Plateaued functions play a significant role in cryptography as they have nice cryptographic properties. How to construct plateaued functions with high algebraic degree is always a challenge in cryptography. A Boolean function over \(\mathbb {F}_{2^n}\) is an idempotent if \(f(x^2)=f(x)\) for all \(x\in \mathbb {F}_{2^n}\) . This paper presents some generic constructions of plateaued idempotents over \(\mathbb {F}_{2^n}\) from known plateaued functions. Some classes of plateaued idempotents with high algebraic degree are obtained, including semi-bent idempotents with any possible algebraic degree. Rotation symmetric Boolean functions are invariant under the action of cyclic group. As there is a bijective correspondence between idempotents and rotation symmetric Boolean functions, a large class of rotation symmetric plateaued functions with high algebraic degree can be obtained.
