Research on the Security of Elliptic Curve Cryptography

Abstract

Elliptic curve cryptography has the characteristics of high-security strength and low computational complexity. Elliptic curve cryptography relies on point multiplication, which is the most time-consuming part of the encryption and decryption process. The Elliptic Curve Cryptosystem is currently the most famous and potential public key cryptosystem. It is proposed based on the computational difficulty of discrete logarithms on the elliptic curve, and its security research is an important research area in academia. This paper analyzes the security of elliptic cryptographic curves from the performance comparison of ECC and RSA. Moreover, this paper implements RSA and ECC using random private keys, and the sample data input is 64-bit, 8-bit, and 256-bit. Experiments are done on MATLAB R2008a on an Intel Pentium dual-core processor. The findings reveal that RSA is efficient at encryption, but sluggish at decryption, whereas ECC is slow at encryption but efficient at decryption. Overall, ECC outperforms RSA in terms of efficiency and security. ECC surpasses RSA in terms of operational security and efficiency, according to this research.