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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...
Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
Optimal ate pairing twists of elliptic curves jacobian coordinates
2019/5/27
In this paper we present a comprehensive comparison between pairing-friendly elliptic curves, considering different curve forms and twists where possible. We define a measure of the efficiency of a pa...
Cocks-Pinch curves of embedding degrees five to eight and optimal ate pairing computation
NFS optimal ate pairing computation
2019/4/28
Recent algorithmic improvements of discrete logarithm computation in special extension fields threaten the security of pairing-friendly curves used in practice. A possible answer to this delicate situ...
Miller Inversion is Easy for the Reduced Tate Pairing on Trace Zero Supersingular Curves
elliptic curve cryptosystem pairing inversion Tate pairing
2019/4/16
We present a simple algorithm for Miller inversion for the reduced Tate pairing on supersingular elliptic curve of trace zero defined over the finite fields with q elements. Our algorithm runs with O(...
Horizontal Collision Correlation Attack on Elliptic Curves
side-channel analysis elliptic curves implementations ECDSA
2019/4/1
Elliptic curves based algorithms are nowadays widely spread among embedded systems. They indeed have the double advantage of providing efficient implementations with short certi cates and of being rel...
A SAT-based approach for index calculus on binary elliptic curves
discrete logarithm index calculus elliptic curves
2019/3/22
Logical cryptanalysis, first introduced by Massacci in 2000, is a viable alternative to common algebraic cryptanalysis techniques over boolean fields. With XOR operations being at the core of many cry...
Hash functions from superspecial genus-2 curves using Richelot isogenies
isogeny-based cryptography genus 2 hyperelliptic curve CGL hash function
2019/3/21
Last year Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed ov...
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...
This paper introduces elliptic curves in generalized Huff's model. These curves endowed with addition are shown to be a group over a finite field. We present formulae for point addition and doubling p...
We construct a genus 2 curve inside the product of 2 elliptic curves. The formula for this construction has appeared in a previous paper. The current paper discusses how this formula arises naturally ...
Fast Scalar Multiplication for Elliptic Curves over Prime Fields by Efficiently Computable Formulas
twisted Edwards curves Edwards curves scalar multiplication
2018/11/6
This paper addresses fast scalar multiplication for elliptic curves over finite fields. In the first part of the paper, we obtain several efficiently computable formulas for basic elliptic curves arit...
Optimal TNFS-secure pairings on elliptic curves with even embedding degree
TNFS-secure optimal pairing twisted Ate pairing
2018/11/6
In this paper we give a comprehensive comparison between pairing-friendly elliptic curves in Jacobi Quartic and Edwards form with quadratic, quartic, and sextic twists. Our comparison looks at the bes...
TNFS Resistant Families of Pairing-Friendly Elliptic Curves
Pairings elliptic curves pairing-friendly parameters
2018/11/2
Recently there has been a significant progress on the tower number field sieve (TNFS) method, reducing the complexity of the discrete logarithm problem (DLP) in finite field extensions of composite de...