arXiv subjects

George C. Ţurcaş

Publications and source records attributed to George C. Ţurcaş.

7 recordsLinked to original sources

arXiv2026

Subgroup Packing for Batched PASTA Transciphering

With transciphering, a server converts symmetrically encrypted records into homomorphic ciphertexts without learning the records or the symmetric key. For the PASTA cipher, this conversion involves dense linear maps whose implementation depends on how record words are arranged in the ciphertext. We ask whether rearranging a fixed batch can reduce its conversion cost. Instead of storing each record's words in a contiguous block, our layout interleaves records so that cyclic word shifts preserve each record's positions, which form a coset of a cyclic subgroup. For direct evaluation as a sum of masked translations, we characterize the required displacements and relate their counts, 255 for the contiguous layout and 128 for the subgroup layout, to a prior transversal-difference invariant. We implement three equally batched schedules for complete PASTA-3 conversion and subsequent public subset-sum queries in HElib. Across twelve paired corpora under six homomorphic keys, all 24 direct and subgroup conversions and all 48 subsequent queries return the expected values and required zeroes. The median paired ratio of direct to subgroup server cost is 1.60, including fresh public generation, conversion and two queries. The reduction comes with less remaining noise capacity. These results establish a packing-dependent cost--noise tradeoff.

cs.CR↗

arXiv2026

CHiPS: Character Histograms and Positional Signals for Lightweight Authorship Attribution in Romanian Texts

We propose CHiPS, a lightweight character-level authorship attribution method for Romanian texts. All reported experiments are closed-set: the true author is one of the candidate authors in the training data. CHiPS studies two complementary fingerprints of writing style: CH-SVM, a character-histogram classifier based on one-character marginal distributions, and FFT12-LR, a positional-signal classifier that represents selected characters and punctuation classes as impulse trains (binary indicator sequences over character positions) and extracts Fourier/Welch spectral descriptors. We also report CHiPS-F, a leakage-safe decision-level fusion variant, and an optional top-5 listwise reranker trained only on out-of-fold predictions. The method requires no tokenization, syntactic analysis, pretrained language model, or transformer fine-tuning, and it avoids character $n$-gram features with $n \geq 2$ in the histogram component. On a locked grouped ROST split comprising 400 files from 392 source-text groups, written by 10 authors, with source-text-level evaluation and grouped five-fold model selection, CHiPS-F reaches 0.9310 accuracy and 0.9341 macro-F1. A matched but unrestricted character 2--5-gram TF--IDF SVM comparator reaches 1.0000 accuracy and macro-F1 on the same held-out groups, so the contribution is not a claim of best possible classification accuracy. Instead, the experiments ask how far restricted, transparent character evidence can go under strict leakage control. On ROSTories-cleaned, a secondary ROST-overlapping corpus comprising 1,248 files from 1,240 source-text groups, written by 19 authors, the same protocol gives 0.8919 accuracy and 0.8708 macro-F1 for CHiPS-R.

cs.CL↗

arXiv2026

Transversal Difference Numbers in Finite Abelian Quotients

Given $H\leq G$ finite abelian groups, a transversal $T\subseteq G$ for $G/H$ has fixed size $|G/H|$, but its ambient difference support $D(T)=T-T$ can vary with the embedding of $H$ in $G$. We call $ δ(G,H)=\min_T |D(T)| $ the transversal difference number of the pair $(G,H)$. This invariant is related to finite abelian factorisation, tiling complements, and small-sumset questions, and is motivated by recent work regarding ambient Galois labels in CRT transforms for cyclotomic-subfield homomorphic encryption. We prove various results regarding this invariant, including a general lower bound $δ(G,H)\geq 2|G/H|-m(G,H), $ where $m(G,H)$ is the largest order of a subgroup of $G$ disjoint from $H$. The bound is sharp for cyclic quotients, and Kneser's theorem gives a cross-transversal estimate leading to exact product families with one nonsplit cyclic coordinate and arbitrary split factors. These results isolate the first genuinely new residual obstruction, namely the same-prime square plane \[ G=(\mathbb Z/p^2\mathbb Z)^2,\qquad H=pG. \] For odd $p$, this case is the technical core of the paper. Here transversals are graphs of functions $\mathbb F_p^2\to \mathbb F_p^2$, and $D(T)$ decomposes into carry-corrected finite-field derivative images. We conjecture that \[ δ(G,H)=(2p-1)^2 \] for all odd primes $p$, prove the unconditional lower bound $3p^2-p-1$, and give small-prime, probabilistic, and fixed-polynomial evidence for the conjecture.

