Public key cryptography, number theory and applications (Q1950030)

The authors provide an excellent presentation of the research progress that has been obtained in the public key cryptography. The paper is organized into four sections as follows: 1. Introduction, 2. Cryptanalysis, 3. Elliptic curves, and 4. Quantum cryptography and a number of interesting applications. It contains fundamental results and beautiful comments about the Canfeld-Erdös-Pomerance Theorem as well as about the theory of elliptic curves. The paper concludes with some interesting notes and comments, and a relevant list of main references in this domain of research.