Radix-4 and radix-8 booth encoded interleaved modular multipliers over general Fp

This paper presents radix-4 and radix-8 Booth encoded modular multipliers over general F_p based on inter-leaved multiplication algorithm. An existing bit serial interleaved multiplication algorithm is modified using radix-4, radix-8 and Booth recoding techniques. The modified radix-4 and radix-8 versions of interleaved multiplication result in 50% and 75% reduction in required number of clock cycles for one modular multiplication over the corresponding bit serial interleaved multipliers, while maintaining a competitive critical path delay. The proposed architectures are implemented in Verilog HDL and synthesized by targeting virtex-6 FPGA platform. Due to an efficient utilization of optimized addition chains available in FPGAs and exploiting the parallelism among operations, the proposed radix-4 and radix-8 multipliers compute one 256 × 256 bit modular multiplication in 1.49μs and 0.93μs respectively, which are 35% and 94% improvement over the corresponding bit serial version. Further, this work also presents a thorough comparison on basis of area, throughput, and area × time per bit value. Which shows that these designs are efficiently optimized for area × time per bit value with a high throughput rate. Thus, these designs are suitable to construct most of the elliptic curve and pairing based cryptographic processors.