FPGA Implementation of a Fast Scalar Point Multiplier for an Elliptic Curve Crypto-Processor

Abstract

This paper presents a fast scalar point multiplier for an elliptic curve crypto-processor in the field ${\text{GF}}\left( {2^{163} } \right)$. Elliptic curve-based cryptographic algorithms have been in wide use since the early 2000s after being introduced in 1986. With the ever-increasing need for information security, it is essential for systems to perform the required operations in a fast and efficient manner. In this work, a hybrid type Karatsuba multiplier has been used for fast field multiplications and a dedicated inverter module based on the extended Euclidean algorithm is used for fast field inversions. The point multiplication is performed using the standard double-and-add algorithm for which the point doubling and point addition are done using standard projective coordinates. The use of the fast multipliers and field inverters makes the implementation a fast one as compared to other high-performance implementations that have been reported over the years, at the cost of increased resource usage. The results obtained, however, justify this increased resource usage as the point multiplication is the most time-intensive operation in the encryption and decryption process of elliptic curve cryptography.