Design of elliptic curve cryptoprocessors over GF(2163) on Koblitz curves

This paper presents the design of cryptoprocessors using two multipliers over finite field GF(2
¹⁶³
) with digit-level processing. The arithmetic operations were implemented in hardware using Gaussian Normal Bases (GNB) representation and the scalar multiplication kP was performed on Koblitz curves using window-τNAF algorithm with w = 2, 4, 8 and 16. The cryptoprocessors were designed using VHDL description, synthesized on the Stratix-IV FPGA using Quartus II 12.0, and verified using SignalTAP II and Matlab. The simulation results show that the cryptoprocessors present a very good performance using low area. In this case, the computation times for calculating the scalar multiplication for w = 2, 4, 8 and 16 were 9.88, 7.37, 6.17 and 5.05 μs.