Advances in Applied Mathematics
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
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
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
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
Preventing SPA/DPA in ECC Systems Using the Jacobi Form
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
The Hessian Form of an Elliptic Curve
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
The resultant of an unmixed bivariate system
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Rational simplification modulo a polynomial ideal
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
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
On the number of distinct elliptic curves in some families
Designs, Codes and Cryptography
The Jacobi model of an elliptic curve and side-channel analysis
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
New formulae for efficient elliptic curve arithmetic
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
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
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
Finite Fields and Their Applications
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We scan a large class of one-parameter families of elliptic curves for efficient arithmetic. The construction of the class is inspired by toric geometry, which provides a natural framework for the study of various forms of elliptic curves. The class both encompasses many prominent known forms and includes thousands of new forms. A powerful algorithm is described that automatically computes the most compact group operation formulas for any parameterized family of elliptic curves. The generality of this algorithm is further illustrated by computing uniform addition formulas and formulas for generalized Montgomery arithmetic.