Advances in Applied Mathematics
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
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Improving the arithmetic of elliptic curves in the Jacobi model
Information Processing Letters
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
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
Jacobi Quartic Curves Revisited
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
New formulae for efficient elliptic curve arithmetic
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Fast scalar multiplication for ECC over GF(p) using division chains
WISA'10 Proceedings of the 11th international conference on Information security applications
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
Twisted jacobi intersections curves
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Efficient arithmetic on hessian curves
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
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
Fast and scalable parallel processing of scalar multiplication in elliptic curve cryptosystems
Security and Communication Networks
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
Tate pairing computation on jacobi's elliptic curves
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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A way for preventing SPA-like attacks on elliptic curve systems is to use the same formula for the doubling and the general addition of points on the curve. Various proposals have been made in this direction with different results. This paper re-investigates the Jacobi form suggested by Liardet and Smart (CHES 2001). Rather than considering the Jacobi form as the intersection of two quadrics, the addition law is directly derived from the underlying quartic. As a result, this leads to substantial memory savings and produces the fastest unified addition formula for curves of order a multiple of 2, as those required for OK-ECDH or OK-ECDSA.