Involutions of finite abelian groups with explicit constructions on finite fields

The article delves into the mathematical properties and applications of involutions in finite abelian groups, with a special focus on finite fields. It introduces a family of involutions and provides characterization and classification results. The paper extends previous work by investigating involutions from the perspectives of multiplicative and additive groups of finite fields. It also presents explicit constructions and applications of involutions in cryptography and coding theory, highlighting their role in symmetric cryptography and the construction of bent functions. The detailed analysis and constructions make this article a valuable resource for researchers and practitioners in the field.