On the Optimum Constructions of Composite Field for the AES Algorithm

Xinmiao Zhang, Keshab K. Parhi

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89 Scopus citations


In the hardware implementations of the Advanced Encryption Standard (AES) algorithm, employing composite field arithmetic not only reduces the complexity but also enables deep subpipelining such that higher speed can be achieved. In addition, it is more efficient to employ composite field arithmetic only in the SubBytes transformation of the AES algorithm. Composite fields can be constructed by using different irreducible polynomials. Nevertheless, how the different constructions affect the complexity of the composite implementation of the SubBytes has not been analyzed in prior works. This brief presents 16 ways to construct the composite field GF(((22)2)2) for the AES algorithm. Analytical results are provided for the effects of the irreducible polynomial coefficients on the complexity of each involved subfield operation. In addition, for each construction, there exist eight isomorphic mappings that map the elements in GF(28) to those in composite fields. The complexities of these mappings vary. An efficient algorithm is proposed in this brief to find all isomorphic mappings. Based on the complexities of both the subfield operations and the isomorphic mappings, the optimum constructions of the composite field for the AES algorithm are selected to minimize gate count and critical path.

Original languageEnglish (US)
Pages (from-to)1153-1157
Number of pages5
JournalIEEE Transactions on Circuits and Systems II: Express Briefs
Issue number10
StatePublished - Oct 2006

Bibliographical note

Funding Information:
Manuscript received July 12, 2005; revised April 14, 2006. This work was supported by the Army Research Office under Grant W911NF-04-1-0272. This paper was recommended by Associate Editor C.-T. Lin.


  • Advanced Encryption Standard (AES) algorithm
  • composite field
  • isomorphic mapping
  • multiplicative inversion


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