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Constructing Composite Field Representations for Efficient Conversion
November 2003 (vol. 52 no. 11)
pp. 1391-1398

Abstract—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.

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Index Terms:
Composite and binary fields, primitive element, change of basis, AES.
Citation:
Berk Sunar, Erkay Savas, Çetin K. Ko?, "Constructing Composite Field Representations for Efficient Conversion," IEEE Transactions on Computers, vol. 52, no. 11, pp. 1391-1398, Nov. 2003, doi:10.1109/TC.2003.1244937
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