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Improvement on Bailey-Paar's Optimal Extension Field Arithmetic  

Lee, Mun-Kyu (인하대학교 컴퓨터정보공학부)
Publication Information
Journal of KIISE:Computer Systems and Theory / v.35, no.7, 2008 , pp. 327-331 More about this Journal
Abstract
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.
Keywords
Cryptography; Elliptic Curve; Optimal Extension Field (OEF); Inversion; Frobenius Map;
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