scholarly journals Analysis and Correction of the Attack against the LPN-Problem Based Authentication Protocols

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 573
Author(s):  
Siniša Tomović ◽  
Milica Knežević ◽  
Miodrag J. Mihaljević
Keyword(s):  
Limit Theorem ◽  
Probability Distributions ◽  
Bayesian Reasoning ◽  
Authentication Protocols ◽  
Root Cause ◽  
The Central Limit Theorem ◽  
Man In The Middle ◽  
Exact Distributions ◽  
Approximate Probability ◽  
Lpn Problem

This paper reconsiders a powerful man-in-the-middle attack against Random-HB# and HB# authentication protocols, two prominent representatives of the HB family of protocols, which are built based on the Learning Parity in Noise (LPN) problem. A recent empirical report pointed out that the attack does not meet the claimed precision and complexity. Performing a thorough theoretical and numerical re-evaluation of the attack, in this paper we identify the root cause of the detected problem, which lies in reasoning based on approximate probability distributions of the central attack events, that can not provide the required precision due to the inherent limitations in the use of the Central Limit Theorem for this particular application. We rectify the attack by employing adequate Bayesian reasoning, after establishing the exact distributions of these events, and overcome the mentioned limitations. We further experimentally confirm the correctness of the rectified attack and show that it satisfies the required, targeted accuracy and efficiency, unlike the original attack.

scholarly journals Understanding the Central Limit Theorem the Easy Way: A Simulation Experiment

Proceedings ◽  
2018 ◽  
Vol 2 (21) ◽  
pp. 1322
Author(s):  
Monica E. Brussolo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Electronic Device ◽  
Probability Distributions ◽  
Online Simulation ◽  
The Central Limit Theorem ◽  
Sampling Distributions ◽  
Initial Stage ◽  
Random Samples

Using a simulation approach, and with collaboration among peers, this paper is intended to improve the understanding of sampling distributions (SD) and the Central Limit Theorem (CLT) as the main concepts behind inferential statistics. By demonstrating with a hands-on approach how a simulated sampling distribution performs when the data used has different probability distributions, we expect to clarify the notion of the Central Limit Theorem, and the use of samples in the hypothesis testing process for populations. This paper will discuss an initial stage to create random samples from a given population (using Excel) with collaboration of the students, which has been tested in the classroom. Then, based on that experience, a second stage in which we created an online simulation, controlled by the professor, and in which the students will participate during class time using an electronic device connected to internet. Students will create simple random samples from a variety of probability distributions simulated online in a collaborative way. Once the samples are generated, the instructor will combine and summarize the resulting sample statistics using histograms and the results will be discussed with the students. The objective is to teach some of the central topics of introductory statistics, the Central Limit Theorem and sampling distributions with an interactive and engaging approach.

scholarly journals A Protocol for Provably Secure Authentication of a Tiny Entity to a High Performance Computing One

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Siniša Tomović ◽  
Miodrag J. Mihaljević ◽  
Aleksandar Perović ◽  
Zoran Ognjanović
Keyword(s):  
High Performance Computing ◽  
High Performance ◽  
Authentication Protocol ◽  
Authentication Protocols ◽  
Man In The Middle ◽  
Lpn Problem ◽  
Secure Authentication ◽  
Performance Computing ◽  
Specific Scenario ◽  
Provably Secure

The problem of developing authentication protocols dedicated to a specific scenario where an entity with limited computational capabilities should prove the identity to a computationally powerful Verifier is addressed. An authentication protocol suitable for the considered scenario which jointly employs the learning parity with noise (LPN) problem and a paradigm of random selection is proposed. It is shown that the proposed protocol is secure against active attacking scenarios and so called GRS man-in-the-middle (MIM) attacking scenarios. In comparison with the related previously reported authentication protocols the proposed one provides reduction of the implementation complexity and at least the same level of the cryptographic security.

scholarly journals A Theory Of Errors in Quantum Measurement

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2439-2450
Author(s):  
S. G. Rajeev
Keyword(s):  
Quantum Theory ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Probability Distribution ◽  
Quantum Measurement ◽  
Probability Distributions ◽  
Matrix Elements ◽  
Random Errors ◽  
The Central Limit Theorem ◽  
The Matrix

It is common to model the random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an observable are distributed normally. We obtain the probability distribution this implies for the outcome of a measurement, exactly for the case of traceless 2 × 2 matrices and in the steepest descent approximation in general. Due to the phenomenon of 'level repulsion', the probability distributions obtained are quite different from the Gaussian.

scholarly journals Man-In-The-Middle Attack against Certain Authentication Protocols Revisited: Insights into the Approach and Performances Re-Evaluation

Electronics ◽  
2020 ◽  
Vol 9 (8) ◽  
pp. 1296
Author(s):  
Milica Knežević ◽  
Siniša Tomović ◽  
Miodrag J. Mihaljević
Keyword(s):  
Experimental Evaluation ◽  
Probability Distributions ◽  
Correct Result ◽  
Hamming Weight ◽  
Authentication Protocols ◽  
Man In The Middle ◽  
The One ◽  
Main Component

We address a class of authentication protocols called “HB” ones and the man-in-the-middle (MIM) attack, reported at the ASIACRYPT conference, called OOV-MIM (Ouafi-Overbeck-Vaudenay MIM). Analysis of the considered attack and its systematic experimental evaluation are given. It is shown that the main component of OOV-MIM, the algorithm for measuring the Hamming weight of noise vectors, outputs incorrect results as a consequence of the employed approximation of the probability distributions. The analysis reveals that, practically, the only scenario in which the OOV-MIM attack is effective is the one in which two incorrect estimations produced by the algorithm for measuring the Hamming weight, when coupled, give the correct result. This paper provides additional insights into the OOV-MIM and corrected claims about the performance/complexity showing that the performances of the considered attack have been overestimated, i.e., that the complexity of the attack has been underestimated. Particularly, the analysis points out the reasons for the incorrect claims and to the components of the attack that do not work as expected.

scholarly journals On the ubiquitous notion of mean in probability and statistics

2019 ◽  
Vol 2 (2) ◽  
pp. 35-41
Author(s):  
Aboubakar MAITOURNAM
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Law Of Large Numbers ◽  
Probability Distributions ◽  
Basic Notion ◽  
The Core ◽  
The Central Limit Theorem ◽  
Large Numbers ◽  
Essential Parameter ◽  
Probability And Statistics

In probability and statistics, the basic notion of probability of an event can be expressed as a mathematical expectation. The latter is a theoretical mean and is an essential parameter of most probability distributions, in particular of the Gaussian distribution. Last but not least, the notion of mean is at the core of two main theorems of probabilities and statistics, that is : the law of large numbers and the central limit theorem. Whether it is a theoretical or empirical version, the concept of mean is omnipresent in probability and statistics, is consubstantial to these two disciplines and is a bridge between randomness and determinism.

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

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