Improving the arithmetic of elliptic curves in the Jacobi model
Information Processing Letters
New formulae for efficient elliptic curve arithmetic
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Optimizing double-base elliptic-curve single-scalar multiplication
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
Extended double-base number system with applications to elliptic curve cryptography
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
A Tree-Based Approach for Computing Double-Base Chains
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
Pairing Computation on Twisted Edwards Form Elliptic Curves
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
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
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
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Novel Precomputation Schemes for Elliptic Curve Cryptosystems
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
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
On the number of distinct elliptic curves in some families
Designs, Codes and Cryptography
Optimizing double-base elliptic-curve single-scalar multiplication
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
Combined implementation attack resistant exponentiation
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
Using 5-isogenies to quintuple points on elliptic curves
Information Processing Letters
On various families of twisted jacobi quartics
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
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
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Edwards curves have attracted great interest for several reasons. When curve parameters are chosen properly, the addition formulas use only 10M+1S. The formulas are strongly unified, i.e., work without change for doublings; even better, they are complete, i.e., work without change for all inputs. Dedicated doubling formulas use only 3M + 4S, and dedicated tripling formulas use only 9M + 4S. This paper introduces inverted Edwards coordinates. Inverted Edwards coordinates (X1: Y1: Z1) represent the affine point (Z1/X1, Z1/Y1) on an Edwards curve; for comparison, standard Edwards coordinates (X1: Y1: Z1) represent the affine point (X1/Z1, Y1/Z1). This paper presents addition formulas for inverted Edwards coordinates using only 9M + 1S. The formulas are not complete but still are strongly unified. Dedicated doubling formulas use only 3M + 4S, and dedicated tripling formulas use only 9M + 4S. Inverted Edwards coordinates thus save 1M for each addition, without slowing down doubling or tripling.