Executive Summary : | Cryptography is crucial in maintaining digital security, ensuring private and honest communication between parties. Two types of cryptosystems, public and symmetric key cryptosystems, are used to achieve secure communication. Block ciphers, a key component of symmetric key cryptosystems, are nonlinear components that are used to create secure block ciphers. The undesirable properties of S-boxes are used to measure the effectiveness of different attacks on block ciphers. Differential cryptanalysis, proposed by Biham and Shamir, is a key method for breaking block ciphers. Researchers have developed various differential distinguishers, such as higher-order differential distinguisher, integral distinguisher, division property, differential-linear distinguisher, and boomerang distinguisher, which have been used to break many well-known block ciphers. The division property and integral attack of block ciphers can be viewed as a generalized concept of its differential distinguisher. Higher-order differential properties play a significant role in measuring the resistance of attacks on block ciphers. The main idea is to generalize the division property based on its algebraic structure.
The project aims to answer these questions by developing theoretical results on different distinguishers on block ciphers, comparing their advantages and disadvantages from a cryptanalysis perspective. It also proposes a design criteria for block ciphers that are secure against known cryptanalytic techniques. |