Post on 01-Jan-2016
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Secure Hill Cipher Modification SHC-M
A.G.ChefranovEastern Mediterranean University, North Cyprus,
Taganrog Institute of Technology, Federal University of South Russia, Russia
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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):2022-20302. Thilaka & Rajalakshmi, Cryptologia, 2005, 29:4,
367-3763. 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
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Hill cipher
Proposed in 1929 C=K·P+B Can be broken in the known plaintext-
ciphertext attack
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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 )1,2,0,3(t
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Secure Hill cipher SHC
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1 tMP
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Secure Hill cipher SHC
1 ttt MKMK
PKC t
tKu S->R: C, u
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Secure Hill cipher SHC
Decryption:
uKt 1
CKP t 1
The weakness of SHC is in the transfer of the Hill encrypted vector u via network channels
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Modification of the secure Hill cipher SHC-M Initial settings. Shared data: K, SEED Encryption. Sender, S, selects a number, n,
and calculates ),( nSEEDPRPGt
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
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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)