Title :
Design of elliptic curve cryptoprocessors over GF(2163) on Koblitz curves
Author :
Realpe-Muñoz, Paulo ; Trujillo-Olaya, V. ; Velasco-Medina, J.
Author_Institution :
Escuela de Ing. Electr. y Electron., Univ. del Valle, Cali, Colombia
Abstract :
This paper presents the design of cryptoprocessors using two multipliers over finite field GF(2163) 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.
Keywords :
Gaussian processes; digital arithmetic; field programmable gate arrays; hardware description languages; mathematics computing; public key cryptography; GNB representation; Gaussian normal bases representation; Koblitz curves; Matlab; Quartus II 12.0; SignalTAP II; Stratix-IV FPGA; VHDL description; arithmetic operations; digit-level processing; elliptic curve cryptoprocessors; finite field GF(2163); scalar multiplication; Algorithm design and analysis; Elliptic curve cryptography; Elliptic curves; Galois fields; Gaussian processes; Hardware; Elliptic curve cryptography; Gaussian normal basis; Koblitz curves; digit-level multiplier;
Conference_Titel :
Circuits and Systems (LASCAS), 2014 IEEE 5th Latin American Symposium on
Conference_Location :
Santiago
Print_ISBN :
978-1-4799-2506-3
DOI :
10.1109/LASCAS.2014.6820253
