Proceedings on Advances in cryptology---CRYPTO '86
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Checking Before Output May Not Be Enough Against Fault-Based Cryptanalysis
IEEE Transactions on Computers
Handbook of Applied Cryptography
Handbook of Applied Cryptography
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
The Montgomery Powering Ladder
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Low-Cost Solutions for Preventing Simple Side-Channel Analysis: Side-Channel Atomicity
IEEE Transactions on Computers
Passive and Active Combined Attacks: Combining Fault Attacks and Side Channel Analysis
FDTC '07 Proceedings of the Workshop on Fault Diagnosis and Tolerance in Cryptography
Distinguishing Multiplications from Squaring Operations
Selected Areas in Cryptography
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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Embedded exponentiation techniques have become a key concern for security and efficiency in hardware devices using public key cryptography. An exponentiation is basically a sequence of multiplications and squarings, but this sequence may reveal exponent bits to an attacker on an unprotected implementation. Although this subject has been covered for years, we present in this paper new exponentiation algorithms based on trading multiplications for squarings. Our method circumvents attacks aimed at distinguishing squarings from multiplications at a lower cost than previous techniques. Last but not least, we present new algorithms using two parallel squaring blocks which provide the fastest exponentiation to our knowledge.