The course covers the main concepts and principles of cryptography with the main emphasis put on public key cryptography. It begins with the review of integers and a thorough coverage of the fundamentals of finite group theory followed by the RSA and ElGamal ciphers. Primitive roots in cyclic groups and the discrete log problem are discussed. Baby-step Giant-step and the Index Calculus probabilistic algorithms to compute discrete logs in cyclic groups are presented. Naor -- Reingold and Blum -- Blum -- Shub Random Number Generators as well as Fermat, Euler and Miller-Rabin primality tests are thoroughly covered. Pollard's Rho, Pollard's and Quadratic Sieve factorization algorithms are presented. The course ends with the coverage of some oblivious transfer protocols and zero-knowledge proofs. There are numerous programming assignments in the course. Prereq: MET CS 248, or instructor's consent.
2023FALLMETCS789 A1, Sep 11th to Dec 11th 2023
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