Principal Investigator: |
prof. RNDr. Otokar Grošek, CSc. |

Contact: |
tel.: 07 - 60291 226 |

grosek@elf.stuba.sk | |

Co-researchers: |
Doc. RNDr. Ladislav Satko, CSc. |

Mgr. Marta Šimovcová | |

Project: |
grant VEGA 1/4289/97 |

FEI STU in Bratislava is the leading institution in the area of Applied Informatics, including Computer Security, and there is a large cooperation with governmental institutions, eg. Ministry of Interior, Ministry of Defense, and National Bank of Slovakia.

Main goals in the area of Cryptology and Discrete structures were to study methods of finding suitable Boolean functions for DES-like cryptosystems, algorithms for finding strong primes on the basis of Pockhlington lemma, acceptable by all short exponents up to 1024 bits (3), and Complexity theory of RSG based on Luby - Rackoff lemma (2). We took advantage of a close cooperation with the Department of Mathematics, Institute of Chemical Technology, Prague, CR, Computer Science Department., University of Nebraska, Lincoln, USA, and Computer Science Department, De Montfort University, Milton Keynees, GB. During this project (1997-99), members of the research team participated domestic and international conferences with their own contributions.

In (1) there was published the first cryptanalysis in an open literature of the block cipher GOST. We analyzed a collision attack, applied to the modified GOST algorithm, and proved that if non – bijective S-boxes are used in the algorithm then it is feasible to break it when a weak key is in use.

In (2) we proved that the approach to this type of generators by U. Maurer is different to that of Luby – Rackoff, serving a new sight in classification of random sequences.

In (3) we proved that approximately 3% of randomly generated 512 bits
long strong primes can be used with arbitrary short exponent, s=2^{k}+1,
0<k<1024. By our experiments, all correspondig decryption exponents are as large that
it is inpossible to use the attack based on so called continuous fractions.

In (4) we described a class of semigroups completely characterized by so called traces of Walsh – Hadamard transform.

**1. Grošek, O.-Nemoga, K.-Zanechal, M.**: Why use bijective S-boxes in
GOST-algorithm. Submitted to INFORMATICA, Ljubljana, Slovenia, 13 strán (17.8.1998).

**2. Grošek. O.-Nemoga, K.-Satko, L.**: A remark to Luby-Rackoff and Ueli
M.Mauer pseudorandom generators, Abstracts of 14^{th} Czech and Slovak International
Conference on Number Theory, Liptovský Ján, September 6-10, 1999, p.1-4.

**3. Grošek, O.,-Nemoga, K.,-Satko, L.**: Remarks to short RSA public exponents.
Annales Mathematicae Silesianae 12(1998), Prace Naukove Universytetu Slaskiego w Katowicach,
pp. 65-74.

**4. Satko, L.-Grošek, O.**: Walsh-Hadamard Traces in Semigroups, Proceedings
of Algebras and Combinatorics. An International Congress, ICAC´ 97, Hong, Kong eds.,
Kar-Ping-Shum, Earl J.Taft, Zhe-Xian Wan, Springer, 1999, pp.373-380.