Implementation Algorithm Optimized And Chip Design Of ECC Over Binary Field

Elliptic Curve Cryptography (ECC) was proposed by Miller and Koblitz in 1985. It is an approach to public-key cryptography based on the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP) in finite fields. The advantages of ECC over classical cryptosystems include lower power consumption, higher speed, lower bandwidth requirements, and less storage requirements. The overall result is the ability to implement high grade security in low power applications.It has great challenge to realize ECC on an appropriative cryptography chip. There are significant advantages at speed and security of hardware implementation compare with software implementation We design and implement the system based on a Koblitz Curve defined over a binary GF(2^m). The parameter 'm' indicates the key/field size of the ECC implementation The parameters 'a' and 'b' and 'm' are appointed. The operands of field elements are represented by polynomial basis. The reduction polynomial of a trinomial is represented by the binary vector. On this base, we optimize the algorithm to improve the performance of critical module both on area and on operation time.The main idea of our design has two base-points. The 1^st one is to accelerate speed at the ECC algorithm level. KOA method based on the divide-and-conquer approach is presented to reduce complexity by shorten the bits of operands. By this means, the multiplication result of two 233 bit's operands is worked out in 9 clocks. And the Montgomery method to realize point multiplication is also efficient by using projective coordinates to reduce the multiplication times and only one time of inversion been needed. Time is saved because inversion is the most time expensed procedure. By reorder the multiply and square steps we got less operation times to count inversion.The 2^nd one is to reduce the area cost by reuse some field operation modules such as GF-MUL and GF-SQR. Fermat's little theorem proves that inversion can be obtained by add and square operations, we needn't design one more module for inversion on condition that inversion only needed for one time when Montgomery point multiplication method been used.The thesis deals with the design and implementation of elliptic curve point multiplication architectures. The architectures are described in Verilog HDL and synthesized on Synopsys Design Compiler using a standard library of SMIC 0.18um CMOS-Technology. Also large scales of testing were done on the Modelsim 6.0d emulator. Area and timing and power consumption reports are provided and compared with others. The experimental results show that our design has advantage at high speed and low power needed to run elliptic curve cryptography. As one tradeoff, the area cost is a little more but can be accepted. The prototype suits for portable applications such as mobile devices.