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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...
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...
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...
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...
Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves
Multilinear maps Non-Interactive Key Exchange Isogenies
2018/7/11
We describe a fhttps://eprint.iacr.org/2018/665.pdframework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n >= 2. Our approach is based on the proble...
On the cost of computing isogenies between supersingular elliptic curves
SIDH CSSI cryptanalysis
2018/4/4
we demonstrate that the van Oorschot-Wiener collision finding algorithm has a lower cost (but higher running time) for solving CSSI, and thus should be used instead of the meet-in-the-middle attack to...
A New Family of Pairing-Friendly elliptic curves
Pairing-Friendly elliptic curves large characteristic
2018/3/5
There have been recent advances in solving the finite extension field discrete logarithm problem as it arises in the context of pairing-friendly elliptic curves. This has lead to the abandonment of ap...
ON ISOGENY GRAPHS OF SUPERSINGULAR ELLIPTIC CURVES OVER FINITE FIELDS
foundations Supersingular isogeny graphs
2018/2/8
We study the isogeny graphs of supersingular elliptic curves over finite fields, with an emphasis on the vertices corresponding to elliptic curves of jj-invariant 0 and 1728.
On the Hardness of Computing Endomorphism Rings of Supersingular Elliptic Curves
Supersingular isogeny based cryptography number theory
2017/10/10
Cryptosystems based on supersingular isogenies have been proposed recently for use in post-quantum cryptography. Three problems have emerged related to their hardness: computing an isogeny between two...
Fast Scalar Multiplication for Elliptic Curves over Binary Fields by Efficiently Computable Formulas
binary elliptic curves point multiplication lambda coordinates
2017/9/7
This paper considers efficient scalar multiplication of elliptic curves over binary fields with a twofold purpose. Firstly, we derive the most efficient 3P3P formula in λλ-projective coordinates and 5...
On the discrete logarithm problem for prime-field elliptic curves
elliptic curve discrete logarithm problem prime field
2017/6/27
In recent years several papers have appeared investigating the classical discrete logarithm problem for elliptic curves by means of the multivariate polynomial approach based on the celebrated summati...
Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography
elliptic curve cryptosystem number theory
2017/5/5
We call a simple abelian variety over FpFp super-isolated if its (FpFp-rational) isogeny class contains no other varieties. The motivation for considering these varieties comes from concerns about iso...