| Zakres tematów: |
Basic concepts of cryptography, symmetric and asymmetric cryptography,
one way functions, computational hard problems, key exchange, digital signatures.
Classical ciphers, substitution and Vigenere's cipher, breaking these ciphers by frequency analysis, Vernam's cipher, Enigma.
Basic facts on arithmetic modulo n, extended Euclid's Algorithm, linear systems mod n, Hill's cipher and its breaking with chosen plaintext attack.
Modern symmetric stream ciphers, pseudorandom number generator, RC4 cipher, Trivium cipher, application.
odern block ciphers Data Encryption Standard (DES), 3DES, Advanced Encryption Standard (AES), security levels, key length, block cipher mode of operation ECB, CBC, CFB, applications.
Hash functions - basic properties, collision resistance, birthday paradox attack, construction of hash functions Merkle-Damgard and Secure Hash Algorithm (SHA).
Asymmetric cryptography, computational hard problems, factorization problem, primality tests, efficient exponentiation - square and multiply method, cryptosystem RSA - applications, implementation of RSA - exercises.
Prime finite fields, cryptographic protocols based in discrete logarithm problem, Diffie-Hellman key exchange, ElGamala encryption, Digital Signature Algorithm (DSA), applications, implementation - exercises.
Elliptic curve cryptography, points addition on elliptic curve, discrete logarithm problem on elliptic curves, protocols of Diffie-Hellman, ElGamala, and Elliptic Curve Digital Signature Algorithm (ECDSA), application and implementation of algorithms, comparison efficiency with other asymmetric cryptosystems.
Computational complexity of chosen methods for breaking RSA and discrete logarithm problem in finite fields and on elliptic curves, Pollard's rho method, index calculus method, Lenstra's elliptic curves factorization algorithm, side channel attack, security levels.
Internet security, public key infrastructure (PKI), protocols and tools for secure communications, Secure Socket Layer (SSL), Secure Shell (SSH), Pretty Good Privacy (PGP), HTTPS protocol.
Protocol of Secure Electronic Transactions (SET), electronic payment systems and their security, PayPal, Google Wallet, cryptocash - bitcoin.
Computer security, encryption software, disc encryption, encryption of files and folders, database encryption, encryption of USB drive,
Cryptographic protocols, zero-knowledge proofs, blind signatures - applications in electronic money, electronic voting, secure multi-party computation, secret sharing.
|
