FPGA implementation of an elliptic curve based integrated system for encryption and authentication

Abstract

The resource constrained applications in the present day communication networks demand the use of new cryptographic protocols and hardware with reduced computational and structural complexity. The use of standard, standalone cryptographic primitives are not suitable for such applications. This paper proposes the implementation of a new integrated system for both encryption and authentication based on elliptic curves. An algorithm for pseudo random sequence generation based on cryptographic one way function of elliptic curve point multiplication is developed. This is combined with an elliptic curve based message authentication code to form the integrated system. EC point multiplication operation is preferred as cryptographic one way function for use in this system due to its high security per bit of the key. The hardware is implemented on a Virtex 5 FPGA using Xilinx ISE. In the proposed hardware implementation a single point multiplication unit is time shared between the operations of pseudo random sequence generation and authentication to reduce the overall hardware complexity. A comparison of the resource requirement of the proposed implementation with existing standalone methods is also done.

Simple method for realizingweil theorem in secure ECC generation

“…Its parameters a and b are small numbers less than q. We can use a simple method called the Weil theorem to calculate their order [19][20][21] . where˛andˇare complex numbers determined from the factorization of T 2 t T C q D .T ˛/.T ˇ/.…”