Secure Hill Cipher Modification SHC-M

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

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

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. Secure Hill cipher SHC

6. Secure Hill cipher SHC S->R: C, u

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

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, nxor SEED • Decryption. Receiver, R, given n and SEED, calculates t. Having t, calculates Kt. Having Kt and C, calculates the plaintext P

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)