Mathematical aspects of division property

This work surveys mathematical aspects of division property, which is a state-of-the-art technique in cryptanalysis symmetric-key algorithms, such as authenticated encryption, block ciphers and stream ciphers. It aims to find integral distinguishers cube attacks, exploit weaknesses the algebraic normal forms output coordinates involved vectorial Boolean functions. Division property can also be used provide arguments for security primitives against these attacks. The focus this formal presentation theory behind including rigorous proofs, were often omitted existing literature. survey covers two major variants namely conventional perfect property. In addition, we explore relationships with classic degree bounds.