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A New Public Key Cryptosystem Based on Edwards Curves
Elliptic curves Twisted Edwards curves RSA cryptosystem
2019/9/19
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...
How to Construct CSIDH on Edwards Curves
Isogeny-based cryptography Montgomery curves Edwards curves
2019/7/22
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...
Optimized Method for Computing Odd-Degree Isogenies on Edwards Curves
Isogeny Post-quantum cryptography Montgomery curves
2019/2/27
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...
New Hybrid Method for Isogeny-based Cryptosystems using Edwards Curves
Isogeny Post-quantum cryptography Montgomery curves
2018/12/24
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...
Parameterization of Edwards curves on the rational field Q with given torsion subgroups
Edwards curve twisted Edwards curve torsion subgroups
2018/1/29
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...
Compression for trace zero points on twisted Edwards curves
elliptic curve cryptography trace-zero subgroup Edwards curves
2017/9/18
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...
Same Value Analysis on Edwards Curves
Elliptic curve cryptography Side-channel attack Same value
2015/12/24
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 ...
Faster point scalar multiplication on NIST elliptic curves over GF(p) using (twisted) Edwards curves over GF(p?
Edwards curves Twisted Edwards curves Finite 謊lds
2015/12/22
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 ...
Isomorphism classes of Edwards curves over finite fields
Elliptic curves Edwards curves Isomorphisms
2012/3/28
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...
On isogeny classes of Edwards curves over finite fields
public-key cryptography / number theory
2012/3/29
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 ...
A complete set of addition laws for incomplete Edwards curves
complete set addition laws incomplete Edwards curves
2009/12/29
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...
Differential Addition on Edwards Curves
Edwards curve addition formula differential addition
2009/12/29
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
...