Cryptography: A New Approach of Classical Hill Cipher

Abdul Rahman, Mohd Nordin and Yusof, Mohd Kamir and Abidin @ Bharun, Ahmad Faisal Amri and Mohamad Usop, Nor Surayati (2013) Cryptography: A New Approach of Classical Hill Cipher. International Journal of Security and it's Application, 7 (2). pp. 179-190. ISSN 1738-9976

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Abstract

The Hill cipher is the first polygraph cipher which has some advantages in symmetric data encryption. However, it is vulnerable to known plaintext attack. Another setback is that an invertible key matrix is needed for decryption and it is not suitable for encrypting a plaintext consisting of zeroes. The objective of this work is to modify the existing Hill cipher to overcome these three issues. Studies on previous results showed that the existing Hill algorithms are not yet sufficient. Some of these algorithms are still vulnerable to known plaintext attack. On the other hand, some of these algorithms have better randomization properties and as a result they are more resistant against known plaintext attack. Nevertheless, these enhanced Hill cipher algorithms still face the non invertible key matrix problem. Moreover, neither of these algorithms are suitable for all zeroes plaintext block encryption. In this paper, a robust Hill algorithm (Hill++) is proposed. The algorithm is an extension of the Affine Hill cipher. A random matrix key is introduced as an extra key for encryption. Moreover, an involuntary matrix key formulation is also implemented in the proposed algorithm. This formulation can produce an involuntary key where a same key can be used for both encryption and decryption. Testing on the proposed algorithm is carried out via two approaches, that is through comparative study and statistical analysis. Comparative study shows that Hill++ is resistant to all zeroes plaintext block encryption and does not face the non invertible key matrix problem as what was faced by the original Hill, AdvHill and HillMRIV algorithms. Apart from this, the encryption quality of the proposed algorithm is also measured by using the maximum deviation and correlation coefficient factors. Results from statistical analysis shows that Hill++ (when compared to Hill, AdvHill and HillMRIV algorithms) has the greatest maximum deviation value and its correlation coefficient value is the closest to zero. The results from these two measures proved that Hill++ has better encryption quality compared to HillMRIV.

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