Essay On Cryptosystems

CHAPTER 1

INTRODUCTION

Cryptography is a method of storing and transmitting information in a particular form so that only those for whom it is intended can understand and then process it. The term is most often associated with scrambling plaintext before transmitter (ordinary text, sometimes referred to as clear text) into cipher text (a process called encryption), then get back again (known as decryption).

Ever increasing use of communication network for digital data transmission which is becoming preferred over traditional documents (paper and microfilm, for example) has created a need for Information security. Governments, banking, commercial businesses, and individuals are all demanding more security for their information, to transfer in

Rather than on a traditional logarithmic function Elliptic Curve cryptosystems are based on solutions to the equation y2 = x3 + ax + b. RSA is the most popular public key cryptosystem. Due to rapidly growing key size of RSA Elliptic Curve cryptosystems has been considered an alternative to RSA. The main advantage of using elliptic curve is that it provides same level of security with the littler keys than in RSA. The fundamental operation ECC of is point multiplication. This point multiplication involves the computation of point addition and point doubling. Point addition this is the case when we perform the multiplication of two different numbers, whereas point doubling this is the case when we perform the multiplication of two similar numbers, each of these operations interns requires arithmetic operation like addition, subtraction, multiplication, squaring and inversion. A review on various algorithms to perform modular inverse on prime fields more effectively has been carried out. From various algorithms Inversion operation is well known to be the slowest operation among all other modular arithmetic operations in ECC [1]. If this inversion operation consumes too much time and area, it will affect the performance of the whole ECC system. To have a fast modular inverse calculation is one of the main reasons to do inversion

• Designing hardware architecture for Binary Inversion Algorithm, specifically for a NIST recommended prime field P521.

• FPGA design and simulation of Binary Inversion Algorithm for a NIST recommended prime field P521.

1.4 Organization of the report

This project focuses on reducing hardware needed for the inverse calculation by replacing adder and shifter which is organized as follows:

• In chapter two, complete discussion on elliptic curve theory, security of ECC and application of ECC is studied.

• Chapter three explains the methodology used in BIA algorithms, architecture of modified modular inverse module and its internal components.

• Chapter four presents the detailed study of implementation of modified modular inverse module.

• Chapter five explains about the HDL tool, software and hardware tool required.

• In chapter six results and discussion, simulation result of some modified modular inverse module are included.

• Chapter seven gives the conclusion of the project and offers suggestions for future