Skip to main navigation Skip to Content

IPM Positions 

Non Resident Researcher (nonresident), School of Mathematics
(2010  2011 ) 

Past IPM Positions 

Associate Researcher (nonresident), School of Mathematics
(2009  2010) (From October ) Associate Researcher, School of Mathematics (2002  2003) PostDoctoral 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 fivetuple (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 e_{K} ? E and a corresponding decryption rule d_{K} ? D. Each e_{K}:P?C and d_{K}:C?P are function such that d_{K}(e_{K}(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 (e_{K} and d_{K}). In these systems that is named privatekey systems, d_{K} is either the same as e_{K}, or easily derived from it. The idea behind a publickey system is that might be possible to find a cryptosystem where it is computationally infeasible to determine d_{K} given e_{K}. If so, then the encryption rule e_{K} could be made public by publishing it in a directory. The idea of a publickey system was due to Diffie and Hellman in 1976. The first realization of a publickey system came in 1977 by Rivest, Shamir and Adleman (who invented the wellknown RSACryptosystem. Since then several publickey 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 NPcomplete). And the MerkleHellman KnapsackCryptosystem and related systems are based on the difficulty of the subset sum problem( which is also NPcomplete). 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 2domination in graphs Ars Combinatoria (Accepted) [abstract] 
3.  H. R. Maimani, R. Torabi and R. Tusserkani (Joint with Ch. Eslahchi) Dynamical 2domination 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), 231238 [abstract] 
6.  H. Kharaghani and R. Torabi On a decomposition of complete graphs Graphs Combin. 19 (2003), 519526 [abstract] 
7.  G. B. Khosrovshahi, H. R. Maimani and R. Torabi An automorphismfree 4(15,5,5) design J. Combin. Math. Combin. Comput. 37 (2001), 187192 [abstract] 
8.  G. B. Khosrovshahi and R. Torabi Maximal trades Ars Combin. 51 (1999), 211223 [abstract] 
9.  G. B. Khosrovshahi, H. R. Maimani and R. Torabi On trades: an update Discrete Appl. Math. 95 (1999), 361376 [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), 5572 [abstract] 
11.  G. B. Khosrovshahi, A. NowzariDalini and R. Torabi Trading signed designs and some new 4(12,5,4) designs Des. Codes Cryptogr. 11 (1997), 279288 [abstract] 
12.  R. Torabi and G. B. Khosrovshahi A note on labelings of graphs Linear Multilinear Algebra 39 (1995), 165169 [abstract] 
13.  G. B. Khosrovshahi, A. NowzariDalini and R. Torabi Some simple and automorphismfree 2(15,5,4) designs J. Combin. Des. 3 (1995), 285292 [abstract] 
[Back]
