## PhD Qualifying Exam in Cryptography

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## Rules and Regulations

The exam covers 3 areas described below.The exam has 2 questions from part A, 3 questions from part B and 3 questions from part C.

You are not to answer all 8 questions, you will choose 1 from A, 2 from B and 2 from C and answer those for a total of 5 questions.The other 3 questions you have not chosen will not be taken into consideration in your evaluation.

There will be an oral exam after the written one.

## A. Applications of Finite Fields

Subjects include groups, rings, polynomial rings, fields, structure of finite fields, polynomials over finite fields, factorization of polynomials, construction of irreducible polynomials, permutation polynomials, normal and optimal normal basis.

### References

- R. Lidl and H. Niederreither, Finite Fields , Cambridge Univ. Press, 1983. (Sections 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1)
- R. Lidl and H. Niederreither, Introduction to Finite Fields and Their Applications, Cambridge Univ. Press, 1986.
- A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography. CRC Press, 1996.
- A. J. Menezes, I.F. Blake, XuHong Gao, R.C. Mullin, S.A. Vanstone, T. Yaghoobian, Applications of Finite Fields, Springer, 1993.

## B. Block and Stream Ciphers

Subjects include boolean functions, correlations and walsh transforms, s-boxes, permutations, block cipher types, many well-known block ciphers, cryptanalysis, block cipher modes of operation, design, evaluation and analysis of block ciphers, statistical analysis, LFSR's, their combinations and stream ciphers using them, linear complexity, generating functions, characterizations and properties of linear recurring sequences.

### References

- H. M. Heys : A Tutorial on Linear and Differential Cryptanalysis. Technical Report CORR 2001-17, Centre for Cryptographic Research, Dept. of Combinatorics and Optimization, University of Waterloo, March 2001.
- A. J. Menezes, P. C. van Oorschot and S. A. Vanstone: Handbook of Applied Cryptography. CRC Press, 1996.
- D. Stinson, Cryptography: Theory and Practice. 4th Edition, CRC Press, 2019.
- Nigel Smart, Cryptography Made Simple, Springer, 2016

## C. Public Key Cryptography

Subjects include general information about public key cryptography, lattice based methods, RSA, primality and factoring algorithms, discrete logarithms and cryptography based on them, elliptic curve cryptography, digital signatures, applications of cryptography, post-quantum cryptography, attacks against public-key systems, key establishment / distribution, cryptographic protocols, complexities and tradeoffs of these algorithms.

### References

- Dan Boneh and Victor Shoup, A Graduate Course in Applied Cryptography, 2023. (http://toc.cryptobook.us/)
- Nigel Smart, Cryptography Made Simple, Springer, 2016
- A.J. Menezes, P.C. van Oorschot and S.A.Vanstone: Handbook of Applied Cryptography. CRC Press, 1996.
- D. Stinson: Cryptography: Theory and Practice. CRC Press, 4th Ed, 2019.