Generalization of Higher Order SAC to Vector Output Boolean Functions

Kaoru KUROSAWA  Takashi SATOH  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E81-A   No.1   pp.41-47
Publication Date: 1998/01/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Strict Avalanche Criterion (SAC),  vector output function,  

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S-boxes (vector output Boolean functions) should satisfy cryptographic criteria even if some input bits (say, k bits) are kept constant. However, this kind of security has been studied only for scalar output Boolean functions. SAC (k) is a criterion for scalar output Boolean functions of this type. This paper studies a generalization of SAC (k) to vector output Boolean functions as the first step toward the security of block ciphers against attacks which keep some input bits constant. We first show a close relationship between such Boolean functions and linear error correcting codes. Then we show the existence, bounds and enumeration of vector Boolean functions which satisfy the generalized SAC (k). A design method and examples are also presented.