Florias Papadopoulos

Privacy-preserving Proximity Testing from Geometric Fuzzy Matching

Mon, 01 Jan 0001 00:00:00 +0000

Cryptography Based on LWE

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

This work navigates the evolving world of post-quantum cryptography, particularly focusing on lattice-based cryptographic constructions. Starting with a thorough exploration of fundamental lattice concepts, the study progresses to delve into well-known hard lattice problems and the algorithms attempting to solve them. Afterwards, the focus is shifted to Learning with Errors (LWE), providing a comprehensive examination of LWE theory, its applications, and a concise study of Ring-LWE, a variant that provides more efficient constructions. The conclusion unfolds with an in-depth exploration of CRYSTALS-Kyber, a cryptographic scheme whose security is based on the hardness of solving hard lattice problems in (module) lattices. Beginning with the necessary preliminaries, we then delve into a detailed analysis of Kyber and its security, finishing with a recent real-world application of the scheme, the X25519Kyber768 hybrid KEM that is used to fortify Google Chrome’s security.

Overview of the Signal Protocol

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

This study was made for an assignment of the class ”Elliptic-Curve Cryptography” of my master’s.
For the assignment, the Signal Protocol (as described in [1] , [2] , [3] , [4] ), had to be studied, analyzed and presented in a more explanatory and student-friendly way.

❖ Files Included

PDF (english)
Presentation (english)

❖ Keywords

Elliptic curve Cryptography, Edwards Curves, Montgomery Curves, Curve25519, Curve448, EdDSA, ECDH, XEdDSA, X3DH protocol, Double Ratchet, Signal Protocol

Semi-Quantum Cryptography

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

I have prepared a presentation on “Semi-Quantum Cryptography” as part of my master’s assignment for the class “Quantum Information & Computation”.
For further details and additional information, I have included references on the final slides.

❖ Files Included

Presentation (english)

❖ Keywords

Semi-Quantum Key Distribution, Semi-Quantum Cryptography, Semi-Quantum Communication

Activity Recognition Algorithms from Accelerometer Signals (team project)

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

In this assignment, we were tasked with developing an activity recognition system from accelerometer signals using machine learning techniques. The process involves preprocessing the data by selecting a mobile phone position, converting the three-dimensional signal to one-dimensional, and handling sensor errors. Feature extraction is performed by dividing the signal into windows and extracting statistical measures and power spectrum estimates. Four classification models, k-nearest neighbors (KNN), SVM with RBF kernel, decision trees, and MLP neural networks, are employed. The evaluation follows the LOSO method, training the models on data from all but one participant and evaluating on the left-out participant’s data. The confusion matrix and accuracy are calculated to assess the classification performance. The report addresses questions regarding parameter optimization, confusion between activities, and the selection of the best classifier. Additionally, we collected our own accelerometer data and evaluated them using the models.

Euclid Attack

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

This report aims to present a student-friendly and explanatory overview of the paper “An application of Euclidean algorithm in cryptanalysis of RSA” [1] . It consists of two chapters: a theoretical chapter that thoroughly explains the main concepts of the paper, and a practical chapter that provides an explanation and implementation of the EUCLID-ATTACK algorithm proposed in [1] . The implementation was carried out using Python, and an accompanying executable program was created for creating toy examples of the algorithm’s application. However, the executable has not been uploaded on the site, one can only see the code for executing EUCLID-ATTACK in the .ipynb file below.

Factoring Algorithms

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

In the context of computational exercises assigned in class, we had to use the following:

Dixon’s algorithm
Pollard’s p-1 algorithm
Pollard’s rho algorithm

for the factorization of a number (mine was $n=902831$). These algorithms play a vital role in breaking down large numbers into their prime factors, a crucial step in modern encryption and decryption techniques.

