Mathematical Foundations of Cryptographic Algorithms

Mathematics provides the foundation for much of cryptography. Shannon’s mathematical foundation of secrecy systems relies on probability theory and analysis of cipher systems from early times heavily draws on statistical methods. Since the late 1970s, cryptography has been closely connected to number theory. Many modern day public key cryptosystems make use of arithmetic in number theoretic structures. Moreover, the security of these schemes is frequently based on the presumed difficulty of a number theoretic problem. Construction of systems with information theoretic security uses combinatorial structures and algebraic codes as the main techniques, and mathematical models and proofs form foundation of today's provable security.