1. 1 Secure Hill Cipher Modification SHC-M A.G.Chefranov Eastern Mediterranean University, North Cyprus, Taganrog Institute of Technology, Federal University of South Russia, Russia

2. 2 Introduction Hill cipher is very attractive due to its simplicity Some recent publications devoted to the Hill cipher: 1. Ismail et al., J. Zhejiang Univ SCIENCE A 2006 7(12):2022-2030 2. Thilaka & Rajalakshmi, Cryptologia, 2005, 29:4, 367-376 3. Lin et al., Zhōngguó gōngchéng xuékān (Zhōngguó gōngchéng xuékān), 2004, vol. 27, no. 5, pp. 743- 746 4. Saeednia, S.: How to Make the Hill Cipher Secure. Cryptologia, Vol. 24. 4 (2000) 353-360

3. 3 Hill cipher Proposed in 1929 C=K·P+B Can be broken in the known plaintext- ciphertext attack

4. 4 Secure Hill cipher SHC Proposed by Saeednia, 2000 Initial settings. All matrices considered below are m·m sized over Zm, (e.g., m=26 for English language texts). A sender, S, and a receiver, R, share an invertible key matrix K. A plaintext, P, and a cipher-text, C, are also matrices. Encryption. The sender S chooses a permutation, t, over Zm, and, using it, builds a permutation matrix, Mt. For example, if then

5. 5 Secure Hill cipher SHC

6. 6 S->R: C, u

7. 7 Secure Hill cipher SHC Decryption: The weakness of SHC is in the transfer of the Hill encrypted vector u via network channels

8. 8 Modification of the secure Hill cipher SHC-M  Initial settings. Shared data: K, SEED  Encryption. Sender, S, selects a number, n, and calculates S->R: C, n xor SEED  Decryption. Receiver, R, given n and SEED, calculates t. Having t, calculates Kt. Having Kt and C, calculates the plaintext P

9. 9 Conclusion Thus far, we proposed a modification to SHC which gives more strength to it due to the avoidance of secret information transfer via network channels. In our approach, only the number of a permutation is transferred (together with a cipher-text)