Highly nonlinear balanced Boolean functions with good local and global avalanche characteristics
Here we deal with an interesting subset of n-variable balanced Boolean functions which satisfy strict avalanche criteria. These functions achieve the sum-of-square indicator value (a measure for global avalanche criteria) strictly less than 2(2n+1) and nonlinearity strictly greater than 2(n-1) - 2([n/2]). These parameters are currently best known. Moreover, these functions do not possess any nonzero linear structure. The technique involves a well-known simple construction coupled with very good initial functions obtained by computer search, which were not known earlier. (C) 2002 Elsevier Science B.V. All rights reserved.
nonlinearity boolean function strict avalanche criteria global avalanche criteria combinatorial problems cryptography balancedness