The Journal of the Korea institute of electronic communication sciences (한국전자통신학회논문지)

Korea Institute of Electronic Communication Science (한국전자통신학회)
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Algorithms for Computing Inverses in Finite Fields using Special ONBs

특수한 정규기저를 이용한 유한체위에서의 역원 계산 알고리즘에 관한 연구

  • 김용태 (광주교육대학교 수학교육과)
  • Received : 2014.06.05
  • Accepted : 2014.08.11
  • Published : 2014.08.31
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Abstract

Since the computation of a multiplicative inverse using MONB includes many squarings and thus calculating inverse is expensive, we, in this paper, propose a low cost inverse algorithm requiring $nb(2^nm-1)+w(2^nm-1)-2$ multiplications and $2^n-1$ squarings to compute an inverse in $GF(2^{2^nm})^*$ using special normal basis over $GF(2^{2^n})$, and give some implementation results using the algorithm and, show that the timing results of our implementation is faster than that of Itoh et al.'s method.

유한체 연산에서 MONB를 사용하면 곱셈 역원 계산시에 대량의 제곱계산이 필요하므로 역원을 계산하는 데에 긴 시간이 필요하게 된다. 이에 본 논문에서는 바탕체 $GF(2^{2n})$ 위의 확대체 $GF(2^{2^nm})^*$에서 특수한 정규기저를 사용하여 역원을 구하는 저 비용의 알고리즘을 제안한다. 제안하는 알고리즘을 사용하면 곱셈 역원 계산에는 $nb(2^nm-1)+w(2^nm-1)-2$번의 곱셈과 $2^n-1$번의 제곱연산이 소요되며, H/W에서 구현한 결과 Itoh 등의 방법 보다 곱셈역원 계산속도가 빠르게 나타났다.

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