Analyzing SNOW and ZUC Security Algorithms Using NIST SP 800-22 and Enhancing their Randomness

Confidentiality and Integrity algorithms are based on SNOW / ZUC stream cipher algorithms. These standardized algorithms are designed by the 3rd Generation Partnership Project (3GPP) for advanced mobile communication systems (4G-LTE Advanced, LTE Advanced Pro, and 5G-Next Generation). In this paper, twenty configurations of SNOW/ZUC algorithms are studied and analyzed to select the one with the best randomness properties. Each configuration has two different S-boxes in the Finite State Machine (FSM) layer of the SNOW algorithm and Nonlinear Function (NLF) layer of the ZUC algorithm. The two S-boxes are selected from the best five S-boxes published in kinds of literature (Rijndael, Dickson, Feistel structure, New Rijndael, and Improved New Rijndael S-boxes). The NIST SP 800-22 statistical test suite involves 15 tests that are used to assess the randomness properties of each configuration. A complete simulation of each configuration SNOW/ZUC with two different S-boxes is applied using C- language. Test results showed that the best pair arrangement of S-boxes in the SNOW algorithm is the configuration (Feistel structure - Rijndael S-boxes) although the standard configuration by 3GPP is (Rijndael - Dickson S-boxes). Also, the best configuration in the ZUC algorithm is (New Rijndael - Rijndael S-boxes) although the standard configuration by 3GPP is (Feistel structure - New Rijndael S-boxes). The best configurations passed all the NIST SP 800-22 suite randomness tests successfully.