arXiv subjects

Eirini Poimenidou

Publications and source records attributed to Eirini Poimenidou.

4 recordsLinked to original sources

arXiv2025

Message Recovery Attack in NTRU via Knapsack

In the present paper, we introduce a message-recovery attack based on the Modular Knapsack Problem, applicable to all variants of the NTRU-HPS cryptosystem. Assuming that a fraction $ε$ of the coefficients of the message ${\bf{m}}\in\{-1,0,1\}^N$ and of the nonce vector ${\bf r}\in\{-1,0,1\}^N$ are known in advance at random positions, we reduce message decryption to finding a short vector in a lattice that encodes an instance of a modular knapsack system. This allows us to address a key question: how much information about ${\bf m}$, or about the pair $({\bf m},{\bf r})$, is required before recovery becomes feasible? A FLATTER reduction successfully recovers the message, in practice when $ε\approx 0.45$. Our implementation finds ${\bf m}$ within a few minutes on a commodity desktop.

cs.CR↗

arXiv2023

Message Recovery Attack in NTRU through VFK Lattices

In the present paper, we implement a message recovery attack to all variants of the NTRU cryptosystem. Our approach involves a reduction from the NTRU-lattice to a Voronoi First Kind lattice, enabling the application of a polynomial CVP exact algorithm crucial for executing the Message Recovery. The efficacy of our attack relies on a specific oracle that permits us to approximate an unknown quantity. Furthermore, we outline the mathematical conditions under which the attack is successful. Finally, we delve into a well-established polynomial algorithm for CVP on VFK lattices and its implementation, shedding light on its efficacy in our attack. Subsequently, we present comprehensive experimental results on the NTRU-HPS and the NTRU-Prime variants of the NIST submissions and propose a method that could indicate the resistance of the NTRU cryptosystem to our attack.

cs.CR↗

arXiv2019

Orbits of Hamiltonian Paths and Cycles in Complete Graphs

We enumerate certain geometric equivalence classes of subgraphs induced by Hamiltonian paths and cycles in complete graphs. Said classes are orbits under the action of certain direct products of dihedral and cyclic groups on sets of strings representing subgraphs. These orbits are enumerated using Burnside's lemma. The technique used also provides an alternative proof of the formulae found by S. W. Golomb and L. R. Welch which give the number of distinct $n$-gons on fixed, regularly spaced vertices up to rotation and optionally reflection.

math.CO↗

arXiv2018

A Method to Construct $1$-Rotational Factorizations of Complete Graphs and Solutions to the Oberwolfach Problem

The concept of a $1$-rotational factorization of a complete graph under a finite group $G$ was studied in detail by Buratti and Rinaldi. They found that if $G$ admits a $1$-rotational $2$-factorization, then the involutions of $G$ are pairwise conjugate. We extend their result by showing that if a finite group $G$ admits a $1$-rotational $k=2^nm$-factorization where $n\geq 1$, and $m$ is odd, then $G$ has at most $m(2^n-1)$ conjugacy classes containing involutions. Also, we show that if $G$ has exactly $m(2^n-1)$ conjugacy classes containing involutions, then the product of a central involution with an involution in one conjugacy class yields an involution in a different conjugacy class. We then demonstrate a method of constructing a $1$-rotational $2n$-factorization under $G \times \mathbb{Z}_n$ given a $1$-rotational $2$-factorization under a finite group $G$. This construction, given a $1$-rotational solution to the Oberwolfach problem $OP(a_{\infty},a_1, a_2 \cdots, a_n)$, allows us to find a solution to $OP(2a_{\infty}-1,^2a_1, ^2a_2\cdots, ^2a_n)$ when the $a_i$'s are even ($i \neq \infty$), and $OP(p(a_{\infty}-1)+1, ^pa_1, ^pa_2 \cdots, ^pa_n)$ when $p$ is an odd prime, with no restrictions on the $a_i$'s.

math.CO↗