Analysis and synthesis of functions over the rings z q with noval cryptographic characteristics

Abstract

In the design of cryptographic algorithms, mathematical techniques, particularly those based on number theory, abstract algebra, and lin- ear algebra, have an inevitable place. Symmetric cryptographic algo- rithms like block ciphers utilize finite field arithmetic and linear alge- bra for their construction. The public key cryptographic algorithms are sound with number-theoretical methods. Modern telecommuni- cations technology is increasingly using advanced algebraic formula- tions. As computational power keeps growing quickly, new ideas and techniques for data encryption are being developed to safeguard infor- mation as it is transmitted over open channels. So developing more effective cryptographic primitives involving algebraic techniques is a task strongly tied to further improving present cryptographic infor- mation protection and communication systems.