Introduction to finite fields and their applications
Introduction to finite fields and their applications
Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
IEEE Transactions on Computers
Efficient Normal Basis Multipliers in Composite Fields
IEEE Transactions on Computers
A Fast Software Implementation for Arithmetic Operations in GF(2n)
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Highly Regular Architectures for Finite Field Computation Using Redundant Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast Multiplication in Finite Fields GF(2N)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Efficient Finite Field Basis Conversion Involving Dual Bases
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Low Complexity Word-Level Sequential Normal Basis Multipliers
IEEE Transactions on Computers
An Efficient Basis Conversion Algorithm for Composite Fields with Given Representations
IEEE Transactions on Computers
Systolic Galois field exponentiation in a multiple-valued logic technique
Integration, the VLSI Journal
Systolic product-sum circuit for GF((22)m) using neuron MOSFETs
Integration, the VLSI Journal
Low-latency factorization architecture for algebraic soft-decision decoding of Reed-Solomon codes
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Multi-gigabit GCM-AES Architecture Optimized for FPGAs
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Systolic product-sum circuit for GF((22)m) using neuron MOSFETs
Integration, the VLSI Journal
Systolic Galois field exponentiation in a multiple-valued logic technique
Integration, the VLSI Journal
The parity of the number of irreducible factors for some pentanomials
Finite Fields and Their Applications
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This paper describes a method of construction of a composite field representation from a given binary field representation. We derive the conversion (change of basis) matrix. The special case of when the degree of the ground field is relatively prime to the extension degree, where the irreducible polynomial generating the composite field has its coefficients from the binary prime field rather than the ground field, is also treated. Furthermore, certain generalizations of the proposed construction method, e.g., the use of nonprimitive elements and the construction of composite fields with special irreducible polynomials, are also discussed. Finally, we give storage-efficient conversion algorithms between the binary and composite fields when the degree of the ground field is relatively prime to the extension degree.