Construction of cryptographically strong boolean functions well suited for symmetric cryptosystems

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2013

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Ahmed Khan, Mansoor

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Boolean functions are amongst the vital ingredients of any symmetric cryptosystem in order to implement principles of confusion and di usion. These are utilized as non-linear filtering functions or combiner functions in LFSR-based stream ciphers and as s-box component functions or non-linear encryption functions in Fiestel structure based block ciphers. Consequently, the cryptographic properties of Boolean functions are 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 propagation criteria, and more recently, algebraic degree and algebraic immunity. Hence cryptographically strong Boolean functions are invariably required to posses superior cryptographic characteristics mentioned above in order to e ectively resist all existing and potential cryptanalytic attack techniques. The purpose of this research work is construction of cryptographically strong Boolean functions that can be utilized in symmetric cryptosystems o ering e ective resistance to existing cryptanalysis techniques. During the course of this research work, existing significant methods of construction would be studied and analyzed in depth. Based on this analysis, construction methods for Boolean functions with good cryptographic properties are aimed to be proposed. More focus would be directed to construction methods based on principles of finite fields and that involving combinatorial design theory. The significant constructions based on finite field principles include use of primitive polynomials, primitive elements and block codes, while those based on combinatorial design theory depend on the use of combinatorial objects, such as relative di erence sets, for constructing Perfectly Non-linear (PN) or Almost Perfectly Nonlinear (APN) functions. In the end, the proposed constructions would be analyzed in terms of their cryptographic properties in comparison with other existing constructions in order to evaluate their e cacy for deployment in symmetric cryptosystems.

Subject Keywords

Algebra, Boolean., Algebraic functions., Symmetric functions., Symmetry (Mathematics)., Cryptography.

URI

http://etd.lib.metu.edu.tr/upload/12616102/index.pdf
https://hdl.handle.net/11511/22835

Collections

Graduate School of Applied Mathematics, Thesis

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Citation Formats

M. Ahmed Khan, “Construction of cryptographically strong boolean functions well suited for symmetric cryptosystems,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.