A course in computational algebraic number theory
A course in computational algebraic number theory
Elliptic curves in cryptography
Elliptic curves in cryptography
Schoof's algorithm and isogeny cycles
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Improving the arithmetic of elliptic curves in the Jacobi model
Information Processing Letters
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
ISA '09 Proceedings of the 3rd International Conference and Workshops on Advances in Information Security and Assurance
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
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 scalar multiplication by isogeny decompositions
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Algebraic curves and cryptography
Finite Fields and Their Applications
Efficient multiplication over extension fields
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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
Low-Cost countermeasure against RPA
CARDIS'12 Proceedings of the 11th international conference on Smart Card Research and Advanced Applications
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Elliptic curve cryptosystems are usually implemented over fields of characteristic two or over (large) prime fields. For large prime fields, projective coordinates are more suitable as they reduce the computational workload in a point multiplication. In this case, choosing for parameter a the value -3 further reduces the workload. Over Fp, not all elliptic curves can be rescaled through isomorphisms to the case a = -3. This paper suggests the use of the more general notion of isogenies to rescale the curve. As a side result, this also illustrates that selecting elliptic curves with a = -3 (as those recommended in most standards) is not restrictive.