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Konstantinos A. Draziotis

Publications and source records attributed to Konstantinos A. Draziotis.

4 recordsLinked to original sources
arXiv2026

Worst--Case to Average--Case Reductions for SIS over integers

In the present paper we study a non-modular variant of the Short Integer Solution problem over the integers. Given a random matrix $A \in \mathbb{Z}^{n\times m}$ with entries $a_{ij}$ such that $0\le a_{ij}< Q,$ for some $Q>0,$ the goal is to find a nonzero vector ${\bf x}\in\mathbb{Z}^m$ such that $A{\bf x}={\bf 0}$ and $\|{\bf x}\|_\infty \le β,$ for a given bound $β.$ We show that an algorithm that solves random instances of this problem with non-negligible probability yields a polynomial-time algorithm for approximating $\mathrm{SIVP}$ within a factor $\widetilde{O}(n^{3/2})$ (with $\ell_2$ norm) in the worst case for any $n-$dimensional integer lattice.

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↗
arXiv2023

Cryptographic Primitives based on Compact Knapsack Problem

In the present paper, we extend previous results of an id scheme based on compact knapsack problem defined by one equation. We present a sound three-move id scheme based on compact knapsack problem defined by an integer matrix. We study this problem by providing attacks based on lattices. Furthermore, we provide the corresponding digital signature obtained by Fiat-Shamir transform and we prove that is secure under ROM. These primitives are post quantum resistant.

cs.CR↗