Optimization And Simulation Of Elliptic Curve Digital Signature Algorithms

With the increasing development and popularization of information, people are more relying on computer and internetwork system. If the internetwork system is endangered, it will seriously impact on our daily lives. Therefore, the information security has more become the focus of attention in our whole society.The information security is the core of cryptosystems, which is also the purpose of the research and development of cryptosystems.The development of cryptosystems has a long and tortuous history, which contains four stages of development:steganographic techniques, the machine cryptography, the traditional and modern phase of the cryptography.In the modern cryptographic system, the elliptic curve cryptosystem (ECC) is an important branch and a relatively new cryptosystem. ECC has the advantages including fast processing speed, less storages and lower bandwidths, which make it especially applicable in constrained environments, such as in IC. These factors of ECC mark its advantages in comparison to other public key cryptography and make it become one of the major cryptographic research topics.ECC not only has great practical values, but also has a very abstruse mathematical theory. In this paper, we briefly introduce some abstract algebraic theory that related to elliptic curve cryptosystems.Elliptic curve cryptosystems include encryption algorithms, elliptic curve digital signature algorithms (ECDSA) and elliptic curve key establishment protocol (ECDKH). We give them a detailed introduction in the third chapter, and mainly make a detail research on elliptic curve digital signature algorithm in this thesis.According to the guidance of modular designing, we adopt the methods "from the top to bottom, gradually thinning", designs the modular structure flowcharts of ECDSA, and then on the basis of flowchart, write C language codes. Finally, we run the codes on VC++6.0 and simulate the implementation of an entire ECDSA.In the simulating procedure of ECDSA implementation, scalar multiplication, modular inversion and modular multiplication are the main time consumed units. In order to achieve more fast and efficient implementation of an ECDSA, based on the other researchers'previous work on ECDSA, we propose two new equations of ECDSA. We try to avoid more scalar multiplication, modular inversion and modular multiplication in these two ECDSA equation structures. We analyze their security and consuming time of the corresponding theoretic algorithms. And we also simulate their implementations separately, which show that the proposed ECDSAs are both secure and more efficient.