Construction Of A Class Of Cryptosystems Based On Quadratic Residue And Image Encryption Research

Nowadays,all kinds of industries cannot exist independently without the Internet.When the Internet provides convenience for our life and learning,it also brings us many problems.How to ensure data security is an important issue.In order to ensure the security of data,the first thing to do is to encrypt,especially the encryption of text document information and digital image.For text document information,it is necessary to construct a cipher system with high cipher strength and a signature scheme to protect the privacy of the information.For digital image information,a secure and effective image encryption algorithm is needed.The most common and widely used encryption scheme in cryptography is what we call public key cryptography.For the public key cryptosystem,its encryption keys are generally unsecret,that is to say,it will be made public,so the public key cryptosystem is at risk of being attacked by selected plaintext,which requires the construction of a cipher system with higher cryptographic strength.Similar to personal handwritten signature and private seal in real life,a document also needs an electronic version of "handwritten signature" and "private seal" to verify the user's identity,which is what we call digital signature.However,sometimes the signer needs to sign a confidential document but does not want the contents of the document to be seen by the signer,which requires a special digital signature,known as a blind signature.As for digital images,there are many ways to encrypt them.In recent years,many researchers have focused their research ideas on chaotic systems and DNA sequences.The main research results are as follows:(1)In view of the problems existing in the deterministic public key cryptosystem,we take the quadratic residual theory and probability encryption as the basis,and further explore the probability public key cryptosystem at the same time,and give a encryption system based on quadratic residual.The proposed encryption system can resist the selective plaintext attack effectively,and the ciphertext expansion rate of this system is relatively low.By comparison,we find that it is even lower than the ciphertext expansion rate of the BG cryptosystem given by Blum and Goldwasser.If we need to encrypt long plaintext,then its ciphertext expansion rate can be regarded as approximately equal to 1.At the same time,the cryptographic system has a strong security,and not lower than the RSA public key cryptographic system.In addition,the proposed cryptographic system is probabilistic encryption for polynomials.If the coefficients of the polynomials are converted into a matrix of quadratic form,the proposed cryptographic system can also encrypt images.(2)Digital signature,as the "handwritten signature" and "personal seal" of electronic documents,is widely used in Internet commerce,finance and other systems.And the special digital signature-blind signature,it can effectively protect the privacy of users not to be violated,so the development of a bright future.In this dissertation,a new blind signature scheme based on quadratic residue is proposed,and its relative characteristics are proved by analyzing the scheme.(3)Chaotic system is widely used in image encryption because of its own characteristics,and DNA sequence can ensure the security of encryption,on this basis,an image secret algorithm is presented,the initial value of the random matrix is determined by the hash value of the plaintext image,and the effect of one secret at a time is achieved.At the same time,the encrypted image is not the whole image,but a small piece of image.The way each piece of DNA is encoded and the DNA operations between them are dynamically determined by two two-dimensional chaotic systems.In this way,a plaintext image contains a variety of encoding and operation methods.The simulation results show that the five parts of the analysis have achieved good results no matter from gray histogram,key space,or information entropy,or key sensitivity and correlation between adj acent pixels.Figure[19]Table[9]Reference[101]...