IPM Positions

Non Resident Researcher (non-resident), School of Mathematics (2010 - 2011 )

Past IPM Positions

Associate Researcher (non-resident), School of Mathematics (2009 - 2010) (From October ) Associate Researcher, School of Mathematics (2002 - 2003) Post-Doctoral Research Fellow, School of Mathematics (1999 - 2001)

Research Interests

Combinatorics and Computer Science: Algorithmic method in Design Theory and Graph Theory, Probabilistic methods in Combinatorics, Algorithm and Computational Complexity, Languages and Automata, Coding Theory and Cryptography and their links

Research Activities

A Cryptosystem is a five-tuple (P,C,K,E,D), where the following conditional are satisfied: 1. P is a finite set of possible plaintexts 2. C is a finite set of possible ciphertexts 3. K, the keyspace, is a finite set of possible keys 4. For each K ? K,there is an encryptionrule eK ? E and a corresponding decryption rule dK ? D. Each eK:P?C and dK:C?P are function such that dK(eK(x))=x for every plaintext x ? P. In the classical model of cryptography people secretly choose the key K. K then gives rise to an encryption and decryption rule (eK and dK). In these systems that is named private-key systems, dK is either the same as eK, or easily derived from it. The idea behind a public-key system is that might be possible to find a cryptosystem where it is computationally infeasible to determine dK given eK. If so, then the encryption rule eK could be made public by publishing it in a directory. The idea of a public-key system was due to Diffie and Hellman in 1976. The first realization of a public-key system came in 1977 by Rivest, Shamir and Adleman (who invented the well-known RSA-Cryptosystem. Since then several public-key systems have been proposed, where security rests on different computational problems. the McEliece Cryptosystem is based on algebraic coding theory. It is based on the problem of decoding a linear code (which is NP-complete). And the Merkle-Hellman Knapsack-Cryptosystem and related systems are based on the difficulty of the subset sum problem( which is also NP-complete). Since there are many hard problems in combinatorial design and related topics, we want to use these problems to generate new kind of cryptosystem.

Present Research Project at IPM

Application of Combinatorial Design in Cryptography

Related Papers

1.	C. Eslahchi. , H.R. Maimani. , R. Torabi. and R. Tuserkani. Proper nearly perfect sets in graphs Ars Combinatoria (Accepted) [abstract]

2.	C. Eslahchi. , H.R. Maimani. , R. Torabi. and R. Tuserkani. Dynamical 2-domination in graphs Ars Combinatoria (Accepted) [abstract]

3.	H. R. Maimani, R. Torabi and R. Tusserkani (Joint with Ch. Eslahchi) Dynamical 2-domination in graphs Ars Combin. (Accepted) [abstract]

4.	H. R. Maimani, R. Torabi and R. Tusserkani (Joint with Ch. Eslahchi) Proper nearly perfect sets in graphs Ars Combin. (Accepted) [abstract]

5.	H. R. Maimani and R. Torabi An algorithm for constructing two disjoint Hadamard designs Ars Combin. 73 (2004), 231-238  [abstract]

6.	H. Kharaghani and R. Torabi On a decomposition of complete graphs Graphs Combin. 19 (2003), 519-526  [abstract]

7.	G. B. Khosrovshahi, H. R. Maimani and R. Torabi An automorphism-free 4-(15,5,5) design J. Combin. Math. Combin. Comput. 37 (2001), 187-192  [abstract]

8.	G. B. Khosrovshahi and R. Torabi Maximal trades Ars Combin. 51 (1999), 211-223  [abstract]

9.	G. B. Khosrovshahi, H. R. Maimani and R. Torabi On trades: an update Discrete Appl. Math. 95 (1999), 361-376  [abstract]

10.	G. B. Khosrovshahi, H. R. Maimani and R. Torabi Classification of simple 2-(6,3) and 2-(7,3) trades Australas. J. Combin. 19 (1999), 55-72  [abstract]

11.	G. B. Khosrovshahi, A. Nowzari-Dalini and R. Torabi Trading signed designs and some new 4-(12,5,4) designs Des. Codes Cryptogr. 11 (1997), 279-288  [abstract]

12.	R. Torabi and G. B. Khosrovshahi A note on labelings of graphs Linear Multilinear Algebra 39 (1995), 165-169  [abstract]

13.	G. B. Khosrovshahi, A. Nowzari-Dalini and R. Torabi Some simple and automorphism-free 2-(15,5,4) designs J. Combin. Des. 3 (1995), 285-292  [abstract]