Proceedings on Advances in cryptology---CRYPTO '86
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Power Analysis Attacks of Modular Exponentiation in Smartcards
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
On the power of simple branch prediction analysis
ASIACCS '07 Proceedings of the 2nd ACM symposium on Information, computer and communications security
Power analysis for secret recovering and reverse engineering of public key algorithms
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Generating provable primes efficiently on embedded devices
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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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.