Syllabus - Applied Cryptography (CY503 (B))

History of cryptography, some background in probability and algorithms, classical cryptography (shift cipher, monoalphabetic substitution cipher, polyalphabetic substitution cipher), encryption with perfect secrecy, one-time pad; implementation aspects: shared secret randomness vs perfect secrecy Some background in algorithms and complexity theory, modern cryptography principles, one-way functions, trapdoor functions, hard-core bits, construction of a public-key cryptosystem based on general cryptographic primitives, implementation aspects: computational efficiency vs hardness.

Algorithmic number theory, number theory and cryptographic assumptions, Reductions, proofs by reductions, number theory candidates for cryptographic primitives (e.g., factoring and related problems), public-key cryptosystems from number theory problems; brief discussion of quantum computing; implementation aspects: large integer arithmetic for implemented public-key cryptosystems Randomness and pseudo-randomness, pseudo-random generators, functions and permutations. Symmetric encryption: introduction, security notions, symmetric encryption schemes based on pseudo-randomness primitives, security proofs, fundamental concepts; implementation aspects: generating and testing randomness.

Symmetric encryption: block ciphers (e.g., DES, Triple-DES, AES), substitution/permutation networks, Feistel networks, modes of operations (e.g., ECB, CBC, OFB, Counter), cryptanalysis attacks (e.g., exhaustive, linear, differential, meet-in-the-middle attack), key lengths; implementation aspects: security-performance-features tradeoffs. Message authentication: introduction, notion and schemes (e.g., CBC-MAC), collision resistant hashing (MD5, SHA-1, SHA-2, SHA-3, HMAC, Merkle-Hellman), CCA security for symmetric encryption, simultaneous message confidentiality and message integrity, the GCM mode, application case study 1: password-based secure computer access; implementation aspects: security performance-features tradeoffs.

number theory candidates for cryptographic primitives (e.g., discrete logarithms, brief discussion of related problems including elliptic curves). Asymmetric encryption: comparison with symmetric encryption, definitions, constructions (e.g., RSA variants, El Gamal), hybrid encryption; tradeoffs. Asymmetric encryption: malleable and homomorphic encryption notion and schemes (e.g., Paillier, brief discussion of various schemes, including Gentry’s), additional schemes achieving various implementation aspects: security-performance-features