Topics from the course:

• introduction: symmetric encryption, asymmetric encryption, applications -- for confidentiality and authentication, attack through trial encryptions, key establishment with asymmetric encryption, man-in-the-middle attack, hybrid algorithms, hash functions, conflict free hash functions, bit commitment, digital signatures based on discrete logarithm problem - ElGamal signatures, Diffie-Hellman key exchange, key transport - Shamir's algorithm, Schnorr's proof of knowledge of discrete logarithm
• algebraic foundations: multiplicative groups modulo n , modulo p, generalized Euclidean algorithm, reverse element modulo n, Euler Theorem, Chinese Reminder Theorem, modular exponentiation: basic algorithm,
• RSA algorithm: soundness of decryption procedure, primality test of Rabin-Miller, attacks: common moduli, small public exponent, cyclic attack, factorization problem: Floyd's Algorithm, rho-Pollard method, p-1 Pollard method, strong prime numbers, multiplication attack, attack through blinding
• other asymmetric algorithms: Rabin's encryption, computing square roots modulo p and modulo n fining square roots and factorization - randomized algorithm, probabilistic encryption of Goldwasser-Micali,
• symmetric encryption: encryption modes: ECB, CBC, CFB, OFB, encryption of file systems, double and triple encryption, attack on double encryption, Feistel scheme, DES, RC5, AES,
• cryptanalysis: differential cryptanalysis: through faults, 3-round DES, 4-round DES, characteristics, linear cryptanalysis, saturation attack, side channel attack: reverse engineering, energy consumption, masking technique, execution time, problems with multiplication modulo 2 to 16 +1, testing cryptographic hardware and trapdoors for cryptanalysis
• hashing functions: hashing based on discrete logarithm, padding, Rabin scheme, Davies scheme, overview of SHA-1 construction, idea of attacks
• pseudorandom number generators: LFSR, A5/1, BBS, unpredictability and unreversability,
• keys: betraying keys and subliminal channels: ElGamal ciphertexts, Newton channel in ElGamal signatures, kleptography based on discrete logarithm systems, dangers and countermeasures, key predistribution: subset construction, user removal schemes based on polynomials,
• signatures: DSS signatures, ring signatures, undeniable signatures, public key infrastructures: key rings of PGP, X.509, SPKI