arXiv subjects

Mohamed Taoufiq Damir

Publications and source records attributed to Mohamed Taoufiq Damir.

6 recordsLinked to original sources

arXiv2022

A Beyond-5G Authentication and Key Agreement Protocol

The standardized Authentication and Key Agreement protocol for 5G networks (5G AKA) have several security and privacy vulnerabilities. In this paper, we propose a novel authentication and key agreement protocol for 5G and beyond that is compatible with the standardized 5G AKA. Our protocol has several privacy and security properties, e.g., perfect forward secrecy, resistance against linkability attacks, and protection against malicious SNs. Moreover, both the user identity protection and the perfect forward secrecy are handled using Key Encapsulation Mechanisms (KEM), which makes our protocol adaptable to the quantum-safe setting. To analyze the performance of the proposed protocol, we use the post-quantum KEM CRYSTALS-Kyber, recently chosen to be standardized by NIST, and NIST post-quantum Round 4 candidate KEMs. The results for communication and computation costs show that utilizing our protocol is feasible in practice and sometimes outperforms the public-key cryptography used in 5G AKA, i.e., ECIES. We further prove the security of our protocol by utilizing ProVerif.

cs.CR↗

arXiv2022

Bases of minimal vectors in tame lattices

Motivated by the behavior of the trace pairing over tame cyclic number fields, we introduce the notion of tame lattices. Given an arbitrary non-trivial lattice $\mathcal{L}$ we construct a parametric family of full-rank sub-lattices $\{\mathcal{L}_α\}$ of $\mathcal{L}$ such that whenever $\mathcal{L}$ is tame each $\mathcal{L}_α$ has a basis of minimal vectors. Furthermore, for each $\mathcal{L}_α$ in the family a basis of minimal vectors is explicitly constructed.

math.NT↗

arXiv2020

Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels

The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. It is concluded that the minimization of the (average) flatness factor of the eavesdropper's lattice leads to the study of well-rounded lattices, which are shown to be among the optimal in order to achieve these minima. Constructions of some well-rounded lattices are also provided.

cs.IT↗

arXiv2020

An Approximation of Theta Functions with Applications to Communications

Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various wireless communication setups. However, the theta series is in general not known in closed form, excluding a small set of very special lattices. In this article, motivated by the practical applications as well as the mathematical problem itself, a simple approximation of the theta series of a lattice is derived. A rigorous analysis of its accuracy is provided. In relation to this, maximum-likelihood decoding in the context of compute-and-forward relaying is studied. Following previous work, it is shown that the related metric can exhibit a flat behavior, which can be characterized by the flatness factor of the decoding function. Contrary to common belief, we note that the decoding metric can be rewritten as a sum over a random lattice only when at most two sources are considered. Using a particular matrix decomposition, a link between the random lattice and the code lattice employed at the transmitter is established, which leads to an explicit criterion for code design, in contrast to implicit criteria derived previously. Finally, candidate lattices are examined with respect to the proposed criterion using the derived theta series approximation.

cs.IT↗

arXiv2019

Canonical basis twists of ideal lattices from real quadratic number fields

Ideal lattices in the plane coming from real quadratic number fields have been investigated by several authors in the recent years. In particular, it has been proved that every such ideal has a basis that can be twisted by the action of the diagonal group into a Minkowski reduced basis for a well-rounded lattice. We explicitly study such twists on the canonical bases of ideals, which are especially important in arithmetic theory of quadratic number fields and binary quadratic forms. Specifically, we prove that every fixed real quadratic field has only finitely many ideals whose canonical basis can be twisted into a well-rounded or a stable lattice in the plane. We demonstrate some explicit examples of such twists. We also briefly discuss the relation between stable and well-rounded twists of arbitrary ideal bases.

math.NT↗

arXiv2018

Well-Rounded Twists of Ideal Lattices from Real Quadratic Fields

We study ideal lattices in $\mathbb{R}^2$ coming from real quadratic fields, and give an explicit method for computing all well-rounded twists of any such ideal lattice. We apply this to ideal lattices coming from Markoff numbers to construct infinite families of non-equivalent planar lattices with good sphere-packing radius and good minimum product distance. We also provide a complete classification of all real quadratic fields such that the orthogonal lattice is the only well-rounded twist of the lattice corresponding to the ring of integers.

math.NT↗