Elliptic curves in cryptography
Elliptic curves in cryptography
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
Improving the arithmetic of elliptic curves in the Jacobi model
Information Processing Letters
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
Fast point multiplication on elliptic curves through isogenies
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
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Curve25519: new diffie-hellman speed records
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Pairing Computation on Twisted Edwards Form Elliptic Curves
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and lIC-Derivatives
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Another Approach to Pairing Computation in Edwards Coordinates
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
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
A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem
ARC '09 Proceedings of the 5th International Workshop on Reconfigurable Computing: Architectures, Tools and Applications
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Jacobi Quartic Curves Revisited
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
On the number of distinct elliptic curves in some families
Designs, Codes and Cryptography
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Efficient techniques for high-speed elliptic curve cryptography
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Differential addition in generalized Edwards coordinates
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
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
High-speed high-security signatures
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Twisted jacobi intersections curves
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Refinement of miller's algorithm over edwards curves
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
Atomicity improvement for elliptic curve scalar multiplication
CARDIS'10 Proceedings of the 9th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Application
On various families of twisted jacobi quartics
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Fast tate pairing computation on twisted Jacobi intersections curves
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
Four-Dimensional gallant-lambert-vanstone scalar multiplication
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Twisted edwards-form elliptic curve cryptography for 8-bit AVR-based sensor nodes
Proceedings of the first ACM workshop on Asia public-key cryptography
Twisted Jacobi intersections curves
Theoretical Computer Science
Elligator: elliptic-curve points indistinguishable from uniform random strings
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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This paper introduces "twisted Edwards curves," a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and shows that twisted Edwards curves save time for many curves that were already expressible as Edwards curves.