The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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On the Computational Cost of Pairing and ECC Scalar Multiplication

페어링 및 ECC 상수배 연산의 계산 비용에 관하여

  • Received : 2009.09.07
  • Accepted : 2010.12.17
  • Published : 2011.01.31
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Abstract

Cryptographic protocols based on bilinear pairings provide excellent alternatives to conventional elliptic curve cryptosystems based on discrete logarithm problems. Through active research has been done toward fast computation of the bilinear pairings, it is still believed that the computational cost of one pairing computation is heavier than the cost of one ECC scalar multiplication. However, there have been many progresses in pairing computations over binary fields. In this paper, we compare the cost of BLS signature scheme with ECDSA with equvalent level of security parameters. Analysis shows that the cost of the pairing computation is quite comparable to the cost of ECC scalar multiplication for the case of binary fields.

겹선형 페어링(bilinear pairing)을 기반으로 하는 암호 프로토콜들은 이산 대수 문제를 기반으로 하는 전통적인 타원 곡선 암호시스템을 대신하여 여러 방면에의 응용성을 제공한다. 겹선형 페어링의 빠른 계산을 위하여 최근 활발한 연구가 진행 중이지만, 여전히 ECC 상수배 연산에 비해서 페어링 연산에 사용되는 계산 비용은 상당히 크다고 여겨진다. 그러나 이진 유한체상의 페어링 계산 연구는 최근 많은 발전이 이루어졌다. 본 논문에서는 이진 유한체상에서의 BLS 서명스킴과 ECDSA 서명 스킴의 복잡도를 비교한다. 공정한 비교를 위하여 1024-bit RSA와 같은 레벨의 보안성을 가지는 160-bit ECDSA와 250-bit BLS를 선택하였다. 분석결과 BLS 스킴은 ECDSA에 비해 하드웨어 복잡도 및 계산 지연시간의 측면에서 많은 차이가 나지 않음을 설명해준다.

Keywords

Acknowledgement

Supported by : 한국학술진흥재단

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