Cryptography

Elements of complexity theory, algebra, group theory, number theory, probability and algorithms. Formal definitions of security, confidentiality, privacy and integrity. Random and pseudorandom sequences. One-way and trapdoor functions. Basing cryptography on factoring numbers, finding discrete-logarithms, decoding codes, solving systems of polynomial equations, performing combinatorial optimization and other problems. Cryptographic primitives including key exchange (such as Diffie-Hellman), digital signatures (such as RSA), public-key encryption (such as ElGamal, Cramer Shoup). The random oracle model as a method to develop security arguments. The simulation-based paradigm for arguing the security of cryptosystems. Applications to secure point-to-point channels, electronic-voting, e-commerce, payments, digital content distribution and others.