Efficient FPGA implementations of point multiplication on binary Edwards and generalized Hessian curves using Gaussian normal basis

Authors:
Reza Azarderakhsh;Arash Reyhani-Masoleh
Affiliations:
Department of Electrical and Computer Engineering, The University of Western Ontario, London, ON, Canada;Department of Electrical and Computer Engineering, The University of Western Ontario, London, ON, Canada
Venue:
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Year:
2012

Citing 32
Cited 1

Introduction to finite fields and their applications

Introduction to finite fields and their applications
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
Look-Up Table-Based Large Finite Field Multiplication in Memory Constrained Cryptosystems

IEEE Transactions on Computers - Special issue on computer arithmetic
An Efficient Optimal Normal Basis Type II Multiplier

IEEE Transactions on Computers
A New Addition Formula for Elliptic Curves over GF(2^n)

IEEE Transactions on Computers
Weierstraß Elliptic Curves and Side-Channel Attacks

PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key 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
A Low Complexity and a Low Latency Bit Parallel Systolic Multiplier over GF(2m) Using an Optimal Normal Basis of Type II

ARITH '03 Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH-16'03)
Guide to Elliptic Curve Cryptography

Guide to Elliptic Curve Cryptography
Efficient Algorithms and Architectures for Field Multiplication Using Gaussian Normal Bases

IEEE Transactions on Computers
Software Multiplication Using Gaussian Normal Bases

IEEE Transactions on Computers
Optimum Digit Serial GF(2^m) Multipliers for Curve-Based Cryptography

IEEE Transactions on Computers
Subquadratic Computational Complexity Schemes for Extended Binary Field Multiplication Using Optimal Normal Bases

IEEE Transactions on Computers
Fast elliptic curve cryptography on FPGA

IEEE Transactions on Very Large Scale Integration (VLSI) Systems
FPGA implementation of high performance elliptic curve cryptographic processor over GF(2163)

Journal of Systems Architecture: the EUROMICRO Journal
Efficient Multiplication Using Type 2 Optimal Normal Bases

WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Binary Edwards Curves

CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
High-Performance Architecture of Elliptic Curve Scalar Multiplication

IEEE Transactions on Computers
Provably Sublinear Point Multiplication on Koblitz Curves and Its Hardware Implementation

IEEE Transactions on Computers
Elliptic-Curve-Based Security Processor for RFID

IEEE Transactions on Computers
Elliptic Curve Cryptography on FPGA for Low-Power Applications

ACM Transactions on Reconfigurable Technology and Systems (TRETS)
Fast point multiplication on Koblitz curves: Parallelization method and implementations

Microprocessors & Microsystems
On parallelization of high-speed processors for elliptic curve cryptography

IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem

ARC '09 Proceedings of the 5th International Workshop on Reconfigurable Computing: Architectures, Tools and Applications
Batch Binary Edwards

CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
A high performance ECC hardware implementation with instruction-level parallelism over GF(2163)

Microprocessors & Microsystems
A modified low complexity digit-level Gaussian normal basis multiplier

WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Type-II optimal polynomial bases

WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Breaking Elliptic Curve Cryptosystems Using Reconfigurable Hardware

FPL '10 Proceedings of the 2010 International Conference on Field Programmable Logic and Applications
Customizable elliptic curve cryptosystems

IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Efficient arithmetic on hessian curves

PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography

On the implementation of unified arithmetic on binary huff curves

CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

Efficient implementation of point multiplication is crucial for elliptic curve cryptographic systems. This paper presents the implementation results of an elliptic curve crypto-processor over binary fields GF(2m) on binary Edwards and generalized Hessian curves using Gaussian normal basis (GNB). We demonstrate how parallelization in higher levels can be performed by full resource utilization of computing point addition and point-doubling formulas for both binary Edwards and generalized Hessian curves. Then, we employ the w-coordinate differential formulations for computing point multiplication. Using a lookup-table (LUT)-based pipelined and efficient digit-level GNB multiplier, we evaluate the LUT complexity and time-area tradeoffs of the proposed crypto-processor on an FPGA. We also compare the implementation results of point multiplication on these curves with the ones on the traditional binary generic curve. To the best of the authors' knowledge, this is the first FPGA implementation of point multiplication on binary Edwards and generalized Hessian curves represented by w-coordinates.