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.
It can be seen that the SAC is equivalent to @math . The same work defines an which regards the SAC as a continuum. Much of the subsequent work ( @cite_17 @cite_23 @cite_2 @cite_7 @cite_13 @cite_12 ) in this area has more closely examined the relationship between PC and nonlinearity characteristics. Many of these extend the PC in interesting ways and examine ways of constructing functions which satisfy @math , but experimental research that targets existing algorithms is scarce.
@cite_7 @cite_23 @cite_2 @cite_13 @cite_12 @cite_17
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The GAC (Global Avalanche Characteristics) were introduced by Zhang and Zheng (1995) as a measure of cryptographic strength of Boolean functions. Two indicators σƒ and Δƒ related to GAC are introduced. (1998) gave a lower bound on σƒ for a balanced Boolean function. In this paper, we provide an improved lower bound. Moreover, we provide bounds on nonlinearity for a balanced Boolean function satisfying the propagation criterion with respect to t vectors. Many practical information authentication techniques are based on such cryptographic means as data encryption algorithms and one-way hash functions. A core component of such algorithms and functions are nonlinear functions. In this paper, we reveal a relationship between nonlinearity and propagation characteristic, two critical indicators of the cryptographic strength of a Boolean function. We also investigate the structures of functions that satisfy the propagation criterion with respect to all but six or less vectors. We show that these functions have close relationships with bent functions, and can be easily constructed from the latter. We determine those Boolean functions on GF(2)n which satisfy the propagation criterion of degree l and order k ≥ n − l - 2. All of theses functions are quadratic. We design nonquadratic Boolean functions satisfying the criterion PC(l) of order k by using the Maiorana-McFarland construction involving nonlinear mappings derived from non-linear codes. We investigate the link between the nonlinearity of a Boolean function and its propagation characteristics. We prove that highly nonlinear functions usually have good propagation properties regarding different criteria. Conversely, any Boolean function satisfying the propagation criterion with respect to a linear subspace of codimension 1 or 2 has a high nonlinearity. We also point out that most highly nonlinear functions with a three-valued Walsh spectrum can be transformed into 1-resilient functions.