Efficient elliptic curve scalar Multiplication architectures For fpga platform

Abstract

In recent days thousands of transactions and communication of information takes place via internet. Numerous issues arises in information security, which can be solved by various cryptographic algorithms. Many algorithms such as public and private key algorithms plays an important role in securing the data. Comparing private key algorithms, public key algorithms are used widely in internet to build secure communication channels, for E-commerce transactions, and in network security protocols. Also, Elliptic Curve Cryptography are widely used in today s security due to their greater security level with smaller key size compared to Rivest-Shamir Adleman (RSA) algorithm. Hardware acceleration of cryptographic algorithms is required to meet the increased demand for speed in today s applications. Another difficulty will be to keep the design strong against side channel attacks. As a result, an efficient encryption system design and implementation are required. newlineElliptic Curve Scalar Multiplication (ECSM) also known as Point Multiplication is the major hardware architecture in ECC. Designing a high-speed multiplier is a general requirement for all cryptographic processors, that has been an attractive field of research for the previous few decades. These researches mainly focus on the reduction of time, area and power consumption. newlineSince polynomial field is more convenient for the hardware implementation, we have chosen polynomial field over prime field. The two operations involved in finding ECSM are Point Addition (PA) and Point Doubling (PD). The ECSM is constructed with repeated PA and PD. This PA and PD further depends on arithmetic operations like modular inversion, modular multiplication and modular addition. Since polynomial field is used, modular addition is simply an ex-or operation newline