A Protected Division Algorithm

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.