Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Exponentiation using canonical recoding
Theoretical Computer Science
CRYPTO '99 Proceedings of the 19th 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
Breaking Public Key Cryptosystems on Tamper Resistant Devices in the Presence of Transient Faults
Proceedings of the 5th International Workshop on Security Protocols
Low Cost Attacks on Tamper Resistant Devices
Proceedings of the 5th International Workshop on Security Protocols
Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
ISC '01 Proceedings of the 4th International Conference on Information Security
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
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
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
On the importance of checking cryptographic protocols for faults
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
On binary signed digit representations of integers
Designs, Codes and Cryptography
Breaking the liardet-smart randomized exponentiation algorithm
CARDIS'02 Proceedings of the 5th conference on Smart Card Research and Advanced Application Conference - Volume 5
On Τ-adic representations of integers
Designs, Codes and Cryptography
International Journal of Information and Computer Security
Recovering Secret Keys from Weak Side Channel Traces of Differing Lengths
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Optimal Recovery of Secret Keys from Weak Side Channel Traces
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
A random M-ary method based countermeasure against side channel attacks
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartII
Simple backdoors for RSA key generation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Generic cryptanalysis of combined countermeasures with randomized BSD representations
CARDIS'06 Proceedings of the 7th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
Side channel cryptanalysis on SEED
WISA'04 Proceedings of the 5th international conference on Information Security Applications
Improvement on ha-moon randomized exponentiation algorithm
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
High-Order attacks against the exponent splitting protection
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
DPA attack on the improved ha-moon algorithm
WISA'05 Proceedings of the 6th international conference on Information Security Applications
Digit set randomization in elliptic curve cryptography
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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Recently it has been shown that smart cards as cryptographic devices are vulnerable to power attacks if they have no defence against them. Randomization on ECC scalar multiplication is one of the fundamental concepts in methods of defence against side-channel attacks. In this paper by using the randomization concept together with the NAF recoding algorithm, we propose an efficient countermeasure for ECCs against power attacks. The countermeasure provides a randomized signed-scalar representation at every scalar multiplication to resist DPA. To protect against SPA it additionally employs a simple SPA-immune addition-subtraction multiplication algorithm. Our analysis shows that it needs no additional computation load compared to the ordinary binary scalar multiplication, where the average number of doublings plus additions for a bit length n is 1.5n+O(1).