arXiv subjects

Wissam Ghantous

Publications and source records attributed to Wissam Ghantous.

5 recordsLinked to original sources

arXiv2026

CARTS: Contextual Autoregressive Rank Transcoding Steganography for Full-Capacity Keyed Text Encoding

Autoregressive language models can be used to transform a payload text into a stegotext of identical token length by preserving per-position rank information across contexts - a methodology we formalize as Contextual Autoregressive Rank Transcoding Steganography (CARTS). While the Calgacus construction of Norelli et al. demonstrated this phenomenon experimentally, no formal security analysis existed. This paper provides the first rigorous treatment of CARTS. We show its exact correctness under deterministic model assumptions, introduce a rank-coordinate representation in which keys act as bijections on rank-vector space, define relevant security notions and the computational problems naturally associated with the construction - context search, key collisions, message equivocation, and non-commutativity of the encoding maps - and study the theoretical relationships between them, including the characterization of message equivocation in terms of context search, and the tension between key collisions and message equivocation. An empirical study on Llama 3 8B confirms exact recovery of the original payload in all tested cases, finds no key collisions under random key generation, establishes that a hand-crafted collision is local rather than global, and finds no commuting key pairs - suggesting resistance to the attack vectors studied. This work opens a formally grounded research agenda for the constructive use of language models in cryptography and privacy-preserving communication.

cs.CR↗

arXiv2026

On a Roll Again: Analysis of a Dice Removal Game

Suppose we have $n$ dice, each with $s$ faces (assume $s\geq n$). On the first turn, roll all of them, and remove from play those that rolled an $n$. Roll all of the remaining dice. In general, if at a certain turn you are left with $k$ dice, roll all of them and remove from play those that rolled a $k$. The game ends when you are left with no dice to roll. For $n,s \in \mathbb{N} \setminus \{0\}$ such that $s \geq n$, let $Y_n^s$ be the random variable for the number of turns to finish the game rolling $n$ dice with $s$ faces. We find recursive and non-recursive solutions for $\mathbb{E}(Y_n^{s})$ and $\mathrm{Var}(Y_n^{s})$, and bounds for both values. Moreover, we show that $Y_n^{s}$ can also be modeled as the maximum of a sequence of i.i.d. geometrically distributed random variables. Although, as far as we know, this game hasn't been studied before, similar problems have.

math.PR↗

arXiv2025

Cycles and Cuts in Supersingular L-Isogeny Graphs

Supersingular elliptic curve isogeny graphs underlie isogeny-based cryptography. For isogenies of a single prime degree $\ell$, their structure has been investigated graph-theoretically. We generalise the notion of $\ell$-isogeny graphs to $L$-isogeny graphs (studied in the prime field case by Delfs and Galbraith), where $L$ is a set of small primes dictating the allowed isogeny degrees in the graph. We analyse the graph-theoretic structure of $L$-isogeny graphs. Our approaches may be put into two categories: cycles and graph cuts. On the topic of cycles, we provide: a count for the number of cycles in the $L$-isogeny graph with cyclic kernels using traces of Brandt matrices; an efficiently computable estimate based on this approach; and a third ideal-theoretic count for a certain subclass of $L$-isogeny cycles. We provide code to compute each of these three counts. On the topic of graph cuts, we compare several algorithms to compute graph cuts which minimise a measure called the edge expansion, outlining a cryptographic motivation for doing so. Our results show that a greedy neighbour algorithm out-performs standard spectral algorithms for computing optimal graph cuts. We provide code and study explicit examples. Furthermore, we describe several directions of active and future research.

math.NT↗

arXiv2025

A symmetric $p$-adic symbol for triples of modular forms

In 2014, Darmon and Rotger defined the Garrett-Rankin triple product $p$-adic $L$- function and related it to the image of certain diagonal cycles under the $p$-adic Abel- Jacobi map. We introduce a new $p$-adic triple symbol based on this $p$-adic $L$- function and show that it satisfies symmetry relations, when permuting the three input modular forms. We also provide computational examples illustrating this symmetry property. To do so, we extend Lauder's algorithm to allow for ordinary projections of nearly overconvergent modular forms -- not just overconvergent modular forms -- as well as certain projections over spaces of non-zero slope. Our work also gives an efficient method to calculate certain Poincaré pairings in higher weight, which may be of independent interest.

math.NT↗

arXiv2021

Loops, Multi-Edges and Collisions in Supersingular Isogeny Graphs

Supersingular isogeny graphs are known to have very few loops and multi-edges. We formalize this idea by studying and finding bounds for the number of loops and multi-edges in such graphs. We also find conditions under which the supersingular isogeny graph $Λ_p(\ell)$ is simple. The methods presented in this paper can be used to study many kinds of collisions in supersingular isogeny graphs. As an application, we introduce the notion of bi-route number for two graphs $Λ_p(\ell_1),Λ_p(\ell_2)$ and compute bounds for it. We also study the number of edges in common between the graphs $Λ_p(\ell_1),Λ_p(\ell_2)$.

math.NT↗