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
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
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
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
Finite Fields and Their Applications
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
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We use two parametrizations of points on elliptic curves in generalized Edwards form x2 + y2 = c2(1 + dx2y2) that omit the x- coordinate. The first parametrization leads to a differential addition formula that can be computed using 6M + 4S, a doubling formula using 1M+ 4S and a tripling formula using 4M+ 7S. The second one yields a differential addition formula that can be computed using 5M + 2S and a doubling formula using 5S. All formulas apply also for the case c ≠ 1 and arbitrary curve parameter d. This generalizes formulas from the literature for the special case c = 1 or d being a square in the ground field. For both parametrizations the formula for recovering the missing X- coordinate is also provided.