IDEM Enough? Evolving Highly Nonlinear Idempotent Boolean Functions
Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These functions are attractive as candidates for cryptographic design, yet their additional algebraic constraints make the search for high nonlinearity substantially more difficult than in the unconstrained case. In this work, we investigate evolutionary methods for constructing highly nonlinear idempotent Boolean functions for dimensions $n=5$ up to $n=12$ using a polynomial basis representation with canonical primitive polynomials. Our results show that the problem of evolving idempotent functions is difficult due to the disruptive nature of crossover and mutation operators. Next, we show that idempotence can be enforced by encoding the truth table on orbits, yielding a compact genome of size equal to the number of distinct squaring orbits.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Idempotent Learned Image Compression with Right-Inverse
We consider the problem of idempotent learned image compression (LIC). The idempotence of codec refers to the stability of codec to re-compression. To achieve idempotence, previous codecs adopt invertible transforms such…
Score-based Idempotent Distillation of Diffusion Models
Idempotent generative networks (IGNs) are a new line of generative models based on idempotent mapping to a target manifold. IGNs support both single-and multi-step generation, allowing for a flexible trade-off between co…
Orthogonal and Idempotent Transformations for Learning Deep Neural Networks
Identity transformations, used as skip-connections in residual networks, directly connect convolutional layers close to the input and those close to the output in deep neural networks, improving information flow and thus…
A* shortest string decoding for non-idempotent semirings
The single shortest path algorithm is undefined for weighted finite-state automata over non-idempotent semirings because such semirings do not guarantee the existence of a shortest path. However, in non-idempotent semiri…
A Non-Adversarial Approach to Idempotent Generative Modelling
Idempotent Generative Networks (IGNs) are deep generative models that also function as local data manifold projectors, mapping arbitrary inputs back onto the manifold. They are trained to act as identity operators on the…