Construction Of Highly Nonlinear Resilient Boolean Function Satisfying Strict Avalanche

Since Shannon proposed the conception of perfect secrecy system and proved the security of One-time Pad(OTP)in 1949. The maneuverability of perfect secrecy system has become the worldwide core concern. Stream cipher overcomes such cumbersome to implement in practice which is facilitate the realization of hardware and faster with encryption and decryption speed. These advantages make stream cipher applied widely in critical occasion like military communication and financial information exchange.In fact, stream ciphers are often applied using key stream generated algorithm through a short seed value to obtain pseudo-random key stream sequence. As the core part of non-linear combination generator, the properties of Boolean function determined the pseudo randomness of key stream. To ensure the security of encryption in some special occasion, several security indicators need to be designed elaborately in order to resist the attack existed.In this paper, we introduce some main attacks against stream cipher system and how to measure the capabilities of a Boolean function against these attacks. For example, the nonlinearity, resilient, strict avalanche criterion, propagation criterion and algebraic immunity aims at the best affine approximation, differential attack, correlation attack and algebraic attack respectively. The problem of design Boolean function satisfying several cryptographic properties is becoming the important direction of research on cryptography.The resilient Boolean function satisfying SAC with high nonlinearity is such kind of Cryptographic function widely applied in stream cipher system and block cipher system, especially in symmetric key stream algorithm. So we introduce several classic construction methods to obtain some special Boolean functions and analysis the properties of these functions followed.In this paper, a method is proposed to construct resilient Boolean functions on n variables(n even) satisfying SAC with relatively high nonlinearity. A large class of cryptographic Boolean functions that were not known earlier are obtained. In the following part, we modified such method and improved the nonlinearity slightly in some conditions.