Advances in Applied Mathematics
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Reducing elliptic curve logarithms to logarithms in a finite field
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Mathematics of Computation
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th 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 Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Elliptic Curve Cryptosystems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
A Fast Software Implementation for Arithmetic Operations in GF(2n)
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Public-key cryptosystems with very small key lengths
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Reconfigurable Implementation of Elliptic Curve Crypto Algorithms
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Efficient Identity Based Parameter Selection for Elliptic Curve Cryptosystems
ACISP '99 Proceedings of the 4th Australasian Conference on Information Security and Privacy
A New Elliptic Curve Scalar Multiplication Algorithm to Resist Simple Power Analysis
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
ACISP '02 Proceedings of the 7th Australian 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
A Cyclic Window Algorithm for ECC Defined over Extension Fields
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
Fast Elliptic Curve Multiplications with SIMD Operations
ICICS '02 Proceedings of the 4th International Conference on Information and Communications Security
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Fast Simultaneous Scalar Multiplication on Elliptic Curve with Montgomery Form
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
On the Power of Multidoubling in Speeding Up Elliptic Scalar Multiplication
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
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Power Analysis Breaks Elliptic Curve Cryptosystems even Secure against the Timing Attack
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Unbelievable Security. Matching AES Security Using Public Key Systems
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
ISC '01 Proceedings of the 4th International Conference on Information Security
Lenient/Strict Batch Verification in Several Groups
ISC '01 Proceedings of the 4th International Conference on Information Security
Elliptic Curve Arithmetic Using SIMD
ISC '01 Proceedings of the 4th International Conference on Information Security
A Second-Order DPA Attack Breaks a Window-Method Based Countermeasure against Side Channel Attacks
ISC '02 Proceedings of the 5th International Conference on Information Security
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
A Fast Parallel Elliptic Curve Multiplication Resistant against Side Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Exceptional Procedure Attackon Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
On Montgomery-Like Representationsfor Elliptic Curves over GF(2k)
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Fast Implementation of Elliptic Curve Defined over GF(pm) on CalmRISC with MAC2424 Coprocessor
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Preventing SPA/DPA in ECC Systems Using the Jacobi Form
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Hessian Elliptic Curves and Side-Channel Attacks
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
The Hessian Form of an Elliptic Curve
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Pipelined Computation of Scalar Multiplication in Elliptic Curve Cryptosystems (Extended Version)
IEEE Transactions on Computers
New Point Addition Formulae for ECC Applications
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Fast Point Multiplication on Elliptic Curves without Precomputation
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Optimization Algorithm for Scalar Multiplication in the Elliptic Curve Cryptography over Prime Field
ICIC '08 Proceedings of the 4th international conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications - with Aspects of Theoretical and Methodological Issues
Faster Multi-exponentiation through Caching: Accelerating (EC)DSA Signature Verification
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Twisted Edwards Curves Revisited
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Improved Implementations of Cryptosystems Based on Tate Pairing
ISA '09 Proceedings of the 3rd International Conference and Workshops on Advances in Information Security and Assurance
Jacobi Quartic Curves Revisited
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
Faster Pairings on Special Weierstrass Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Co-Z addition formulæ and binary ladders on elliptic curves
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Coordinate blinding over large prime fields
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
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
An efficient mobile PACE implementation
Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security
Toric forms of elliptic curves and their arithmetic
Journal of Symbolic Computation
ARES'11 Proceedings of the IFIP WG 8.4/8.9 international cross domain conference on Availability, reliability and security for business, enterprise and health information systems
Compressed jacobian coordinates for OEF
VIETCRYPT'06 Proceedings of the First international conference on Cryptology in Vietnam
Efficient implementation of public key cryptosystems on mote sensors (short paper)
ICICS'06 Proceedings of the 8th international conference on Information and Communications Security
Efficient and secure elliptic curve point multiplication using double-base chains
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information 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
Scalar multiplication on elliptic curves defined over fields of small odd characteristic
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Sign change fault attacks on elliptic curve cryptosystems
FDTC'06 Proceedings of the Third international conference on Fault Diagnosis and Tolerance in Cryptography
Fast multi-computations with integer similarity strategy
PKC'05 Proceedings of the 8th international conference on Theory and Practice in Public Key Cryptography
New minimal weight representations for left-to-right window methods
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Novel efficient implementations of hyperelliptic curve cryptosystems using degenerate divisors
WISA'04 Proceedings of the 5th international conference on Information Security Applications
Countermeasures for preventing comb method against SCA attacks
ISPEC'05 Proceedings of the First international conference on Information Security Practice and Experience
Using an RSA accelerator for modular inversion
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Exact analysis of montgomery multiplication
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
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
A general methodology for pipelining the point multiplication operation in curve based cryptography
ACNS'06 Proceedings of the 4th international conference on Applied Cryptography and Network Security
Improving the randomized initial point countermeasure against DPA
ACNS'06 Proceedings of the 4th international conference on Applied Cryptography and Network Security
Atomicity improvement for elliptic curve scalar multiplication
CARDIS'10 Proceedings of the 9th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Application
Efficient, non-optimistic secure circuit evaluation based on the elgamal encryption
WISA'05 Proceedings of the 6th international conference on Information Security Applications
SPA resistant left-to-right integer recodings
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Improved precomputation scheme for scalar multiplication on elliptic curves
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
ISC'07 Proceedings of the 10th international conference on Information Security
Complete atomic blocks for elliptic curves in jacobian coordinates over prime fields
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Shifting primes on OpenRISC processors with hardware multiplier
ICT-EurAsia'13 Proceedings of the 2013 international conference on Information and Communication Technology
Secure JTAG Implementation Using Schnorr Protocol
Journal of Electronic Testing: Theory and Applications
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Elliptic curve cryptosystems, proposed by Koblitz ([12]) and Miller ([16]), can be constructed over a smaller field of definition than the ElGamal cryptosystems ([6]) or the RSA cryptosystems ([20]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate efficient elliptic curve exponentiation. We propose a new coordinate system and a new mixed coordinates strategy, which significantly improves on the number of basic operations needed for elliptic curve exponentiation.