【文章內(nèi)容簡介】 cal learning, including how to data encryption and how to send encrypted data, how to decrypt the encrypted data, so that the legitimate needs of those who have their own data to the data Cryptography is the preparation of the password and decrypt the password of the technical sciences. Cryptography usually consists of two branches of the unity of opposites: Cryptography and cryptanalysis. Cryptography and cryptanalysis plementary study were in the unity of cryptography. In addition to including modern cryptography and cryptanalysis Cryptography study two main subjects, but also includes a new branch of production the password key learning. It is based password system, the core part of the key as the study subjects. Key management is a point of order, which includes key generation, distribution, storage, protection, destruction and other links. Constitute the three branches of the major modern scientific system of cryptography. Public key cryptosystem is the most important of modern cryptography invention and progress. Send and receive information of the real identity verification, on the issue / receive information after the fact of nonrepudiation and data integrity protection is the subject of modern cryptography, on the other hand. The main features of public key cryptography algorithm is the encryption and decryption use different keys (public key and private key), and the encryption key can open, but only conservative in the confidential decryption key cryptographic algorithm. Public key and private key are a pair, if the public key used to encrypt the data, only using the corresponding private key can decrypt。 if the private key used to encrypt the data, then only the corresponding public key can be used decryption. In this encryption algorithm, encryption key from the public can not derive the secret decryption key, can not ciphertext from the encryption key and the corresponding plaintext recovery. The most influential public key cryptography algorithm is RSA, it can resist all the passwords so far known attacks. In the public key system, the encryption key is different from the decryption key. It will be made public encryption key, anyone can use。 the decryption key only to decrypt themselves know. So far all the public key system, RSA system is the best known and most widely used one. 華北科技學(xué)院畢業(yè)論文 第 7 頁共 62 頁 Asymmetric cryptography features: intensity of plex algorithms, security depends on the algorithm and key, but because of its putational plexity, and makes encryption and decryption speed is not fast symmetric encryption and decryption. Symmetric encryption system is only one key, and nonpublic, if you want to have to let each other know the decryption key. Therefore, to ensure their safety is to ensure security of the keys rather than symmetric key system, there are two keys, one of which is open, so that you can transfer without the other party as symmetric encryption key as a. This security on large lot. This research project mainly in the nonsymmetric encryption algorithm encryption algorithm code RSA. On cryptography is briefly introduced, highlighting the basics of public key cryptography: as binary operations, integer division, modular arithmetic, Euler function, Fermat39。s little theorem, Euclidean algorithm, probabilistic algorithms, remendation primality test。 the fundamental theorem of arithmetic, Chinese Remainder Theorem, divide and conquer the basic idea. And analyze the RSA encryption and decryption process and the algorithm。 for a brief analysis of RSA attack, such as factoring attack, chosen ciphertext attack on the encryption exponent attack, the attack on the decryption exponent, plaintext attack, on the mode of attack, an attack 。 RSA encryption algorithm analyzes the advantages and disadvantages. RSA algorithm is based on theoretical foundation design procedures and software platform to achieve in RSA algorithm encryption and decryption. RSA algorithm is the first not only for data encryption can be used for digital signature algorithm, the algorithm39。s name to the inventor39。s name. Algorithm using the public key and private key are two large prime numbers (greater than 100 decimal places) of the function. It is assumed that key and ciphertext from a plaintext of the difficulty to infer equivalent deposition of the product of two large prime numbers. First select two large prime numbers p and q (), and. Calculation: n = p * q and then randomly selected encryption key e, e and requirements (p1) * (q1) are coprime. Finally, Euclid algorithm decryption key d, to satisfy e * d = 1 (mod (p1) * (q1)) where n and d have coprime. E and n is the number of public key, d is the private key. Two primes p and q are no longer needed, it should be discarded, do not let anyone know. Encrypted message m, first of all the m divided into equal length blocks of data m1, m2, ... ... mi, block size s, where 2 ^ s = n, s as large as possible. Corresponding ciphertext is: (a)。 decryption calculated as follows: (b). This is the RSA encryption and decryption process. 非對稱 密碼學(xué) 加密算法的研究與設(shè)計―― RSA算法的程序 設(shè)計 第 8 頁共 62 頁 RSA can be used for digital signatures, using (a) type signature, (b) authentication. Specific operation, take into account the large amount of information security and m factors, generally the first operations for HASH. RSA39。s security depends on the integer factorization, but is equivalent to factoring has not been proved theoretically. Currently, RSA algorithm for some variants have been proven equivalent to factoring. In any case, deposition of n is the most obvious attack method. Now, more than 140 people have been able to depose a large prime number decimal places. Therefore, the modulus n must be selected larger, because of the specific application conditions. As a result of large numbers are calculated, making