Journal of the Korea Institute of Information Security & Cryptology (정보보호학회논문지)

Korea Institute of Information Security and Cryptology (한국정보보호학회)
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Efficiency in the Password-based Authenticated Key Exchange

패스워드 기반 인증 키 공유 프로토콜에서의 효율성

  • 황정연 (고려대학교 정보보호 기술센터) ;
  • 홍석희 (고려대학교 정보보호 기술센터) ;
  • 박혜영 (고려대학교 정보보호 기술센터) ;
  • 장상운 (고려대학교 정보보호 기술센터) ;
  • 박영호 (세종 사이버 대학교) ;
  • 류희수 (한국전자통신연구원)
  • Published : 2002.12.01
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Abstract

Proposals for a password-based authenticated key exchange protocol that have been published so far almost concentrated on the provable security. But in a real environment such as mobile one, efficiency is a critical issue as security. In this paper we discuss the efficiency of PAK which is secure in the random oracle model ［l］. Among 4 hash functions in PAK the instantiation for $H_1$, which outputs a verifier of the password, has most important effect on the computational efficiency. We analyze two different methods for $H_1$ suggested in ［1］ and we show that $H_{lq}$ has merits in transforming to EC or XTR variants as well as in the efficiency. As an efficient variant. we propose PAK2-EC and PAK2-XTR which do not require any additional step converting a hash output into a point of elliptic curve or XTR subgroup when compared to the previous work on the PAK［2］. Finally we compare PAK2 with the password-based authenticated key exchange protocols such as SPEKE, SRP, and AMP.

지금까지 연구된 패스워드 기반 인증 키 공유 프로토콜에 대한 제안은 대부분이 증명 가능한 안전성 논의에 초점이 맞추어져 있었다. 하지만 모바일(mobile) 환경과 같은 실제적인 환경에서는 안전성만큼이나 효율성은 매우 중요한 논의사항이다. 본 논문에서는 랜덤 오라클(random oracle) 모델에서 안전성이 증명된 $PAK^{[1]}$의 효율성에 대해 논의한다. PAK을 구성하는데 쓰이는 4개의 해쉬 함수 $H_i, (1\leq i\leq 4)$ 가운데 패스워드의 증명자를 생성하는 첫 번째 해쉬 함수는 PAK의 효율성에 가장 중요한 영향을 미친다. ［1］에서 제시된 $H_1$의 구성에 대한 두 가지 방법을 분석하고, 위수 q인 또 다른 생성원을 사용하는 $H_{1q}$ 방법이 효율성에 장점을 가짐을 보인다. ［2］에서 제안과는 다르게, 패스워드에 대한 해쉬 함수 출력 값을 타원곡선 위의 점 또는 XTR 부분군의 원소로 변환시키는 부가적인 절차를 요구하지 않는 PAK2-EC와 PAK2-XTR을 제시한다. 마지막으로, PAK2 프로토콜을 SPEKE, AMP 그리고 SRP와 같은 패스워드 기반 인증 키 공유 프로토콜들과 계산량을 비교한다.

Keywords

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