Generalization of Higher Order SAC to Vector Output Boolean Functions

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 show the existence, bounds and enumeration of vector Boolean functions which satisfy the generalized SAC(k). A design method and examples are also presented.

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