Elliptic Curve Cryptographic Co-Processor Components for Security On Medical Embedded Systems

Abstract

Elliptic Curve Cryptography(ECC)has become popular due to its superior strength per bit compared to existing public key algorithms RSA.This superiority translates to equivalent security levels with smaller keys,bandwidth savings,and faster implementations,making ECC very appealing.The area of ECC that is researched is the arithmetic blocks of elliptic curve cryptographic co-processor over GF("2").The proposed structure is capable of calculating point multiplication,point addition,and squaring.The most time consuming and critical operation in the Elliptic Curve Cryptography is the scalar multiplication,P=kQ over a finite field where k is a scalar integer and P&Q are elliptic points.Due to its importance,the design of point multiplication need to be taken care of effectively.The most expensive finite field operation that is needed by point addition and point doubling is the finite field inversion.However,inversion can be transformed by using projective coordinates into less expensive finite field operation,such as finite field addition and multiplication.All the elliptic curve cryptographic blocks are simulated using FPGA advantage,version 8.2 of Mentor Graphics and synthesized using Xilinx Lse 8.2i together with Synopsis Design vision D-2010.03-SPI version.The total dynamic power for GF(2163) comes out to be 989.00842uW with cell leakage power of 1.3613uW.The total number of cells used are 2847 and area required is 325291.682362 as per results extracted from synopsis.The IEEE proposed standard IEEE P1363-2000,[4] recognizes ECC-based key agreement and digital signature algorithms.In [11],a list of secure curves is given by the U.S Government National Institute of Standards and Technology(NIST).The others ECC standards are ANSI X9.62 and FIPS 186-3.