In recent years, algebraic attacks and fast algebraic attacks have received a lot of attention in the cryptographic community. There are three Boolean functions achieving optimal algebraic immunity based on primitive element of F2n. The support of Boolean functions in [1]-[3] have the same parameter s, which makes us have a large number of Boolean functions with good properties. However, we prove that the Boolean functions are affine equivalence when s takes different values.

MICKEY-family ciphers are lightweight cryptographic primitives and include a register R determined by two related maximal-period linear transformations. Provided that primitivity is efficiently decided in finite fields, it is shown by quantitative analysis that potential parameters for R can be found in probabilistic polynomial time.