Abstract. A method is proposed for obtaining the lower bounds of data complexity of statistical attacks on block or stream ciphers. The method is based on the Fano inequality and, unlike the available methods, doesn’t use any asymptotic relations, approximate formulas or heuristic assumptions about the considered cipher. For a lot of known types of attacks the obtained data complexity bounds have the classical form. For other types of attacks these bounds allow us to introduce reasonable parameters that characterize the security of symmetric cryptosystems against these attacks.

Keywords: symmetric cryptography, statistical hypotheses testing, statistical attack, block cipher, stream cipher, correlation attack, data complexity, Fano’s inequality.