A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
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The Montgomery Inverse and Its Applications
IEEE Transactions on Computers
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the Selected Areas in Cryptography
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
A Scalable Dual-Field Elliptic Curve Cryptographic Processor
IEEE Transactions on Computers
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Elliptic-Curve-Based Security Processor for RFID
IEEE Transactions on Computers
ECC Is Ready for RFID --- A Proof in Silicon
Selected Areas in Cryptography
An ECDSA pocessor for RFID athentication
RFIDSec'10 Proceedings of the 6th international conference on Radio frequency identification: security and privacy issues
Low-resource hardware design of an elliptic curve processor for contactless devices
WISA'10 Proceedings of the 11th international conference on Information security applications
Memory-constrained implementations of elliptic curve cryptography in co-Z coordinate representation
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
Low-Cost elliptic curve cryptography for wireless sensor networks
ESAS'06 Proceedings of the Third European conference on Security and Privacy in Ad-Hoc and Sensor Networks
A hardware processor supporting elliptic curve cryptography for less than 9 kGEs
CARDIS'11 Proceedings of the 10th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
Hardware architectures for MSP430-based wireless sensor nodes performing elliptic curve cryptography
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
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In this paper, we answer the question whether binary extension field or prime-field based processors doing multi-precision arithmetic are better in the terms of area, speed, power, and energy. This is done by implementing and optimizing two distinct custom-made 16-bit processor designs and comparing our solutions on different abstraction levels: finite-field arithmetic, elliptic-curve operations, and on protocol level by implementing the Elliptic Curve Digital Signature Algorithm (ECDSA). On the one hand, our $\mathbb{F}_{2^{m}}$ based processor outperforms the $\mathbb{F}_p$ based processor by 19.7% in area, 69.6% in runtime, 15.9% in power, and 74.4% in energy when performing a point multiplication. On the other hand, our $\mathbb{F}_p$ based processor (11.6kGE, 41.4,μ W, 1,313kCycles, and 54.3μ J) improves the state-of-the-art in $\mathbb{F}_{p_{192}}$ ECC hardware implementations regarding area, power, and energy results. After extending the designs for ECDSA (signature generation and verification), the area and power-consumption advantages of the $\mathbb{F}_{2^{m}}$ based processor vanish, but it still is 1.5-2.8 times better in terms of energy and runtime.