Advances in Applied Mathematics
Elliptic curves in cryptography
Elliptic curves in cryptography
Lattice Attacks on Digital Signature Schemes
Designs, Codes and Cryptography
CRYPTO '99 Proceedings of the 19th 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
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Improved Elliptic Curve Multiplication Methods Resistant against Side Channel Attacks
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
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
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
Weierstraß Elliptic Curves and 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
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
Randomized Signed-Scalar Multiplication of ECC to Resist Power Attacks
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Preventing Differential Analysis in GLV Elliptic Curve Scalar Multiplication
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
Secure Elliptic Curve Implementations: An Analysis of Resistance to Power-Attacks in a DSP Processor
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
DPA Countermeasures by Improving the Window Method
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Recovering Secret Keys from Weak Side Channel Traces of Differing Lengths
CHES '08 Proceeding sof the 10th 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
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
Optimal Recovery of Secret Keys from Weak Side Channel Traces
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Faster addition and doubling on elliptic curves
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Toric forms of elliptic curves and their arithmetic
Journal of Symbolic Computation
Division polynomials for Jacobi quartic curves
Proceedings of the 36th international symposium on Symbolic and algebraic computation
On XTR and side-channel analysis
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Power analysis to ECC using differential power between multiplication and squaring
CARDIS'06 Proceedings of the 7th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Applications
SPA-resistant simultaneous scalar multiplication
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
Signed MSB-set comb method for elliptic curve point multiplication
ISPEC'06 Proceedings of the Second international conference on Information Security Practice and Experience
Twisted jacobi intersections curves
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Countermeasures for preventing comb method against SCA attacks
ISPEC'05 Proceedings of the First international conference on Information Security Practice and Experience
Further hidden markov model cryptanalysis
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Simple power analysis on fast modular reduction with NIST recommended elliptic curves
ICICS'05 Proceedings of the 7th international conference on Information and Communications Security
Efficient arithmetic on hessian curves
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
A DPA countermeasure by randomized frobenius decomposition
WISA'05 Proceedings of the 6th international conference on Information Security Applications
On the automatic construction of indistinguishable operations
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
SPA resistant left-to-right integer recodings
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
On various families of twisted jacobi quartics
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Zero-value point attacks on kummer-based cryptosystem
ACNS'12 Proceedings of the 10th international conference on Applied Cryptography and Network Security
Digit set randomization in elliptic curve cryptography
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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
Fast tate pairing computation on twisted Jacobi intersections curves
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
Twisted Jacobi intersections curves
Theoretical Computer Science
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In this paper we show how using a representation of an elliptic curve as the intersection of two quadrics in P3 can provide a defence against Simple and Differental Power Analysis (SPA/DPA) style attacks. We combine this with a 'random window' method of point multiplication and point blinding. The proposed method offers considerable advantages over standard algorithmic techniques of preventing SPA and DPA which usually require a significant increased computational cost, usually more than double. Our method requires roughly a seventy percent increase in computational cost of the basic cryptographic operation, although we give some indication as to how this can be reduced. In addition we show that the Jacobi form is also more efficient than the standard Weierstrass form for elliptic curves in the situation where SPA and DPA are not a concern.