Research On Fast Implementation Of RSA Algorithm And Its Improvement

The public-key cryptosystem extends the cryptology from the traditional government and military applications to commercial and civilian areas, making the commercial and social values of modern cryptography widely recognized. Currently, RSA is the most widely used public-key cryptosystem. However, RSA algorithm is based on large prime numbers decomposition problems. In particular, to prevent the attacks, the mold length is increasing. Its main operations are large integer modular exponentiation and modular multiplication, and the algorithm's low speed becomes a prominent RSA defect. Therefore, it is worthwhile to research on accelerating the large integer modular exponentiation and modular multiplication algorithm. This paper focuses on the acceleration of RSA implementation technology.Currently, research on RSA mainly includes key generation optimization, primality testing optimization, large integer modular multiplication, exponentiation of the optimization model, and so on. This paper focuses on modular multiplication and modular exponentiation of the optimization problem.Suggested by the popular Montgomery algorithm, this paper proposes a theorem on predigesting modular operation and proves it. We research on the algorithm based on sliding window coding, design a novel run-length limited coding and apply to design new large integer modular multiplication and modular exponentiation algorithm.And this article analyses the algorithm's time and space complexity. Contrast to the efficiency of the existing correlation algorithm, in theory, our algorithm proves the superiority of the algorithm. In addition, simulation program implementes algorithm and experiments prove the efficiency of the algorithm greatly improved. We also study the run-length coding and try to directly apply it to design run-length encoding modular multiplication and modular exponentiation algorithm. However, through the analysis, we got the conclusion that the run-length encoding is not suitable for modular multiplication and modular exponentiation algorithm, which further proof of our designed limits run-length limited coding is the better coding technique can be applied to design large integer modular multiplication and modular exponentiation algorithm.The completion of this paper contributes great for the further promotion of public-key cryptosystem. It has vast commercial value, with a contribution to greatly improve the modular operation efficiency, which is widely used in the public-key cryptographical algorithm.