Improvement And Implementation Of Rsa Cryptographic Algorithm

RSA algorithm has been proposed for more than 30 years and it still remains an active research area in public key cryptography. RSA algorithm has a good safety and easy to implement and understand, which is the most widely used public key cryptography algorithm. When RSA algorithm decrypts the ciphertext and generates the signatures, more computation capacity and time will be required. Since RSA is based on arithmetic modulo large numbers, it can be slow in constraining environments. Especially when the RSA key strength is high, the performance of RSA is limited very serious. Because as a broad application of RSA algorithm, the performance of RSA algorithm decryption will have a major impact on quality of the information security services. So it is very important to improve the RSA algorithm decryption performance of the current and future security strength and minimize the resource consumption in cryptography research.This paper aims at speeding up RSA algorithm decryption. The mathematical knowledge of RSA algorithm is analyzed. Some RSA variants are analyzed in the paper and some improved RSA algorithms are proposed. These improved RSA algorithms make the decryption performance of RSA algorithm improve significantly. The main contents include:Firstly, the load transferring technique and multi-prime technique are applied to the RSA algorithm, and two improved algorithms, EAPRSA algorithm and EAMRSA algorithm, are proposed to the standard RSA algorithm. The two improved RSA algorithms make the performance of the RSA algorithm decryption greatly improve.Secondly, the load transferring technique and multi-prime technique are applied to Batch RSA algorithm decryption,the improved algorithms which are BMRSA algorithm,BEARSA algorithm and BEAIRSA algorithm,greatly accelerate the decryption process of Batch RSA algorithm.Thirdly,the improved RSA algorithms which are BEAMRSA algorithm,BEAMIRSA algorithm and BEAPORSA algorithm are proposed by combining the load transferring technique and multi-prime technique in the Batch RSA algorithm. These improved RSA algorithms further improve the decryption performance of Batch RSA algorithm.Fourthly, take full advantage of the current multi-core computer equipment and the overall performance of the RSA algorithm decryption has been substantially improved and the variant can be efficiently implemented in parallel on multi-core devices. And the decryption bringing load in the encryption of RSA algorithm which is improved by load transferring technique is minimized by parallel optimization encryption.Fifthly, the use of lattice reduction techniques EASIRSA algorithm cryptanalysis. Security of EAS1RSA algorithm with two private exponents is analyzed. EAS1RSA can be broken efficiently when the two decryption exponents d1 and d2 are less than N0.083...