Construction of cryptographically strong Boolean functions well suited for symmetric cryptosystems

Abstract

Boolean functions are amongst the vital ingredients of any symmetric cryptosystemin order to implement principles of confusion and diusion. These are utilized asnon-linear filtering functions or combiner functions in LFSR-based stream ciphers andas s-box component functions or non-linear encryption functions in Fiestel structurebased block ciphers. Consequently, the cryptographic properties of Boolean functionsare amongst the main contributors to the strength of these ciphers against cryptanalysis.The key cryptographic characteristics of Boolean functions include balanced-ness,non-linearity, correlation immunity and resilience, strict avalanche criteria and propagationcriteria, and more recently, algebraic degree and algebraic immunity. Hencecryptographically strong Boolean functions are invariably required to posses superiorcryptographic characteristics mentioned above in order to eectively resist all existingand potential cryptanalytic attack techniques.The purpose of this research work is construction of cryptographically strong Booleanfunctions that can be utilized in symmetric cryptosystems oering eective resistanceto existing cryptanalysis techniques. During the course of this research work, existingsignificant methods of construction would be studied and analyzed in depth. Basedon this analysis, construction methods for Boolean functions with good cryptographicproperties are aimed to be proposed. More focus would be directed to constructionmethods based on principles of finite fields and that involving combinatorial designtheory. The significant constructions based on finite field principles include use ofviiprimitive polynomials, primitive elements and block codes, while those based on combinatorialdesign theory depend on the use of combinatorial objects, such as relativedierence sets, for constructing Perfectly Non-linear (PN) or Almost Perfectly Nonlinear(APN) functions. In the end, the proposed constructions would be analyzed interms of their cryptographic properties in comparison with other existing constructionsin order to evaluate their ecacy for deployment in symmetric cryptosystems.