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This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 1 8M for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted)(More)
This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic(More)
This paper provides new results about efficient arithmetic on (extended) Jacobi quartic form elliptic curves y 2 = dx 4 + 2ax 2 + 1. Recent works have shown that arithmetic on an elliptic curve in Jacobi quartic form can be performed solidly faster than the corresponding operations in Weierstrass form. These proposals use up to 7 coordinates to represent a(More)
One of the five AES finalists, MARS, makes use of a 9x32 s-box with very specific combinatorial, differential and linear correlation properties. The s-box used in the cipher was selected as the best from a large sample of pseudo randomly generated tables, in a process that took IBM about a week to compute. This paper provides a faster and more effective(More)