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

Korea Institute of Information Security and Cryptology (한국정보보호학회)
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SPA-Resistant Unsigned Left-to-Right Receding Method

SPA에 안전한 Unsigned Left-to-Right 리코딩 방법

  • Kim, Sung-Kyoung (Graduate School of Information Management and Security, Korea University) ;
  • Kim, Ho-Won (Electronics and Telecommunications Research Institute) ;
  • Chung, Kyo-Il (Electronics and Telecommunications Research Institute) ;
  • Lim, Jong-In (Graduate School of Information Management and Security, Korea University) ;
  • Han, Dong-Guk (Electronics and Telecommunications Research Institute)
  • 김성경 (고려대학교 정보경영공학전문대학원) ;
  • 김호원 (한국전자통신연구원) ;
  • 정교일 (한국전자통신연구원) ;
  • 임종인 (고려대학교 정보경영공학전문대학원) ;
  • 한동국 (한국전자통신연구원)
  • Published : 2007.02.28
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Abstract

Vuillaume-Okeya presented unsigned receding methods for protecting modular exponentiations against side channel attacks, which are suitable for tamper-resistant implementations of RSA or DSA which does not benefit from cheap inversions. The proposed method was using a signed representation with digits set ${1,2,{\cdots},2^{\omega}-1}$, where 0 is absent. This receding method was designed to be computed only from the right-to-left, i.e., it is necessary to finish the receding and to store the receded string before starting the left-to-right evaluation stage. This paper describes new receding methods for producing SPA-resistant unsigned representations which are scanned from left to right contrary to the previous ones. Our contributions are as follows; (1) SPA-resistant unsigned left-to-right receding with general width-${\omega}$, (2) special case when ${\omega}=1$, i.e., unsigned binary representation using the digit set {1,2}, (3) SPA-resistant unsigned left-to-right Comb receding, (4) extension to unsigned radix-${\gamma}$ left-to-right receding secure against SPA. Hence, these left-to-right methods are suitable for implementing on memory limited devices such as smartcards and sensor nodes

Vuillaume-Okeya는 스칼라 모듈러 지수승 연산에서 SPA공격에 안전한 리코딩 방법을 제안하였다. 제안한 방법은 역원 연산의 비용이 큰 RSA 또는 DSA 같은 시스템에서 효율적으로 구성 될 수 있게 비밀키의 표현을 0을 포함하지 않는 양의 디짓 셋 ${1,2,{\cdots},2^{\omega}-1}$을 이용해 리코딩 하였다. 제안된 방법은 비밀키의 최하위 비트부터 스캔하면서 리코딩하는 Right-to-Left기법이다. 따라서 지수승 연산 전에 리코딩이 연산되고 그 결과를 저장하는 추가적인 공간이 필요하게 된다. 본 논문은 Left-to-Right 방향으로 수행하는 새로운 리코딩 방법들을 제안한다. 본 논문에서 제안하는 방법은 (1) 일반적으로 윈도우 크기가 ${\omega}$인 SPA에 안전한 부호가 없는 Left-to-Right리코딩 방법이고 (2) 윈도우 크기 ${\omega}=1$(즉, {1,2}로 구성된 부호가 없는 이진 표현)인 경우는 일반적인 윈도우 크기 ${\omega}$에 제안된 기법보다 훨씬 간단하게 변형할 수 있다. 또한 (3) 제안된 리코딩 방법은 부호가 없는 comb 방법에도 적용하여 SPA에 안전하게 수행할 수 있고, (4) 기수가 ${\gamma}$인 경우에도 확장하여 SPA에 안전하게 대응할 수 있다. 본 논문에서 제안한 Left-to-Right리코딩 기법들은 메모리의 제약을 받는 장비인 스마트 카드, 센서 노드에 적합하다.

Keywords

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