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A new elliptic curve point compression method based on Fp-rationality of some generalized Kummer surfaces
elliptic cryptography point compression Barreto-Naehrig curves
2019/9/19
In the article we propose a new compression method (to 2log2(p)+32log2(p)+3 bits) for the Fp2Fp2-points of an elliptic curve Eb:y2=x3+bEb:y2=x3+b (for b∈F∗p2b∈Fp2∗) of jj-invariant ...
A New Attack on RSA and Demytko's Elliptic Curve Cryptosystem
RSA Cryptanalysis Coppersmith's method
2019/9/19
Let N=pqN=pq be an RSA modulus and ee be a public exponent. Numerous attacks on RSA exploit the arithmetical properties of the key equation ed−k(p−1)(q−1)=1ed−k(p−1)(q...
Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem
public-key cryptography KMOV
2019/9/19
This paper presents two new improved attacks on the KMOV cryptosystem. KMOV is an encryption algorithm based on elliptic curves over the ring ZNZN where N=pqN=pq is a product of two large primes of eq...
A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem
Intersection of Curves Grobner Basis Vanishing Ideals
2019/9/19
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
Algorithmic aspects of elliptic bases in finite field discrete logarithm algorithms
discrete logarithm problem finite fields elliptic representation
2019/7/10
Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by sever...
Distributing any Elliptic Curve Based Protocol: With an Application to MixNets
cryptographic protocols SPDZ
2019/7/8
We show how to perform a full-threshold nn-party actively secure MPC protocol over a subgroup of order pp of an elliptic curve group E(K)E(K). This is done by utilizing a full-threshold nn-party activ...
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...
Fast and simple constant-time hashing to the BLS12-381 elliptic curve
hash functions elliptic curve cryptosystem implementation
2019/4/23
Pairing-friendly elliptic curves in the Barreto-Lynn-Scott family have experienced a resurgence in popularity due to their use in a number of real-world projects. One particular Barreto-Lynn-Scott cur...
Degenerate Fault Attacks on Elliptic Curve Parameters in OpenSSL
OpenSSL Elliptic curve cryptography Invalid curve attack
2019/4/22
In this paper, we describe several practically exploitable fault attacks against OpenSSL's implementation of elliptic curve cryptography, related to the singular curve point decompression attacks of B...
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...
Code-based Cryptosystem from Quasi-Cyclic Elliptic Codes
code-based cryptography post quantum cryptograp elliptic code
2018/12/6
With the fast development of quantum computation, code based cryptography arises public concern as a candidate of post quantum cryptography. However, the large key-size becomes a main drawback such th...
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...