Elliptic curve cryptosystem — The answer to strong, fast public-key cryptography for securing constrained environments

Abstract

This article presents a personal view on the current status of an important new area of cryptography — Elliptic Curves. Only three classes of public-key cryptosystems are today considered both secure and efficient: Integer Factorization Systems, Discrete Logarithm Systems, and the Elliptic Curve Cryptosystem (ECC). While the security of all three is based on the difficulty of an underlying mathematical problem, extensive research has concluded that, for a given key size, ECC is the strongest public-key cryptographic system known today. This article compares the three cryptosystems, and explains the significant strength and efficiency advantages in terms of computational overheads, key sizes and bandwidth. In implementations, these savings mean higher processing speeds, lower power consumption and code size reductions. This article also provides an overview of current ECC standards and applications in which the use of ECC is highly advantageous.