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The elliptic curve cryptography plays a central role in various cryptographic schemes and protocols. For efficiency reasons, Edwards curves and twisted Edwards curves have been introduced. In this pap...
CSIDH is an isogeny-based key exchange protocol proposed by Castryck, Lange, Martindale, Panny, and Renes in 2018. CSIDH is based on the ideal class group action on FpFp-isomorphic classes of Montgome...
In this paper, we present an efficient method to compute arbitrary odd-degree isogenies on Edwards curves. By using the ww-coordinate, we optimized the isogeny formula on Edwards curves by Moody \text...
Along with the resistance against quantum computers, isogeny-based cryptography offers attractive cryptosystems due to small key sizes and compatibility with the current elliptic curve primitives. Whi...
This paper presents the basic concepts of the Edwards curves, twisted Edwards curves and the point addition laws on these curves. The main result is the parameterization of the Edward curve with the g...
We propose two optimal representations for the elements of trace zero subgroups of twisted Edwards curves. For both representations, we provide efficient compression and decompression algorithms. The ...
Edwards elliptic curve form is popular in modern cryptographic implementations thanks to their fast, strongly unified addition formulas. Twisted Edwards curves with a = −1 are slightly faster...
In this paper, we analyze the existence of special points whose use in SCA is known as Same Value Analysis (SVA), for Edwards curves. These special points show up as internal collisions under power ...
In this paper we present a new method for fast scalar multiplication on elliptic curves over GF(p) in FPGA using Edwards and twisted Edwards curves over GF(p 3 ). The presented solution works for ...
Edwards curves are an alternate model for elliptic curves, which have attracted notice in cryptography. We give exact formulas for the number of $\Fq$-isomorphism classes of Edwards curves and twisted...
We count the number of isogeny classes of Edwards curves over finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a {\em compl...
R. Feng, and H. Wu recently established a certain mean-value formula for the x-coordinates of the n-division points on an elliptic curve given in Weierstrass form (A mean value formula for elliptic ...
Edwards curves have attracted great interest for their efi- cient addition and doubling formulas. Furthermore, the addition formulas are strongly unified or even complete, i.e., work without change ...
Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes in...
We give two parametrizations of points on Edwards curves that omit the X coordinate. The first parametrization leads to a differential addition formula that has the cost 5M+ 4S, a doubling formula ...

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