Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: 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
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
New Methods for Digital Generation and Postprocessing of Random Data
IEEE Transactions on Computers
IEEE Transactions on Computers
A highly efficient cipher processor for dual-field elliptic curve cryptography
IEEE Transactions on Circuits and Systems II: Express Briefs
A high-performance unified-field reconfigurable cryptographic processor
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Correlation power-analysis (CPA) attacks are a serious threat for cryptographic device because the key can be disclosed from data-dependent power consumption. Hiding power consumption of encryption circuit can increase the security against CPA attacks, but it results in a large overhead for cost, speed, and energy dissipation. Masking processed data such as randomized scalar or primary base point on elliptic curve is another approach to prevent CPA attacks. However, these methods requiring pre-computed data are not suitable for hardware implementation of real-time applications. In this paper, a new CPA countermeasure performing all field operations in a randomized Montgomery domain is proposed to eliminate the correlation between target and reference power traces. After implemented in 90-nm CMOS process, our protected 521-bit dual-field elliptic curve cryptographic (DF-ECC) processor can perform one elliptic curve scalar multiplication (ECSM) in 4.57ms over GF(p521) and 2.77ms over GF(2409) with 3.6% area and 3.8% power overhead. Experiments from an FPGA evaluation board demonstrate that the private key of unprotected device will be revealed within 103 power traces, whereas the same attacks on our proposal cannot successfully extract the key value even after 106 measurements.