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Breaking the Bluetooth Pairing – The Fixed Coordinate Invalid Curve Attack
Bluetooth elliptic curve cryptosystem Diffie-Hellman
2019/9/19
Bluetooth is a widely deployed standard for wireless communications between mobile devices. It uses authenticated Elliptic Curve Diffie-Hellman for its key exchange. In this paper we show that the aut...
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...
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...
Prime, Order Please! Revisiting Small Subgroup and Invalid Curve Attacks on Protocols using Diffie-Hellman
formal verification symbolic model tamarin prover
2019/5/21
Diffie-Hellman groups are a widely used component in cryptographic protocols in which a shared secret is needed. These protocols are typically proven to be secure under the assumption they are impleme...
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...
We apply Smith's construction to generate four-dimensional GLV curves with fast arithmetic in the group law as well as in the base field. As Costello and Longa did in [5] for a 128-bit security level,...
In search of CurveSwap: Measuring elliptic curve implementations in the wild
elliptic curve cryptography invalid curve attack curveswap
2018/3/30
We survey elliptic curve implementations from several vantage points. We perform internet-wide scans for TLS on a large number of ports, as well as SSH and IPsec to measure elliptic curve support and ...
A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem
public-key cryptography algorithm depends
2018/2/8
In this paper, we describe a new Las Vegas algorithm to solve the elliptic curve discrete logarithm problem. The algorithm depends on a property of the group of rational points of an elliptic curve an...
On hybrid SIDH schemes using Edwards and Montgomery curve arithmetic
SIDH public-key cryptography
2017/12/19
Supersingular isogeny Diffie-Hellman (SIDH) is a proposal for a quantum-resistant key exchange. The state-of-the-art implementation works entirely with Montgomery curves and basically can be divided i...
Fast FPGA Implementations of Diffie-Hellman on the Kummer Surface of a Genus-2 Curve
Diffie-Hellman key exchange hyperelliptic curve cryptography Kummer surface
2017/9/1
We present the first hardware implementations of Diffie-Hellman key exchange based on the Kummer surface of Gaudry and Schost's genus-22 curve targeting a 128128-bit security level. We describe a sing...
Computational problems in supersingular elliptic curve isogenies
public-key cryptography supersingular elliptic curve isogenies
2017/8/16
We give a brief survey of elliptic curve isogenies and the computational problems relevant for supersingular isogeny crypto. Supersingular isogeny cryptography is attracting attention due to the fact ...