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Universal Exponentiation Algorithm
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
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CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Passive and Active Combined Attacks: Combining Fault Attacks and Side Channel Analysis
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Selected Areas in Cryptography
Power analysis for secret recovering and reverse engineering of public key algorithms
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Combined implementation attack resistant exponentiation
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
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COSADE'13 Proceedings of the 4th international conference on Constructive Side-Channel Analysis and Secure Design
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We present modular reduction algorithms over finite fields of large characteristic that allow the use of redundant modular arithmetic. This technique provides constant time reduction algorithms. Moreover, it can also be used to strengthen the differential side-channel resistance of asymmetric cryptosystems. We propose modifications to the classic Montgomery and Barrett reduction algorithms in order to have efficient and resistant modular reduction methods. Our algorithms are called dynamic redundant reductions as random masks are intrinsically added within each reduction for a small overhead. This property is useful in order to thwart recent refined attacks on public key algorithms.