• Journal of KIISE:Computer Systems and Theory
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• v.35 no.7
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• pp.327-331
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• 2008

Optimal Extension Fields (OEFs) are finite fields of a special form which are very useful for software implementation of elliptic curve cryptosystems. Bailey and Paar introduced efficient OEF arithmetic algorithms including the $p^ith$ powering operation, and an efficient algorithm to construct OEFs for cryptographic use. In this paper, we give a counterexample where their $p^ith$ powering algorithm does not work, and show that their OEF construction algorithm is faulty, i.e., it may produce some non-OEFs as output. We present improved algorithms which correct these problems, and give improved statistics for the number of OEFs.