math.NT↗

arXiv2026

High-level convexity for products of squared Euclidean distance functions

We study smooth functions on Euclidean space whose Hessian is positive definite outside a bounded set, with emphasis on products of squared distance functions. More precisely, we first prove a simple convexity principle: if the superlevel region $f^{-1}([c,\infty))$ is contained in the Hessian-positive region of $f$, then the sublevel set $\{f\le c\}$ is convex. We apply this to finite products $F_P(x)=\prod_{p\in P}\|x-p\|^2$, proving that their Hessian-positive complements are bounded. For the two-centre product $F_{p,q}(x)=\|x-p\|^2\|x-q\|^2$ in dimension $n\ge2$, we compute the Hessian-positive region and the exact value \[ h_{max}(F_{p,q})=\frac{\|p-q\|^4}{4}. \] This value is sharp for convexity of sublevel sets in the following sense: we prove convexity above it and nonconvexity below it. This also gives the exact convexity and quasiconvexity truncation levels for the two-centre model.

math.CA↗

arXiv2026

Support-sensitive bounds for shortest zero-sum subsequences

For a sequence $S$ over a finite abelian group, let $MZ(S)$ denote the length of the shortest nonempty zero-sum subsequence of $S$. We prove that if $G$ is finite abelian of order $n$ and $S$ has length $n$, then $MZ(S)\le n-|\supp(S)|+1$. The same bound holds for every sequence of length at least $|G|$. In cyclic groups we combine this elementary support bound with the Savchev--Chen structure theorem for long zero-sumfree sequences and obtain the sharper estimate $MZ(S)\le n-t(t-1)/2$, where $t=|\supp(S)|$, whenever $S$ has length $n$ over $C_n$ and $MZ(S)-1>n/2$. As a consequence, every length-$n$ sequence over $C_n$ with support size $3$ has a zero-sum subsequence of length at most $n-3$, and this is sharp for $n\ge 5$. We also give an arithmetic application to products of prime ideals in a number field, phrased in the standard class-group and block-monoid setting and a corresponding cyclic class-group sharpening.

math.NT↗

arXiv2023

On the $p$-isogenies of elliptic curves with multiplicative reduction over quadratic fields

Let $q > 5$ be a prime and $K$ a quadratic number field. In this article we extend a previous result of Najman and the author and prove that if $E/K$ is an elliptic curve with potentially multiplicative reduction at all primes $\mathfrak q \mid q$, then $E$ does not have prime isogenies of degree greater than $71$ and different from $q$. As an application to our main result, we present a variant of the asymptotic version of Fermat's Last Theorem over quadratic imaginary fields of class number one.

math.NT↗

arXiv2023

Composing Bridges

The present work builds on previous investigations of the authors (and their collaborators) regarding bridges, a certain type of morphisms between encryption schemes, making a step forward in developing a (category theory) language for studying relations between encryption schemes. Here we analyse the conditions under which bridges can be performed sequentially, formalizing the notion of composability. One of our results gives a sufficient condition for a pair of bridges to be composable. We illustrate that composing two bridges, each independently satisfying a previously established IND-CPA security definition, can actually lead to an insecure bridge. Our main result gives a sufficient condition that a pair of secure composable bridges should satisfy in order for their composition to be a secure bridge. We also introduce the concept of a complete bridge and show that it is connected to the notion of Fully composable Homomorphic Encryption (FcHE), recently considered by Micciancio. Moreover, we show that a result of Micciancio which gives a construction of FcHE schemes can be phrased in the language of complete bridges, where his insights can be formalised in a greater generality.

cs.CR↗