Most mathematical concepts used in modern cryptography arise from the branch of mathematics known as number theory. This course on cryptography introduces students the fundamental mathematical ideas which are central to cryptography and related fields. Topics include: Elementary cryptography and number theory, Public key cryptography, finite groups, rings and fields, Factorization and the RSA cryptosystem, Digital signatures, Probability and combinatorics, Elliptic curves and cryptography, Lattices and cryptography .