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This paper proposes an efficient division algorithm protected against simple side-channel analysis. The proposed algorithm applies equally well to software and hardware implementations. Furthermore, it does not impact the running time nor the memory requirements. | A Protected Division Algorithm Published in P. Honeyman Ed. Fifth Smart Card Research and Advanced Application Conference CARDIS 02 pp. 69-74 Usenix Association 2002. Marc Joye and Karine Villegas Gemplus Card International Card Security Group La Vigie Avenue des Jujubiers ZI Athelia IV 13705 La Ciotat Cedex France marc.joye karine.villegas @gemplus.com http www.geocities.com MarcJoye http www.gemplus.com smart Abstract. Side-channel analysis is a powerful tool for retrieving secrets embedded in cryptographic devices such as smart cards. Although several practical solutions have been proposed to prevent the leakage of sensitive data mainly the protection of the basic cryptographic operation itself has been thoroughly investigated. For example for exponentiation-based cryptosystems including RSA DH or DSA various exponentiation algorithms protected against side-channel analysis are known. However the exponentiation algorithm itself or the underlying crypto-algorithm often involve division operations for computing a quotient or a remainder . The first case appears in the normalization resp. denormalization process in fast exponentiation algorithms and the second case appears in the data processing before resp. after the call to the exponentiation operation. This paper proposes an efficient division algorithm protected against simple side-channel analysis. The proposed algorithm applies equally well to software and hardware implementations. Furthermore it does not impact the running time nor the memory requirements. Keywords. Division algorithms smart cards side-channel analysis SPA protected implementations. 1 Introduction Significant progress has been made these last years to secure cryptographic devices e.g. smart cards against side-channel analysis. Side-channel analysis 2 3 is a clever technique exploiting side-channel information e.g. power consumption to retrieve secret information involved in the execution of a carelessly implemented crypto-algorithm. The .
