The Security Analysis On Cryptographic Functions

The hardcore problem in information security is the art of cipher. However, one of the key of the art on cipher is the security analysis on cryptographic functions. In this work, both the security on cryptographic functions and the relation of security measure indexes are mainly researched. In chapter one, both the signification and the new advance in cryptographic functions are mainly introduced, which include the applied background and the studying status in quo on cryptographic functions and so on. In chapter two, the security measure indexes on cryptographic functions are researched by the numbers, which include the slowness and balance of both the static state information leakage (such as balance and correlation immunity and so on) and dynamic information leakage (such as the diffusion and high order autocorrelations and so on) on cryptographic functions. In the end of the chapter, the security of several kinds of important cryptographic functions is deeply analyzed. In chapter three, the construction methods of cryptographic functions which satisfy synthetical- -security index are research by the numbers ,which include the construction of resilient functions with satisfying PC(l) , and the construction of resilient functions which have not linear structure ,and the construction of cryptographic functions with satisfying PC(l)of order k and so on . Further more, it also show that these cryptographic functions still satisfying other good cryptographic properties. In chapter four, the security of the local and the integer on cryptographic functions are analyzed, and a new measure index of local security, namely local nonlinearity is also introduced .Moreover, the relation of both the local nonlinearity and nonlinearity of cryptographic functions was opened out. Further more, the new nonlinear method for constructing high order resilient functions is present, and a lower boundary of these functions' nonlinearity is also obtained by using the definition of local nonlinearity. In chapter five, the security on cryptographic functions under B-M attack is mainly analyzed ,which include the theory of B-M attack and a new type of stream cipher which is designed by using cryptographic functions .Moreover, the security of the stream cipher is discussed, which contain the studying information leakage of cryptographic functions .