A survey of fast exponentiation methods
Journal of Algorithms
Elliptic curves in cryptography
Elliptic curves in cryptography
Elliptic curve cryptography on smart cards without coprocessors
Proceedings of the fourth working conference on smart card research and advanced applications on Smart card research and advanced applications
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Examining Smart-Card Security under the Threat of Power Analysis Attacks
IEEE Transactions on Computers
Software Implementation of the NIST Elliptic Curves Over Prime Fields
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
A Countermeasure against One Physical Cryptanalysis May Benefit Another Attack
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Towards Sound Approaches to Counteract Power-Analysis Attacks
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
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
Power Analysis Breaks Elliptic Curve Cryptosystems even Secure against the Timing Attack
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
A Fast Software Implementation for Arithmetic Operations in GF(2n)
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
A Fast Parallel Elliptic Curve Multiplication Resistant against Side Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Weierstraß Elliptic Curves and Side-Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
On the Performance of Signature Schemes Based on Elliptic Curves
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
DES and Differential Power Analysis (The "Duplication" Method)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Power Analysis Attacks of Modular Exponentiation in Smartcards
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Preventing SPA/DPA in ECC Systems Using the Jacobi Form
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Universal Exponentiation Algorithm
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Randomized Addition-Subtraction Chains as a Countermeasure against Power Attacks
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Hessian Elliptic Curves and Side-Channel Attacks
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
On XTR and side-channel analysis
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Blinded fault resistant exponentiation
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
High-Order attacks against the exponent splitting protection
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
On the automatic construction of indistinguishable operations
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
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Many software implementations of public key cryptosystems have been concerned with efficiency. The advent of side channel attacks, such as timing and power analysis attacks, force us to reconsider the strategy of implementation of group arithmetic. This paper presents a study of software counter measures against side channel attacks for elliptic curve cryptosystems.We introduce two new counter measures. The first is a new implementation technique, namely, homogeneous group operations, which has the property that addition and doubling on elliptic curves cannot be distinguished from side channel analysis. Being inexpensive time-wise, this technique is an alternative to a well-known Montgomery ladder. The second is a non-deterministic method of point exponentiation with precomputations. Although requiring rather large ROM, it provides an effective resistance against high-order power analysis attacks for the price of index re-computations and ROM accesses.An experimental implementation of NIST-recommended elliptic curves over binary fields with a balanced suite of counter measures built-in in group arithmetic is presented, and the penalty paid is analyzed. The results of the implementation in C on an AMD Duron 600 MHz running Linux are included in the paper.