Advantages Of Elliptic Curve Cryptography

Elliptic curve cryptography is a public key cryptographic method. It is a cryptographic method based on elliptic curves over finite fields. The elliptic curves defined over finite fields are used in elliptic curve cryptography since a practical digital system can handle only finite number of values. In finite fields the binary extensions fields are ideal, because of the ease with which they can be implemented in a digital system in comparison with other finite fields. The main advantage of elliptic curve cryptography is that it offers higher security with smaller key size in comparison with other existing schemes like RSA etc. Elliptic curve cryptography because of its small key size has smaller latency and lesser computational/hardware complexities

The Diffie-Hellman key exchange method based on elliptic point multiplication unit can be used for the exchange of initial shared secret between the neighboring nodes. The other important steps in key management like pseudo random key generation, authentication etc. can also be implemented using the same elliptic curve multiplication unit. So using just a single elliptic curve multiplication unit, all the operations required in the key exchange system can be carried out.This is a significant advantage over other key management systems which uses different one way function for each these functionalities.

Hence our primary aim in this project is the optimized implementation of elliptic curve point multiplication unit so that the latency is less and the hardware requirement (and area) is not very high. The elliptic curve multiplication unit has to be designed in such a manner that it suits the requirement of all the processes involved in the key exchange mechanism.

The time sharing of the multiplication unit between different key management stages can reduce the hardware and power requirements of the overall system.This time sharing will not increase latency since the key management stages

The proposed design is that of an elliptic curve based key exchange system.The implementation is carried out using

Very High speed integrated circuit Hardware Description

Language (VHDL) in Xlinx ISE Design Suite software and then finally the code will be flashed to an FPGA. The main challenge involved in the FPGA implementation of the above mentioned system is the optimization of the design of point multiplication unit.

We are aiming to implement the elliptic curve point multiplication unit over GF(2 163 ) i.e. with a key size of 163 bits. 163 bit ECC is generally considered as equivalent(in terms of security) to RSA with 1024 bit key size[14].

Instead of directly implementing the elliptic curve point multiplication over such a large extension field, we first implemented it in a lower extension field GF(2 11 ). At first a

MATLAB simulation of the system was carried out and then the corresponding algorithm was coded using VHDL.Various possible optimization methods have to be explored,once an optimized design is developed over GF(2 11 ), it is to be extended to the 163 bit size.

The main steps involved in the implementation of the point multiplication unit includes choosing an