FPGA DESIGN AND SIMULATION OF MODIFIED MODULAR INVERSE FOR ELLIPTIC CURVE CRYPTOGRAPHY

Abstract

Elliptic Curve Cryptography is a public-key cryptography based on the algebraic structure of elliptic curves over finite fields. Elliptic Curve Cryptography recently gained a lot of attention in security areas. ECC contrasted with RSA is that it utilizes littler keys to accomplish equivalent level of security, in this manner decreasing handling overhead. With Elliptic Curve Cryptography abnormal state of security can be accomplish with minimal effort, little key size and littler equipment acknowledgment. The fundamental operation of ECC is point multiplication. This point multiplication includes operations like point addition and point doubling. These operation in turn include addition, subtraction, multiplication, inversion and squaring over a prime number. Out of these operation inversion is the most expensive modular operation with data dependent delays in ECC processor. A review on various algorithms to perform modular inverse on prime fields more effectively has been carried out. There are several inversion algorithms like Euclidean Algorithm, Extended Euclidean Algorithm, Montgomery algorithm, Binary Inversion Algorithm and Little Fermat thermo. Out of this Binary Inversion Algorithm division operation performed by cheap shift and adds operation. This work replace both adder and shifter unit by rotate unit. With that replacement can achieve 25% reduction in hardware results in improved performance, speed, area and also reduce power consumption This makes BIA even more well suitable for implementation in any hardware platform. Hence the main objective of the paper is to design the modified Binary Inversion Algorithm in FPGA for NIST recommended prime field p521.