Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Low-Energy Digit-Serial/Parallel Finite Field Multipliers
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
Elliptic curves in cryptography
Elliptic curves in cryptography
High-Radix Montgomery Modular Exponentiation on Reconfigurable Hardware
IEEE Transactions on Computers
Reconfigurable Implementation of Elliptic Curve Crypto Algorithms
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
A High Performance Reconfigurable Elliptic Curve Processor for GF(2m)
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
A Compact Fast Variable Key Size Elliptic Curve Cryptosystem Coprocessor
FCCM '99 Proceedings of the Seventh Annual IEEE Symposium on Field-Programmable Custom Computing Machines
Rapid Prototyping for Hardware Accelerated Elliptic Curve Public-Key Cryptosystems
RSP '01 Proceedings of the 12th International Workshop on Rapid System Prototyping
From Euclid's GCD to Montgomery Multiplication to the Great Divide
From Euclid's GCD to Montgomery Multiplication to the Great Divide
Generic implementations of elliptic curve cryptography using partial reduction
Proceedings of the 9th ACM conference on Computer and communications security
Elliptic and hyperelliptic curves on embedded μP
ACM Transactions on Embedded Computing Systems (TECS)
TinyPK: securing sensor networks with public key technology
Proceedings of the 2nd ACM workshop on Security of ad hoc and sensor networks
Reconfigurable Elliptic Curve Cryptosystems on a Chip
Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Optimum Digit Serial GF(2^m) Multipliers for Curve-Based Cryptography
IEEE Transactions on Computers
High-speed hardware implementations of Elliptic Curve Cryptography: A survey
Journal of Systems Architecture: the EUROMICRO Journal
Journal of VLSI Signal Processing Systems
An efficient polynomial multiplier in GF(2m) and its application to ECC designs
Proceedings of the conference on Design, automation and test in Europe
Fast elliptic curve cryptography on FPGA
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Public key cryptography empowered smart dust is affordable
International Journal of Sensor Networks
FPGA implementation of high performance elliptic curve cryptographic processor over GF(2163)
Journal of Systems Architecture: the EUROMICRO Journal
A unified security framework with three key management schemes for wireless sensor networks
Computer Communications
High Speed Compact Elliptic Curve Cryptoprocessor for FPGA Platforms
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
On parallelization of high-speed processors for elliptic curve cryptography
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Optimizing the Control Hierarchy of an ECC Coprocessor Design on an FPGA Based SoC Platform
ARC '09 Proceedings of the 5th International Workshop on Reconfigurable Computing: Architectures, Tools and Applications
FPGA Implementation of Elliptic Curve Point Multiplication over GF(2191)
ISA '09 Proceedings of the 3rd International Conference and Workshops on Advances in Information Security and Assurance
A cryptographic processor for arbitrary elliptic curves over GF(2m)
A cryptographic processor for arbitrary elliptic curves over GF(2m)
Sizzle: a standards-based end-to-end security architecture for the embedded internet
Sizzle: a standards-based end-to-end security architecture for the embedded internet
Flexible hardware processor for elliptic curve cryptography over NIST prime fields
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
High speed modular divider based on GCD algorithm
ICICS'07 Proceedings of the 9th international conference on Information and communications security
Efficient implementation of elliptic curve cryptography using low-power digital signal processor
ICACT'10 Proceedings of the 12th international conference on Advanced communication technology
Optimized System-on-Chip Integration of a Programmable ECC Coprocessor
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
Optimizing the HW/SW boundary of an ECC SoC design using control hierarchy and distributed storage
Proceedings of the Conference on Design, Automation and Test in Europe
Customizable elliptic curve cryptosystems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Design of flexible GF(2m) elliptic curve cryptography processors
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Superscalar coprocessor for high-speed curve-based cryptography
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
ICICS'09 Proceedings of the 11th international conference on Information and Communications Security
Integration, the VLSI Journal
Pushing the limits of high-speed GF(2m) elliptic curve scalar multiplication on FPGAs
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
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Since its proposal by Victor Miller [17] and Neal Koblitz [15] in the mid 1980s, Elliptic Curve Cryptography (ECC) has evolved into a mature public-key cryptosystem. Offering the smallest key size and the highest strength per bit, its computational efficiency can benefit both client devices and server machines. We have designed a programmable hardware accelerator to speed up point multiplication for elliptic curves over binary polynomial fields GF(2m). The accelerator is based on a scalable architecture capable of handling curves of arbitrary field degrees up to m = 255. In addition, it delivers optimized performance for a set of commonly used curves through hard-wired reduction logic. A prototype implementation running in a Xilinx XCV2000E FPGA at 66.4 MHz shows a performance of 6987 point multiplications per second for GF(2163). We have integrated ECC into OpenSSL, today's dominant implementation of the secure Internet protocol SSL, and tested it with the Apache web server and open-source web browsers.