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

Korea Institute of Electronic Communication Science (한국전자통신학회)
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A Fast Multiplier of Composite fields over finite fields

유한체의 합성체위에서의 고속 연산기

  • 김용태 (광주교육대학교 수학교육과)
  • Received : 2011.04.26
  • Accepted : 2011.06.15
  • Published : 2011.06.30
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Abstract

Since Elliptic Curve Cryptosystems(ECCs) support the same security as RSA cryptosystem and ElGamal cryptosystem with 1/6 size key, ECCs are the most efficient to smart cards, cellular phone and small-size computers restricted by high memory capacity and power of process. In this paper, we explicitly explain methods for finite fields operations used in ECC, and then construct some composite fields over finite fields which are secure under Weil's decent attack and maximize the speed of operations. Lastly, we propose a fast multiplier over our composite fields.

타원곡선 암호법(ECC)은 RSA나 ElGamal 암호법에 비하여 1/6정도의 열쇠(key) 크기로 동일한 안전도를 보장하므로, 메모리 용량이나 프로세서의 파워가 제한된 휴대전화기(cellular phone), 스마트카드, HPC(small-size computers) 등에 더욱 효과적인 암호법이다. 본 논문에서는 효과적인 타원곡선 암호법에 많이 사용되는 유한체위에서의 연산방법을 설명하고, Weil의 강하공격법(descent attack)에 안전하면서, 연산속도를 최대화하는 유한체의 합성체를 구축하여, 그 합성체위에서의 고속 연산기를 제안하려고 한다.

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References

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