| This thesis focuses on the design of VLSI architectures for fundamental finite field arithmetic operations and their applications including Reed-Solomon error-control codecs and elliptic-curve public-key cryptography systems that are extensively used to achieve secure and reliable transmission and storage in digital communication and recording systems.; The basic concepts of finite fields, and the algorithms for RS encoding and decoding, and elliptic curve cryptography are well understood. Previous research in this area addressed design of low-complexity and high-speed dedicated (application-specific) VLSI architectures to cut the cost and meet real-time speed requirements. The work presented in this thesis carries on this design trend for high-speed and low-complexity; moreover, it emphasizes the design of low-energy programmable VLSI architectures for finite field applications.; At the arithmetic units level, various architectures are presented to perform finite field multiplication more efficiently. Low-area and low-latency programmable semi-systolic parallel multiplier, squarer, and exponentiator are proposed. Design of low-complexity dedicated finite field multipliers and dual-basis divider are also presented in this thesis. Moreover, a novel digit-serial multiplication scheme is presented, which has much smaller energy-latency product than the digit-serial multiplier obtained by folding the parallel multiplier.; At the system level, hardware/software codesign is considered for the design of programmable Reed-Solomon codecs and energy-scalable elliptic curve encryption processor. These systems are to be implemented as a combination of hardware and software in application-specific DSP processors with specially designed programmable datapath and dedicated and optimized software to reduce total energy consumption. The cross-talk between hardware and software design ensures that the resulting system best exploited the trade-off between programmability and performance optimization. Energy reduction in RS codecs is achieved by using a novel datapath architecture with low-energy finite field multiplication units; and by reducing the total number of energy-consuming computations through use of a modified RS decoding algorithm and effective software coding. The energy-scalable elliptic curve encryption processor is based on a composite finite field representation, which makes it possible to reduce the total energy consumption by sacrificing some security for low-priority data while adequately protecting the important information. |
