Generating and expanding of an encryption key based on knight tour problem

Abstract

The encryption key considers as a vital part in designing of a cryptosystem. Whereas these keys must be random as can as possible. The ability to regenerate the same sequence with small initial value is still a major problem that faces the designer of encryption key system. The current paper designs a new method of random number generator with the ability to expand the generated encryption key to fit the proper image size. The knight tour problem was employed as a random number generator and used for encryption key expansion. The expansion process contains two steps, first one generate a random number with (64 × 64) key size and the second step consider the boundary numbers as from the previous step to initiate the knight tour as a second time, the second step continue until the image size was reached. Generated random numbers acquired from the knight tour problem have been subjected to the NIST 800.22 statistical test and successfully passed all statistical tests without requiring any additional processing. Per these results, it has been proved that the proposed system meets the security requirement and can be used in cryptographic applications. Furthermore, the knight tour generator provides a small initial value with the ability to regenerate the same sequence when feed up with the same initial value.