Group Structure of Special Parabola and Its Application in Cryptography
Bin Li · Applied and Computational Mathematics · 2019
Public key cryptography is one of the most important research contents in modern cryptography. Curve-based public key cryptosystems have attracted widespread attention in recent years because they have more obvious advantages in speed and key length than general public key cryptosystems. People have done a lot of research on elliptic cryptosystem, among which the realization of elliptic cryptosystem is a key content. In this paper, the definition of special parabola in algebraic closed domain is proposed, the group structure of special parabola in finite field is studied, and several forms of public key cryptosystem based on this parabola are given. The results show that the parabola, together with the additive operations defined above, form an Abelian group. The radix of this parabola can be easily determined, so that the factors it contains can be large prime. The security of its public key cryptosystem is based on the difficulty of solving the discrete logarithm problem on this parabola. Moreover, these parabolic public key cryptosystems are easy to code and decode in plaintext, and easier to design and implement than elliptic curve public key cryptosystems.