A survey of fast exponentiation methods
Journal of Algorithms
Elliptic curves in cryptography
Elliptic curves in cryptography
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th 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
Power Analysis Breaks Elliptic Curve Cryptosystems even Secure against the Timing Attack
INDOCRYPT '00 Proceedings of the First International Conference on Progress 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
Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
ISC '01 Proceedings of the 4th International Conference on Information Security
Elliptic Curves with the Montgomery-Form and Their Cryptographic Applications
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First 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
Universal Exponentiation Algorithm
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
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Fast Elliptic Curve Multiplications with SIMD Operations
ICICS '02 Proceedings of the 4th International Conference on Information and Communications Security
Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
ISC '02 Proceedings of the 5th 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
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
Enhancing Simple Power-Analysis Attacks on Elliptic Curve Cryptosystems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
The Montgomery Powering Ladder
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Address-Bit Differential Power Analysis of Cryptographic Schemes OK-ECDH and OK-ECDSA
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Side-channel resistant system-level design flow for public-key cryptography
Proceedings of the 17th ACM Great Lakes symposium on VLSI
Efficient elliptic curve scalar multiplication algorithms resistant to power analysis
Information Sciences: an International Journal
IEEE Transactions on Computers
Highly Regular Right-to-Left Algorithms for Scalar Multiplication
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
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
Computers and Electrical Engineering
Secure signed radix-r recoding methods for constrained-embedded devices
ISPEC'07 Proceedings of the 3rd international conference on Information security practice and experience
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
Co-Z addition formulæ and binary ladders on elliptic curves
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Arithmetic of split kummer surfaces: montgomery endomorphism of Edwards products
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Memory-constrained implementations of elliptic curve cryptography in co-Z coordinate representation
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
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
Superscalar coprocessor for high-speed curve-based cryptography
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Efficient simultaneous inversion in parallel and application to point multiplication in ECC
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
Signed MSB-set comb method for elliptic curve point multiplication
ISPEC'06 Proceedings of the Second international conference on Information Security Practice and Experience
A tutorial on physical security and side-channel attacks
Foundations of Security Analysis and Design III
Improving the randomized initial point countermeasure against DPA
ACNS'06 Proceedings of the 4th international conference on Applied Cryptography and Network Security
Fast and scalable parallel processing of scalar multiplication in elliptic curve cryptosystems
Security and Communication Networks
Information Sciences: an International Journal
Message blinding method requiring no multiplicative inversion for RSA
ACM Transactions on Embedded Computing Systems (TECS)
| Hi-index | 0.00 |
This paper proposes a fast elliptic curve multiplication algorithm applicable for any types of curves over finite fields Fp (p a prime), based on [Mon87], together with criteria which make our algorithm resistant against the side channel attacks (SCA). The algorithm improves both on an addition chain and an addition formula in the scalar multiplication. Our addition chain requires no table look-up (or a very small number of pre-computed points) and a prominent property is that it can be implemented in parallel. The computing time for n-bit scalar multiplication is one ECDBL + (n - 1) ECADDs in the parallel case and (n - 1) ECDBLs + (n - 1) ECADDs in the single case. We also propose faster addition formulas which only use the x-coordinates of the points. By combination of our addition chain and addition formulas, we establish a faster scalar multiplication resistant against the SCA in both single and parallel computation. The improvement of our scalar multiplications over the previous method is about 37% for two processors and 5.7% for a single processor. Our scalar multiplication is suitable for the implementation on smart cards.