FPGA based elliptic curve cryptosystem

Hassan Saad Al-Azawi
Dr. Siddeeq Y. Ameen
Dr.Ali A. Ati

Abstract : Elliptic Curve Algorithms (ECA) has been developed to be a desirable algorithm to other public-key cryptosystems such as the Rivest-Shamir- Adleman algorithm (RSA) by offering the smallest key size and the highest strength per bit. It is based on the discrete logarithm in finite field and integer factorization problem. This thesis proposes the design and implementation of cryptosystem used for generation of session key based on elliptic curve. The underlying structures are the standard Galois Fields GF (2m) in standard base representation. The proposed cryptosystem design and software implementation is based on elliptic curve point multiplication architectures. As an addition feature, the system is developed for a reconfigurable platform based on Field Programmable Gate Arrays (FPGAs). FPGAs combine the flexibility of software solutions with the security of traditional hardware implementations. In particular, it is possible to change all algorithm parameters easily such as the curve coefficients, field order, or field representation. The selected device for the proposed cryptosystem is the XC2V1000 (Virtex-II) from Xilinx Inc. and the software used is the Xilinx ISE 6.1i.The architectures are described in VHDL and mapped to FPGA device. The implemented design was tested at a clock frequency of 33.21 MHz. for the selected elliptic curve over GF (232). The output of this cryptosystem is the session key, which is widely used by modern encryption algorithms. It is shown that a full point multiplication on elliptic curves of real world size can be implemented on commercially available FPGAs