2 research outputs found
Proof of a Conjecture about Rotation Symmetric Functions
Rotation symmetric Boolean functions have important applications in the
design of cryptographic algorithms. In this paper, the Conjecture about
rotation symmetric Boolean functions (RSBFs) of degree 3 proposed by Cusik and
St\u{a}nic\u{a} is proved. As a result, the nonlinearity of such kind of
functions is determined
Nonlinearity of quartic rotation symmetric Boolean functions
Nonlinearity of rotation symmetric Boolean functions is an important topic on
cryptography algorithm. Let be any given integer. In this paper, we
investigate the following question: Is the nonlinearity of the quartic rotation
symmetric Boolean function generated by the monomial equal
to its weight? We introduce some new simple sub-functions and develop new
technique to get several recursive formulas. Then we use these recursive
formulas to show that the nonlinearity of the quartic rotation symmetric
Boolean function generated by the monomial is the same as
its weight. So we answer the above question affirmatively. Finally, we
conjecture that if is an integer, then the nonlinearity of the
rotation symmetric Boolean function generated by the monomial
equals its weight.Comment: 10 page