Based on the relationship between cheating immune secret sharing and cryptographic criteria of Boolean functions, to design a cheating immune secret sharing scheme, a 1-resilient function satisfying the strict avalanche criterion （SAC） is needed. In this paper, a technique on constructing a cheating immune secret sharing function is studied. By using Maiorana-McFarland construction technique, two new methods to construct cheating immune secret sharing functions are proposed.
McCullagh-Barreto key agreement protocol and its variant achieve perfect forward security and key generation center （KGC） forward security, but provide no resistance to key compromise impersonation attack （KCI attack）. In this paper, we give a formal treatment of key compromise impersonation （KCI） attack and define the security notion against it. Then an variant of McCullagh-Barreto protocol is presented with only one more Hash operation. The improved protocol preserves perfect forward security and KGC forward security, and furthermore is proved to be secure against KCI attack under k-Gap-BCAA1 assumption.
A number of methods for constructing new plateaued functions from known ones are presented.Byproperly combining the known plateaued functions it is possible to get highly nonlinear resilient plateauedfunctions.The order,resiliency and propagation characteristics of the constructed plateaued functions arediscussed.We show the new functions could possess the desirable cryptographic property.
The main results in this paper are to construct two classes of plateaued functions with desirable cryptographic properties. By using the Maiorana-McFarland construction, a class of highly nonlinear resilient plateaued functions satisfying the propagation criterion has been obtained. Johansson,s et al＇ s construction is modified slightly to obtain highly nonlinear multi-output resilient plateaued functions.
