Extention and cryptanalysis of golden cryptography - Sharabyan, Mohammad Tahghighi (2015)
There are some symmetric cryptosystems which use matrices in the encryption and decryption of initial data and the golden cryptosystem (GC) is one of the cryptosystems. It uses a kind of matrices that is normally called the golden matrices,which is a generalization of the Fibonacci Q-matrices for continuous domain. The GC, like other matrix cryptosystems, cannot resist against chosen-plaintext attack. On the other hand, the encryption algorithm of GC is more suitable for textual data and cannot be directly applied to images. This is because image data usually have special features such as bulk capacity, high redundancy, and high correlation among pixels that impose special requirements on the encryption technique used. The problems of golden matrix mentioned are the motivation for the proposal of more secured GC. In this thesis, the mathematical technique was used to check the security of twoextend versions of GC; the GC using k-Fibonacci number (KGC) and GC using Hadamard product (HGC). Utilizing chosen-plaintext attack for both extended versions (the golden cryptosystem using k-Fibonacci number and Hadamard product) are proven not secured. Then a new extension to the original GC using discrete logarithm problem and hash function (GCHDLP) was proposed and the tests have shown that these versions of GC can resist the four basic attacks; the chosen plaintext attack, known-plaintext attack, the ciphertext-only attack, and chosen-ciphertext attack. Finally, the experimental results, using several images (Lena, Nike, Micky, and Damavand) and three measuring factors were evaluated. These measuring factors were the maximum deviation measure (M1), the correlation coe±cient measure (M2), and the irregular deviation measure (M3). The proposed method GCHDLP can encrypt identical plaintext blocks to totally di®erent ciphertext blocks, whereas the original GC cipher cannot do so. Thus, the proposed method has advantages.in hiding data patterns over original GC.