❖ Files Included

Interactive Python Notebook - Dixon Algorithm (english)
Interactive Python Notebook - Pollard’s p-1 Algorithm (english)
Interactive Python Notebook - Pollard’s rho Algorithm (english)

❖ Keywords

Factoring algorithms, Dixon algorithm, Pollard’s p-1 algorithm, Pollard rho algorithm

Discrete Logarithm Algorithms

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

In the context of computational exercises assigned in class, we had to use the following

Shanks’ algorithm (also named Baby-step Giant-step algorithm)
Adleman’s algorithm
Discrete Pollard’s algorithm (otherwise known as Pollard’s rho algorithm for logarithms)
Pohlig-Hellman algorithm (also named Index calculus algorithm)

for calculating the discrete logarithm of a number. My task was to calculate the discrete logarithm $x$ inside $Z_N$ = $Z_{1693}$, where $17^x ≡ 101 \, (mod \, 1693)$.

Numerical methods for solving systems of chaotic first-order differential equations

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

In my master’s program assignment for “Numerical Methods with Applications to Ordinary and Partial Differential Equations” I initially chose to solve the Lorenz chaotic equations and their extensions using numerical methods in Python due to my interest in cryptology. However, my project evolved to encompass solving all chaotic systems of first-order differential equations by creating a versatile Python script.

In the accompanying pdf, I summarized key facts about the Lorenz system and presented a generalized problem in Chapter 1, introduced three numerical methods in Chapter 2, and showcased the diverse and intriguing results obtained from solving the problem for various chaotic systems in Chapter 3.

Studying steady speed movement with Kalman filter

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

A script was made for an assignment of the class ”Optimal Control Theory” of my master’s program:

Assignment. Perform a simulation of the movement of an object based on Example 2 (can be seen in the .ipynb file). Give estimations of the states for 20* steps.
Assume that $\Delta t$ is stable, e.g. $\Delta t = 0.1$, and choose matrices Q and R of the form

$$ Q = \begin{bmatrix} \frac{q_1(\Delta t)^3}{3} & 0 & \frac{q_1(\Delta t)^2}{2} & 0 \\ 0 & \frac{q_2(\Delta t)^3}{3} & 0 & \frac{q_2(\Delta t)^2}{2} \\ \frac{q_1(\Delta t)^2}{2} & 0 & q_1 \Delta t & 0 \\ 0 & \frac{q_2(\Delta t)^2}{2} & 0 & q_2 \Delta t \end{bmatrix} , \quad R = \begin{bmatrix} \sigma_1^2 & 0 \\ 0 & \sigma_2^2 \end{bmatrix} $$

setting “proper” values for the parameters (e.g. $\sigma_1=\sigma_2 = 1/2$ and $q_1=q_2=1$).

Cryptography In The Post-Quantum Era

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

📍 This presentation was made for my participation in the Graduate Seminars of the Mathematics Department of Aristotle University of Thessaloniki.

In this speech, I begin by introducing basic concepts from the fields of Cryptography and Quantum Computing, with the aim of analyzing the so-called “Quantum Threat” to Cryptography. Then, I proceed by presenting the main approach to addressing this threat, which is Post-Quantum Cryptography, and analyzing it by describing some families of cryptographic schemes and systems that belong to it, in particular some of those belonging to the fields of Hash-Based Cryptography, Code-Based Cryptography & Lattice Cryptography. Finally, the speech concludes with a reference to current and future perspectives and actions of organizations actively involved in the topic, in order to provide a global outlook on the subject.

Cryptography In The Post-Quantum Era - Bachelor Thesis

Mon, 01 Jan 0001 00:00:00 +0000

❖ Abstract

In this thesis, I explore Cryptography in the Post-Quantum era, addressing the impending threat of quantum computers to communication security. I begin by examining Cryptography techniques and gradually delve into Quantum Mechanics and Quantum Computing, emphasizing Post-Quantum Cryptography as the most promising solution. I analyze two key families: Hash-based Cryptography and Code-Based Cryptography, discussing their schemes, strengths, weaknesses, and security levels. For this purpose, I also provide a concise introduction to Coding Theory. The study concludes by exploring initiatives by organizations like NIST and ANSSI to counter the quantum threat, bridging theory and practical implementation for the future.