptographic algorithm depends on the strength of the algorithm and the length of the cryptographic key. When the algorithm does not have a known and exploitable flaw in its internal structure, the only cryptanalytic attack that can be applied to it is the method of Exhaustive Key Search (Brute Force Attack). This process is extremely time consuming and if the cryptographic key has an adequate length, then the Exhaustive Key Search is practically inapplicable and therefore we say that the algorithm is practically secure. In this study, we examine the various parameters which influence the time for the Exhaustive Key Search, and based on them we calculate the minimum key length of a symmetric cryptographic algorithm in order to be secure against the cryptanalytic attacks which use the current computer technology (in software and hardware). After this, we calculate the minimum key length for the years in the future, according to the expected technological progress.