Studies on Practical Cryptographic Security Analysis for Block Ciphers With Random Substitutions

Abstract

In up-to-date information and communication systems (ICS) cryptography is used for ensuring data confidentiality. The symmetric block ciphers (BC) are implemented in different ICS including critical applications. Today theory of analysis and security verification of BC with fixed substitution nodes against linear and differential cryptanalysis (LDC) is developed. There are also BC with substitution nodes defined by round keys. Random substitution nodes improve security of ciphers and complicate its cryptanalysis. But through it all, quantitative assessment is an actual and not simple task as well as the derivation of formulas for practical security verification for BC with random substitution nodes against LDC. In this paper analytical upper bounds of parameters characterized practical security of BC with random substitution nodes against LDC were given. These assessments generalize known analogs on BC with random substitution nodes and give a possibility to verify security improving against LDC. By using the example of BC Kalyna-128, it was shown that the use of random substitution nodes allows improving upper bounds of linear and differential parameters average probabilities in 246 and 290 times respectively. The study is novel as it is one of the few in the cryptology field to calculate analytical upper bounds of BC practical security against LDC methods as well as to show and prove that using random substitutions allows improving upper bounds of linear and differential parameters. The security analysis using quantitative parameters gives possibility to evaluate various BCs or other cryptographic algorithms and their ability to provide necessary and sufficient security level in ICS. A future research study can be directed on improving analytical upper bounds for analyzed LDC in context to practical security against LDC, as well as practical cryptographic security assessment for other BC with random substitutions against LDC and other cryptanalysis methods including quantum cryptanalysis (Shor, Grover, Deutsch-Jozsa algorithms).