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
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
Fast Implementation of Public-Key Cryptography ona DSP TMS320C6201
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
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
An Improvement of the Guajardo-Paar Method for Multiplication on Non-Supersingular Elliptic Curves
SCCC '98 Proceedings of the XVIII International Conference of the Chilean Computer Science Society
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)
Trading Inversions for Multiplications in Elliptic Curve Cryptography
Designs, Codes and Cryptography
Extending scalar multiplication using double bases
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Extended double-base number system with applications to elliptic curve cryptography
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
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 analysis of double base number systems and a sublinear scalar multiplication algorithm
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
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 scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Field inversion and point halving revisited
IEEE Transactions on Computers
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
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
A graph theoretic analysis of double base number systems
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Using 5-isogenies to quintuple points on elliptic curves
Information Processing Letters
Fast scalar multiplication for ECC over GF(p) using division chains
WISA'10 Proceedings of the 11th international conference on Information security applications
An efficient mobile PACE implementation
Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security
Division polynomials for Jacobi quartic curves
Proceedings of the 36th international symposium on Symbolic and algebraic computation
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
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
Information Sciences: an International Journal
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In the current work we propose two efficient formulas for computing the 5-fold (5P) of an elliptic curve point P. One formula is for curves over finite fields of even characteristic and the other is for curves over prime fields. Double base number systems (DBNS) have been gainfully exploited to compute scalar multiplication efficiently in ECC. Using the proposed point quintupling formulas one can use 2, 5 and 3, 5 (besides 2, 3) as bases of the double base number system. In the current work we propose a scalar multiplication algorithm, which uses a representation of the scalar using three bases 2, 3 and 5 and computes the scalar multiplication very efficiently. The proposed scheme is faster than all sequential scalar multiplication algorithms reported in literature.