Efficient Hardware Implementations For The Gaussian Normal Basis Multiplication Over Gf(2163)

This article presents efficient hardware implementations for the gaussian normal basis multiplication over GF(2163), Hardware implementations of GF(2m) multiplication algorithms are suitable to design elliptic curve cryptoprocessors, which allow that elliptic curve based cryptosystems implemented in hardware provide more physical security and higher performance than software implementations. In this case, the multipliers were designed using conventional, modified and fast-parallel algorithms for the gaussian normal basis multiplication, the synthesis and simulation were carried out using Quartus II of Altera, and the designs were synthesized on the device EP2A15B724C7. The simulation results show that the multipliers designed: present a very good performance using small area. © 2007 IEEE.4550Jung, M., FPGA Based Implementation Of An Elliptic Curve Coprocessor Utilizing Synthesizable VHDL code, , http://www.vlsi.informatik.tudarmstadt.de/staff/mjung/publications/ comprehensive.pdf, Darmstadt University of Technology. Available atElia, M., Leone, M., (2004) A basis-independent algorithm to design fast parallel multipliers over GF (2m), , http://doi. ieeecomputersociety.org/10.1109/ITCC.2004.12 86712(2000) Digital Signature Standard, , http://csrc.nist.gov/fips, National Institute of Standards and Technology, FIPS Publication 186-2, February, Available atItoh, T., Tsujii, S., (1988) A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases, , Information and ComputationDahab, R., Hankerson, D., Hu, F., Long, M., Lopez, J., Menezes, A., Software multiplication using normal, , www.cacr.math.uwaterloo.ca/ techreports/2004/cacr2004-12.pdf, base