Cryptography is used to hide information. It is not only use by spies but for phone, fax and e-mail communication, bank transactions, bank account security, PINs, passwords and credit card transactions on the web. It is also used for a variety of other information security issues including electronic signatures, which are used to prove who sent a message.
This Master’s program is a brief introduction to the modern cryptography and its applications. The course includes mathematical foundations of cryptography, and various cryptographic protocols. As an applications we consider voting systems, e-banking systems, etc.
- Mathematical background: Number Theory, Euclidean algorithm, Euler’s function, Chinese remainder theorem, finite fields, etc.
- A brief historical overview of the development of cryptography.
- Block and stream ciphers. A mathematical model of substitution cipher. Attacks on ciphers, perfect ciphers, Shannon's theorem. Modes of block ciphers. GOST 28147-89 and DES encryption standards.
- General methods of cryptanalysis.
- The principles of public key cryptography. One-way functions. Hash Functions. Digital signatures. Diffie-Hellman key exchange.
- Cryptosystem RSA. Factorization of large numbers.
- Cryptosystems of ElGamal type. Digital signature DSA. GOST P34.10-94. Schnorr signature. Smart-cards.
- Blind digital signatures. Electronic moneys. Payment systems.
- Discrete logarithms. Baby-Step/Giant-Step Method. Index Calculus.
- Elliptic Curve Cryptosystems.
- The notion of cryptographic protocol. Secret sharing protocols. Voting protocols. Remote coin flip protocols. Playing poker on the phone. Zero-knowledge proofs. Distribution of secret keys protocols.
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- J. Hoffstein, J. Pipher, and J. H. Silverman. An Introduction to Mathematical Cryptography. Undergraduate Texts in Mathematics. Springer Science+Business Media, LLC, 2008.
- A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone. Handbook of Applied Cryptography. CRC Press, 1997.
- S.Vaudenay. A Classical Introductoin to Cryptography. Applications for Communications Security. Springer Science+Business Media, Inc., 2006.
- T. Baignkres, P. Junod, Yi Lu, J. Monnerat, and S.Vaudenay. A Classical Introduction to Cryptography. Exercise Book. Springer Science+Business Media, Inc., 2006.
- D.R.Stinson. Cryptography. Theory and Practice. Third Edition. Chapman & Hall/CRC, 2006.
- S. Goldwasser and M. Bellare. Lecture Notes on Cryptography. 2008. URL: http://computing.unn.ac.uk/staff/cgmb3/projects/CryptLectureNotes.pdf
- D. Hankerson, A. Menezes, and S. Vanstone. Guide to elliptic curve cryptography. Springer-Verlag New York, Inc., 2004.
- Handbook of Elliptic and Hyperelliptic Curve Cryptography / H.Cohen, G.Frey, R.Avanzi, C. Doche, T. Lange, Kim Nguyen, and F. Vercauteren. Taylor & Francis Group, LLC, 2006.
- B.Schneier. Applied Cryptography: Protocols, Algorithms and Source Code. Second Edition. N.Y.: John Wiley & Sons. 1996.
- H.Cohen. A Course in Computational Algebraic Number Theory. Third, corrected printing. Springer-Verlag, 1996. 545 pp.