Scalable and Unified Digit-Serial Processor Array Architecture for Multiplication and Inversion Over GF( $2^{m}$ )

Abstract

This paper proposes a scalable and unified digit-serial structure, with low space complexity to perform multiplication and inversion operations in $GF(2^{m})$ , based on the bit serial multiplication algorithm and the previously modified extended Euclidean inversion algorithm. In this structure, the multiplier and inverter shares the data-path and thus saves more area resources and power than the case of using separate data-path for each operation. Also, this structure is suitable for fixed size processor that only reuse the core and does not require to modulate the core size when the field size $m$ is modified. This structure is extracted by applying a nonlinear methodology that gives the designer more flexibility to control the processing element workload. Implementation results for of the proposed scalable and unified digit-serial design and previously reported efficient designs show that the proposed scalable structure achieves a significant reduction in area ranging from 64.3% to 85.5% and also achieves a significant saving in energy ranging from 21.9% to 92.5% over them, but it has lower throughput compared with them. This makes the proposed design more suitable for constrained implementations of cryptographic primitives in ultra-low power devices, such as wireless sensor nodes and radio frequency identification devices.