Geometrical Transformations Dependent Quantum Image Encryption and Decryption

Abstract

Over thousands of years ago, cryptography already come into know to make certain the secrecy of data, such as the ancient Egyptians, who used cipher to transmit military intelligence [1]. However not before the arrival of the secure communication information theory by C.E.Shannon in 1949 [2], did cryptography elaborated to a real science subject of cryptology. In 1967, Diffie Hellman put forward the public-key cryptosystem [3] which constitute two branches of modern cryptography with the symmetric cryptosystem. However, with the fast development of calculations and advent of various advanced algorithms, including the classical [4] and quantum compliment [5,6], the security of symmetric and asymmetric cryptography has to be faced with the sever challenges. In 1994, Shor proposed the factorization of large number algorithm [5] which has formed a great threat to the public key cryptosystem that based on the problem of large number decomposition and discrete logarithm solution over finite field. The arrival of Grover quantum search algorithm in 1995 further proved the powerfulness of quantum computer [6]. Looking from other areas, as the great powerfulness of quantum computation, a supply of issues remained by classical computation are fixed. Therefore, more and more comprehensive disciplines combined with quantum information appeared [7] in which the quantum image processing included. In point of view of development of quantum image processing, there are two branches exposed their huge capacity: quantum image signal processing and quantum image transformation. The storage of quantum image in quantum states is different in literature and can be studied in the [8], [9], [10], [11], [12]. Elementary gates which are used in this study are also given in [13] and the storage in quantum array is in [14] and the formation ix of full binary tree is given in [15]. The geometric transformation which are major contribution in this thesis to perform the encryption and decryption procedure in image process is given in [16]. Chapter 1 contain the notations, basic discussions and notations used in the rest of the thesis. These specific definitions and discussions can be read out separately when needed. All the necessary prerequisites of quantum mechanics and cryptography may be found in many basic books of these subjects. Chapter 2 contains the basic discussion about the storing expression of quantum image and all the quantum geometric transformations which are used in this thesis. Chapter 3 describes the geometric transformations that can be used in designing the encryption and decryption algorithm based of information given in chapter 1 and chapter 2, and the conclusion