A course in number theory and cryptography
A course in number theory and cryptography
Discrete Applied Mathematics
A survey of fast exponentiation methods
Journal of Algorithms
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
Handbook of Applied Cryptography
Handbook of Applied Cryptography
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Efficient Multiplication on Certain Nonsupersingular Elliptic Curves
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
An Elliptic Curve Implementation of the Finite Field Digital Signature Algorithm
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
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
Software Implementation of the NIST Elliptic Curves Over Prime Fields
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Integer Decomposition for Fast Scalar Multiplication on Elliptic Curves
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Speeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Speeding up the Scalar Multiplication in the Jacobians of Hyperelliptic Curves Using Frobenius Map
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
An Improved Method of Multiplication on Certain Elliptic Curves
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Validation of Elliptic Curve Public Keys
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Random small hamming weight products with applications to cryptography
Discrete Applied Mathematics - Special issue on the 2000 com2MaC workshop on cryptography
An Improved Algorithm for uP + vQ on a Family of Elliptic Curves
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 17 - Volume 18
Elliptic curve cryptography: Java implementation
Proceedings of the 1st annual conference on Information security curriculum development
A New Minimal Average Weight Representation for Left-to-Right Point Multiplication Methods
IEEE Transactions on Computers
A note on window τ-NAF algorithm
Information Processing Letters
Analysis of Fractional Window Recoding Methods and Their Application to Elliptic Curve Cryptosystems
IEEE Transactions on Computers
Software Multiplication Using Gaussian Normal Bases
IEEE Transactions on Computers
Pipelined Computation of Scalar Multiplication in Elliptic Curve Cryptosystems (Extended Version)
IEEE Transactions on Computers
On binary signed digit representations of integers
Designs, Codes and Cryptography
On Τ-adic representations of integers
Designs, Codes and Cryptography
High-performance public-key cryptoprocessor for wireless mobile applications
Mobile Networks and Applications
Fast elliptic curve cryptography on FPGA
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Extractors for binary elliptic curves
Designs, Codes and Cryptography
FPGA Design of Self-certified Signature Verification on Koblitz Curves
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
The GPS Identification Scheme Using Frobenius Expansions
Research in Cryptology
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 New Upper Bound for the Minimal Density of Joint Representations in Elliptic Curve Cryptosystems
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
TinyECCK: Efficient Elliptic Curve Cryptography Implementation over GF(2m) on 8-Bit Micaz Mote
IEICE - Transactions on Information and Systems
Unbalanced digit sets and the closest choice strategy for minimal weight integer representations
Designs, Codes and Cryptography
A note on window τ-NAF algorithm
Information Processing Letters
Delaying and merging operations in scalar multiplication: applications to curve-based cryptosystems
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
On redundant T-adic expansions and non-adjacent digit sets
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
Secure signed radix-r recoding methods for constrained-embedded devices
ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
Generic GF(2m) arithmetic in software and its application to ECC
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
Fast batch verification of multiple signatures
PKC'07 Proceedings of the 10th international conference on Practice and theory in public-key cryptography
New Frobenius expansions for elliptic curves with efficient endomorphisms
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Improved techniques for fast exponentiation
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Improved algorithms for efficient arithmetic on elliptic curves using fast endomorphisms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Affine precomputation with sole inversion in elliptic curve cryptography
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Koblitz curves and integer equivalents of frobenius expansions
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
Efficient arithmetic on subfield elliptic curves over small finite fields of odd characteristic
ISPEC'08 Proceedings of the 4th international conference on Information security practice and experience
wNAF, an efficient left-to-right signed digit recoding algorithm
ACNS'08 Proceedings of the 6th international conference on Applied cryptography and network security
Efficient software implementation of binary field arithmetic using vector instruction sets
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Designs, Codes and Cryptography
Faster and lower memory scalar multiplication on supersingular curves in characteristic three
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
On the distribution of the coefficients of normal forms for Frobenius expansions
Designs, Codes and Cryptography
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Extending scalar multiplication using double bases
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Scalar multiplication on koblitz curves using double bases
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
Left-to-Right signed-bit τ-adic representations of n integers
ICICS'06 Proceedings of the 8th international conference on Information and Communications Security
An advanced method for joint scalar multiplications on memory constraint devices
ESAS'05 Proceedings of the Second European conference on Security and Privacy in Ad-Hoc and Sensor Networks
FPGA implementation of point multiplication on koblitz curves using kleinian integers
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Efficient representations on koblitz curves with resistance to side channel attacks
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
A note on signed binary window algorithm for elliptic curve cryptosystems
CANS'05 Proceedings of the 4th international conference on Cryptology and Network Security
Efficiently computable endomorphisms for hyperelliptic curves
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Two new fast methods for simultaneous scalar multiplication in elliptic curve cryptosystems
ICCNMC'05 Proceedings of the Third international conference on Networking and Mobile Computing
New minimal weight representations for left-to-right window methods
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Short memory scalar multiplication on koblitz curves
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Advances in alternative non-adjacent form representations
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
Fractional windows revisited: improved signed-digit representations for efficient exponentiation
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
ISPEC'10 Proceedings of the 6th international conference on Information Security Practice and Experience
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
A DPA countermeasure by randomized frobenius decomposition
WISA'05 Proceedings of the 6th international conference on Information Security Applications
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Sublinear scalar multiplication on hyperelliptic koblitz curves
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Fast and scalable parallel processing of scalar multiplication in elliptic curve cryptosystems
Security and Communication Networks
Finite Fields and Their Applications
Improved fixed-base comb method for fast scalar multiplication
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
Faster implementation of scalar multiplication on koblitz curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Batch verification suitable for efficiently verifying a limited number of signatures
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Information Sciences: an International Journal
Securing ZigBee smart energy profile 1.x with OpenECC library
Proceedings of the first ACM workshop on Smart energy grid security
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It has become increasingly common to implementdiscrete-logarithm based public-key protocols on elliptic curvesover finite fields. The basic operation is scalar multiplication:taking a given integer multiple of a given point on the curve.The cost of the protocols depends on that of the elliptic scalarmultiplication operation.Koblitz introduceda family of curves which admit especially fast elliptic scalarmultiplication. His algorithm was later modified by Meier andStaffelbach. We give an improved version of the algorithm whichruns 50 than any previous version. It is based on a new kindof representation of an integer, analogous to certain kinds ofbinary expansions. We also outline further speedups using precomputationand storage.