Design of Gaussian Normal and Polynomial Basis Multipliers over Gf(2)

This article address efficient hardware implementations for multiplication over GF(2). Hardware implementations of multiplication algorithms are suitable for elliptic curve cryptoprocessor designs, which allow that elliptic curve based cryptosystems implemented in hardware provide more physical security and higher speed than software implementations. In this case, the multipliers were designed using conventional, modified and fast multiplication algorithms, the synthesis and simulation were carried out using Quartus II v.5.0 of Altera, and the designs were synthesized on the Stratix II EP2S60F1020C3. The simulation results show that the multipliers designed present a very good performance using small area. DESIGN OF GAUSSIAN NORMAL AND POLYNOMIAL BASIS MULTIPLIERS OVER GF(2) Vladimir Trujillo-Olaya, Jaime Velasco-Medina, Julio C. López-Hernández* Grupo de Bionanoelectrónica, Escuela EIEE, Universidad del Valle, Cali, Colombia * Instituto de computacao, UNICAMP, Campinas, Brasil E-mail: [email protected], [email protected], [email protected] ABSTRACT This article address efficient hardware implementations for multiplication over GF(2). Hardware implementations of multiplication algorithms are suitable for elliptic curve cryptoprocessor designs, which allow that elliptic curve based cryptosystems implemented in hardware provide more physical security and higher speed than software implementations. In this case, the multipliers were designed using conventional, modified and fast multiplication algorithms, the synthesis and simulation were carried out using Quartus II v.5.0 of Altera, and the designs were synthesized on the Stratix II EP2S60F1020C3. The simulation results show that the multipliers designed present a very good performance using small area.This article address efficient hardware implementations for multiplication over GF(2). Hardware implementations of multiplication algorithms are suitable for elliptic curve cryptoprocessor designs, which allow that elliptic curve based cryptosystems implemented in hardware provide more physical security and higher speed than software implementations. In this case, the multipliers were designed using conventional, modified and fast multiplication algorithms, the synthesis and simulation were carried out using Quartus II v.5.0 of Altera, and the designs were synthesized on the Stratix II EP2S60F1020C3. The simulation results show that the multipliers designed present a very good performance using small area.