Boolean functions play important role in cryptography, since in convention a symmetric encryption algorithm can be designed by composing Boolean functions satisfying good cryptographic criteria. In this paper; state of the art in mathematical and practical study of the most important cryptographic criteria of Boolean functions and how to implement algorithms that fulfill these criteria are introduced. Also; the most known constructions for generating Boolean functions that satisfy good cryptographic criteria are summarized. | International Journal of Computer Networks and Communications Security C VOL. 1, NO. 3, AUGUST 2013, 88–94 Available online at: ISSN 2308-9830 N C S State of the ART in Boolean Functions Cryptographic Assessment ADHAM M. ELHOSARY1, NABIL HAMDY2, ISMAIL ABDEL-GHAFAR FARAG3, ALAA ELDIN ROHIEM4 1 Departement of Communications, Military Technical College, Egypt 2 Misr International University, Egypt 3 Arab Academy for Science and Technology and Maritime Transport (AASTMT) 4 Technical Research Center of the Armed Forces, Egypt E-mail: 1adhosary@ ABSTRACT Boolean functions play important role in cryptography, since in convention a symmetric encryption algorithm can be designed by composing Boolean functions satisfying good cryptographic criteria. In this paper; state of the art in mathematical and practical study of the most important cryptographic criteria of Boolean functions and how to implement algorithms that fulfill these criteria are introduced. Also; the most known constructions for generating Boolean functions that satisfy good cryptographic criteria are summarized. Keywords: Boolean Functions, Vectorial Boolean Functions, Cryptographic Criteria. 1 INTRODUCTION This paper presents the state of the art in Boolean functions representation and cryptographic assessment that should be considered as a starting point in cryptographic algorithm design and analysis, namely block ciphers, stream ciphers, and also hash functions. It starts by a brief introduction of Boolean functions and their representation methodology. Afterwards; most of the well-known Boolean functions cryptographic criteria are studied giving illustrative examples for the proof of concept. 2 BOOLEAN FUNCTIONS In Boolean Algebra the set {0,1} is set algebra of interest, since 0 and 1 represent binary elements which are the basic representation of data in computer architecture and therefore F2 is the finite field of choice. F2: {0, 1, +, -} which is equivalent to
