VLSI architectures for computations in finite rings and fields

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This thesis describes the four basic arithmetic operations in finite algebraic rings and fields with respect to very large scale integration (VLSI). The conditions for a successful integration of algorithms based on such operations are investigated. For many of the operations presented, new schemes and VLSI architectures are proposed. Applying these architectures, algorithms based on finite field arithmetic can be implemented very efficiently on applicaiton-specific integrated circuits.