Cryptography

Learning Results

The course of Cryptography covers fundamentals of modern cryptographic algorithms and schemes for secure systems and information transmission. The aim of the course is to create a framework that consists of theoretical and practical knowledge of cryptographic techniques, the importance of their use, the examination and assessment of the adequacy each provides, depending on the level of security required. This knowledge will be an additional specialization for the student in the labor market in the field of Information and Communication Systems Security.

Upon successful completion of the course, the student:

• Will be aware of the security problems that cryptography solves,
• Will know modern Symmetric cryptographic algorithms (permutations, block ciphers, stream ciphers, AES),
• Will know modern Asymmetric cryptographic algorithms (public key encryption, RSA, Diffie-Helman, ElGamal),
• Will know one-way cryptographic hash functions and their applications,
• Will know digital signatures and their applications,
• Will know authentication methods (eg. passwords) and
• Will know public key infrastructure (PKI),
• Will know the tolerance of all the above cryptographic algorithms and methods of cryptanalysis against them, and
• Will be able, depending on the level of security required, to evaluate and select the proper cryptographic algorithm,
• Will comprehend the Blockchain Technology.

Skills acquired

• Examine, retrieve, analyze and synthesize data and information by utilizing necessary technologies
• Decision-Making
• Work independently / Teamwork
• Work in an interdisciplinary environment
• Production of new research ideas
• Promoting free, creative and inductive thinking

The course includes the topics described in the following list:

• Elements of Number Theory,
• Encryption Schemes,
• Symmetric Cryptosystems (permutations, block ciphers, stream ciphers, Affine, Vigenere, Hill, AES),
• Asymmetric Cryptosystems (public key encryption, RSA, Diffie-Helman, ElGamal),
• the Birthday Paradox,
• Perfect Privacy,
• Advanced Encryption System (AES),
• RSA,
• Diffie-Helman,
• ElGamal,
• One-way Hash Functions (SHA1, MAC, MD5),
• Collision resistance hashing,
• Digital Signatures (RSA signatures, ElGamal signatures, DSA, Blind Signatures),
• Elliptic Curves,
• Passwords, One-Time passwords,
• PKI,
• Protocols for identification and login,
• Authenticated key exchange,
• Two-party and multi-party secure computation,
• Blockchain Technology.

1. Rolf, Oppliger, Cryptography 101: From Theory to Practice, 2021, Artech House.

2. Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, Third Edition, 2021, CRC Press.

3. Buchmann J., Introduction to Cyptography, 2nd Ed., Springer, 2004.

4. Paul Erd ̋os and J ́anos Sur ́anyi. Topics in the Theory of Numbers. Springer-Verlag, New York, 2003.

5. Joseph H. Silverman. A Friendly Introduction to Number Theory. Prentice-Hall, 2001.

6. James J. Tettersall. Elementary Number Theory in Nine Chapters. Cambridge University Press, 2005.

Related scientific journals:

1. Journal of Cryptology, Springer
2. Cryptography, MDPI.

Internet sources:

1. Dan Boneh and Victor Shoup, A Graduate Course in Applied Cryptography, 2020, http://toc.cryptobook.us/book.pdf
2. CryptTool Portal, www.cryptool.org.