Algorithmica
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Computation of discrete logarithms in prime fields
Designs, Codes and Cryptography
Parallel collision search with application to hash functions and discrete logarithms
CCS '94 Proceedings of the 2nd ACM Conference on Computer and communications security
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
Constructing Elliptic Curve Cryptosystems in Characteristic 2
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Constructing elliptic curves with given group order over large finite fields
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Non supersingular elliptic curves for public key cryptosystems
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems with very small key lengths
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Resource requirements for the application of addition chains in modulo exponentiation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Fast exponentiation with precomputation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Some remarks on parallel exponentiation (extended abstract)
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
The Montgomery Modular Inverse-Revisited
IEEE Transactions on Computers - Special issue on computer arithmetic
ACM SIGMOBILE Mobile Computing and Communications Review
Irreducible trinomials over finite fields
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
IEEE Transactions on Computers
Generic implementations of elliptic curve cryptography using partial reduction
Proceedings of the 9th ACM conference on Computer and communications security
Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes
Designs, Codes and Cryptography
VLSI Algorithms, Architectures, and Implementation of a Versatile GF(2m) Processor
IEEE Transactions on Computers
Bit-Parallel Finite Field Multiplier and Squarer Using Polynomial Basis
IEEE Transactions on Computers
A New Addition Formula for Elliptic Curves over GF(2^n)
IEEE Transactions on Computers
Elliptic Curve Cryptography on a Palm OS Device
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in Cryptography
Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)
SAC '98 Proceedings of the Selected Areas in Cryptography
An Improved Implementation of Elliptic Curves over GF(2) when Using Projective Point Arithmetic
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd 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
Elliptic Curve Public-Key Cryptosystems - An Introduction
State of the Art in Applied Cryptography, Course on Computer Security and Industrial Cryptography - Revised Lectures
Monkey: Black-Box Symmetric Ciphers Designed for MONopolizing KEYs
FSE '98 Proceedings of the 5th International Workshop on Fast Software Encryption
Elliptic Curve Arithmetic Using SIMD
ISC '01 Proceedings of the 4th International Conference on Information Security
A New Aspect of Dual Basis for Efficient Field Arithmetic
PKC '99 Proceedings of the Second International Workshop on Practice and Theory in Public Key Cryptography
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: 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 High Performance Reconfigurable Elliptic Curve Processor for GF(2m)
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Multiplicative Masking and Power Analysis of AES
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
A Low-Power Design for an Elliptic Curve Digital Signature Chip
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Computer Standards & Interfaces
FPGA Implementation of a Microcoded Elliptic Curve Cryptographic Processor
FCCM '00 Proceedings of the 2000 IEEE Symposium on Field-Programmable Custom Computing Machines
Irreducible trinomials over finite fields
Mathematics of Computation
Constructing Composite Field Representations for Efficient Conversion
IEEE Transactions on Computers
Fast Normal Basis Multiplication Using General Purpose Processors
IEEE Transactions on Computers
Elliptic and hyperelliptic curves on embedded μP
ACM Transactions on Embedded Computing Systems (TECS)
IEEE Transactions on Computers
A threshold signature scheme for group communications without a shared distribution center
Future Generation Computer Systems - Special issue: Computational science of lattice Boltzmann modelling
IEEE Transactions on Computers
An Efficient Basis Conversion Algorithm for Composite Fields with Given Representations
IEEE Transactions on Computers
PGP in constrained wireless devices
SSYM'00 Proceedings of the 9th conference on USENIX Security Symposium - Volume 9
Elliptic curve DSA (ECSDA): an enhanced DSA
SSYM'98 Proceedings of the 7th conference on USENIX Security Symposium - Volume 7
Hardware organization to achieve high-speed elliptic curve cryptography for mobile devices
Mobile Networks and Applications
Implementing public-key infrastructure for sensor networks
ACM Transactions on Sensor Networks (TOSN)
Effects of Optimizations for Software Implementations of Small Binary Field Arithmetic
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Highly Regular Right-to-Left Algorithms for Scalar Multiplication
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Multi-core Implementation of the Tate Pairing over Supersingular Elliptic Curves
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Finding good random elliptic curves for cryptosystems defined over IF2n
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Efficient inversion algorithm for optimal normal bases type II
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Generic GF(2m) arithmetic in software and its application to ECC
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
Backdoor attacks on black-box ciphers exploiting low-entropy plaintexts
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
Improved techniques for fast exponentiation
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Provably secure and efficient identification and key agreement protocol with user anonymity
Journal of Computer and System Sciences
Efficient software implementations of large finite fields GF(2n) for secure storage applications
ACM Transactions on Storage (TOS)
Fractional windows revisited: improved signed-digit representations for efficient exponentiation
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Accelerating inverse of GF(2n) with precomputation
ISPEC'10 Proceedings of the 6th international conference on Information Security Practice and Experience
Efficient hardware implementation of elliptic curve cryptography over GF(pm)
WISA'05 Proceedings of the 6th international conference on Information Security Applications
Rings of Low Multiplicative Complexity
Finite Fields and Their Applications
On the reducibility of some composite polynomials over finite fields
Designs, Codes and Cryptography
International Journal of Communication Networks and Distributed Systems
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The Diffie-Hellman key exchange algorithm can be implemented using the group of points on an elliptic curve over the field F2n. A software version of this using n = 155 can be optimized to achieve computation rates that are slightly faster than non-elliptic curve versions with a similar level of security. The fast computation of reciprocals in F2n is the key to the highly efficient implementation described here.