Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
An algorithm for modular exponentiation
Information Processing Letters
Theory and Applications of the Double-Base Number System
IEEE Transactions on Computers
Elliptic curves in cryptography
Elliptic curves in cryptography
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th 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
Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress 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
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
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
Fast Implementation of Public-Key Cryptography ona DSP TMS320C6201
CHES '99 Proceedings of the First 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
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Low-Cost Solutions for Preventing Simple Side-Channel Analysis: Side-Channel Atomicity
IEEE Transactions on Computers
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Fast elliptic curve arithmetic and improved weil pairing evaluation
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Field inversion and point halving revisited
IEEE Transactions on Computers
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
A Tree-Based Approach for Computing Double-Base Chains
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
Fast Multibase Methods and Other Several Optimizations for Elliptic Curve Scalar Multiplication
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Double-Base Number System for Multi-scalar Multiplications
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Elliptic Curve Scalar Multiplication Combining Yao's Algorithm and Double Bases
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
New formulae for efficient elliptic curve arithmetic
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
A graph theoretic analysis of double base number systems
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Optimizing double-base elliptic-curve single-scalar multiplication
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Efficient window-based scalar multiplication on elliptic curves using double-base number system
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Minimizing hamming weight based on 1's complement of binary numbers over GF(2m)
ICACT'10 Proceedings of the 12th international conference on Advanced communication technology
Fast scalar multiplication for ECC over GF(p) using division chains
WISA'10 Proceedings of the 11th international conference on Information security applications
Bounds and trade-offs for Double-Base Number Systems
Information Processing Letters
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
Extended double-base number system with applications to elliptic curve cryptography
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
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 arithmetic on hessian curves
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Efficient scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
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
A duality in space usage between left-to-right and right-to-left exponentiation
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
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
Hub: heterogeneous bucketization for database outsourcing
Proceedings of the 2013 international workshop on Security in cloud computing
Information Sciences: an International Journal
| Hi-index | 0.00 |
In this paper, we propose a efficient and secure point multiplication algorithm, based on double-base chains. This is achieved by taking advantage of the sparseness and the ternary nature of the so-called double-base number system (DBNS). The speed-ups are the results of fewer point additions and improved formulæ for point triplings and quadruplings in both even and odd characteristic. Our algorithms can be protected against simple and differential side-channel analysis by using side-channel atomicity and classical randomization techniques. Our numerical experiments show that our approach leads to speed-ups compared to windowing methods, even with window size equal to 4, and other SCA resistant algorithms.