Weightwise perfectly balanced functions with high weightwise nonlinearity profile
This work addresses cryptographic security needs in stream ciphers by improving resistance to attacks, though it is incremental as it builds on existing WPB function constructions.
The paper tackled the problem of constructing weightwise perfectly balanced (WPB) Boolean functions with high weightwise nonlinearity for cryptographic applications like the FLIP stream cipher, resulting in a new class of functions not equivalent to known ones and providing general lower bounds on nonlinearity, with a subclass shown to have very high nonlinearity profiles.
Boolean functions with good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the recent FLIP stream cipher. In this paper, we propose a large class of weightwise perfectly balanced (WPB) functions, which is not extended affinely (EA) equivalent to the known constructions. We also discuss the weightwise nonlinearity profile of these functions, and present general lower bounds on $k$-weightwise nonlinearity, where $k$ is a power of $2$. Moreover, we exhibit a subclass of the family. By a recursive lower bound, we show that these subclass of WPB functions have very high weightwise nonlinearity profile.