Secure Hill Cipher Modification SHC-M

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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, 294,
  367-376
• Lin et al., Zhongguó gongchéng xuékan  (Zhongguó
  gongchéng xuékan), 2004, vol. 27, no.
  5, pp. 743-746 
• 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
• CKPB
• 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 mm sized over Zm, (e.g., m26 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

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Secure Hill cipher SHC
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Secure Hill cipher SHC
S-gtR C, u
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Secure Hill cipher SHC

• Decryption

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

S-gtR 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)