Randomness analysis and generation of key-derived s-boxes

Although many ciphers use fixed, close to ideal, s-boxes (like AES e.g.), random s-boxes offer an interesting alternative since they have no underlying structure that can be exploited in cryptanalysis. For this reason, some cryptosystems generate pseudorandom s-boxes as a function of the key (key-derived). We analyse the randomness properties of key-derived s-boxes generated by some popular cryptosystems like the RC4 stream cipher, and the Blowfish and Twofish block ciphers with the aim of establishing if this kind of s-boxes are indistinguishable from purely random s-boxes. For this purpose we have developed a custom software framework to generate and evaluate random and key-derived s-boxes. We also detail and analyse several mechanisms for the generation of proper key-derived s-boxes, including fixed-point filtering and different sizes based on 8 × 8 s-boxes.Partially supported by grants TIN2011-25452 (TUERI) and TEC2014-54110-R (CASUS)

Permutation rotation-symmetric S-boxes, liftings and affine equivalence

In this paper, we investigate permutation rotation-symmetric (shift-invariant) vectorial Boolean functions on n bits that are liftings from Boolean functions on k bits, for k≤n. These functions generalize the well-known map used in the current Keccak hash function, which is generated via the Boolean function on 3 variables, x1+(x2+1)x3. We provide some general constructions, and also study the affine equivalence between rotation-symmetric S-boxes and describe the corresponding relationship between the Boolean function they are associated with