On a Conjecture about Binary Strings Distribution

It is a difficult challenge to find Boolean functions used in stream ciphers achieving all of the necessary criteria and the research of such functions has taken a significant delay with respect to cryptanalyses. A lot of attacks has led to design criteria for these functions; mainly: balancedness, a high algebraic degree, a high nonlinearity, a good behavior against Fast Algebraic Attacks and also a high algebraic immunity (which is now an absolutely necessary criterion (but not sufficient) for cryptographic Boolean functions). Very recently, an infinite class of Boolean functions has been proposed by Tu and Deng having many good cryptographic properties under the assumption that the following combinatorial conjecture about binary strings is true:

• Type: Journal
• Year: 2010
• Where: SETA
• Authors: Jean-Pierre Flori, Hugues Randriam, Gérard D. Cohen, Sihem Mesnager
• Keywords: Algebraic Attacks, Boolean Functions, Cryptographic Boolean Functions, Mathematics, SETA 2010