Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Elliptic curves in cryptography
Elliptic curves in cryptography
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
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
The Montgomery Powering Ladder
CHES '02 Revised Papers from the 4th 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
Sign change fault attacks on elliptic curve cryptosystems
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
Programmable and Parallel ECC Coprocessor Architecture: Tradeoffs between Area, Speed and Security
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Combined implementation attack resistant exponentiation
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
An updated survey on secure ECC implementations: attacks, countermeasures and cost
Cryptography and Security
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The elliptic curve cryptosystem(ECC) is increasingly being used in practice due to its shorter key sizes and efficient realizations. However, ECC is also known to be vulnerable to various side channel attacks, including power attacks and fault injection attacks. This paper proposes new countermeasures for ECC scalar multiplications against differential power attacks and fault attacks. The basic idea of proposed countermeasures lies in extending the definition field of an elliptic curve to its random extension ring and performing the required elliptic curve operations over the ring. Moreover, new methods perform a point validation check in a small subring of the extension ring to give an efficient fault attack countermeasure.