The Strict Avalanche Criterion (SAC) is a measure of both confusion and diffusion, which are key properties of a cryptographic hash function. This work provides a working definition of the SAC, describes an experimental methodology that can be used to statistically evaluate whether a cryptographic hash meets the SAC, and uses this to investigate the degree to which compression function of the SHA-1 hash meets the SAC. The results ( @math ) are heartening: SHA-1 closely tracks the SAC after the first 24 rounds, and demonstrates excellent properties of confusion and diffusion throughout.
Pseudonoise generators for cryptographic applications consisting of several linear feedback shift registers with a nonlinear combining function have been proposed as running key generators in stream ciphers. These running key generators eau sometimes be broken by (ciphertext-only) correlation attacks on individual subsequences. A new class of combining functions is presented, which provides better security against such attacks. The security is quantified by the smallest number m + 1 of subsequences that must be simultaneously considered in a correlation attack. A necessary condition for such m th-order correlation-immunity is proved. A recursive construction is given that permits the construction of an m th-order immune combining function for n subsequences for any m and n with 1 m . Finally, the trade-off between the length of the linear equivalent of the nonlinear generator and the order m of its immunity against correlation attacks is considered.  We study the notion of linear structure of a function defined from ^m to ^n, and in particular of a Boolean function. We characterize the existence of linear structures by means of the Fourier transform of the function. For Boolean functions, this characterization can be stated in a simpler way. Finally, we give some constructions of resilient Boolean functions which have no linear structure. Abstract Let P ( x ) be a function from GF (2 n ) to GF (2). P ( x ) is called “bent” if all Fourier coefficients of (−1) P(x) are ±1. The polynomial degree of a bent function P ( x ) is studied, as are the properties of the Fourier transform of (−1) P(x) , and a connection with Hadamard matrices.