arXiv subjects

Bartosz Naskrecki

Publications and source records attributed to Bartosz Naskrecki.

6 recordsLinked to original sources

arXiv2026

AI Grinding for Fun and Cryptanalysis

We present an autonomous cryptanalysis workflow in which agents generate, test, and refine hypotheses before human review. The autonomous stage returns reproducible candidates with exact witnesses, controls, code, and run records. A researcher then decides whether the evidence establishes a break, defect, or coverage gap. Two failure modes recur. First, a public algebraic map or input representation erases or exposes a relation that a construction must hide. Examples include multiplication by zero, boundary coefficients of a polynomial product, quotients, characters, Schur squares, and variable-length byte encodings without boundaries. Second, a simulator, error law, or parameter certification uses a distribution different from the one claimed. Several targets fail in both ways. Every result has an exact witness and a discriminating control; every stated boundary has a proof. Three further targets yielded no attack but support narrower guarantees than a generic reading suggests. Eight published constructions fail at stated parameters or claims. A Ring-LWR commitment opens to every message with probability one. One ciphertext reveals two middle-product encryption rows. A lattice e-voting protocol loses receipt-freeness. A permutation-recovery attack against updatable encryption extends by linear algebra to the old decryption key. An explicit normal basis splits a degree-63 instance into seven degree-nine instances. A signature hash outside the lattice setting maps two printable equal-length messages to the same digest. A rerandomisable scheme's accept bit is a threshold oracle on its decryption noise. Separately, a group-ring decision claim and a multivariate MinRank hardening fail at the assumption or accounting level rather than as complete construction breaks. Each failure occurs one level above its supporting assumption.

cs.CR↗

arXiv2026

Key Recovery from Residue-Confined Errors in Pradhan CRT-RLWE

We show that the CRT-FHE scheme of Pradhan et al.\ is insecure for laws within its assumed error distribution range. The secret key follows from the public key by a single ring inversion whenever the public multiplier is a unit. The plaintext is recovered from any ciphertext under such a law without the secret key, for every multiplier, giving chosen-plaintext advantage $1/2$. We further show that the transformation from ordinary Ring-LWE to CRT-RLWE does not preserve the error distribution, so it does not establish that CRT-RLWE is at least as hard as Ring-LWE. One mechanism underlies both. The Chinese remainder theorem (CRT) function is reduced modulo $p_1p_2$ while its output is used modulo a coprime modulus $q$, so under every zero-preserving section an error in $p_2\R$ encodes to zero. The law $p_2B_1$ is so confined, meets the stated conditions, and decrypts correctly. Confinement is not a weakness of scale: scaling any baseline law by $p_2$ leaves its ordinary Ring-LWE problem exactly equivalent, while the reduced encoder destroys every error it produces. The reduction discrepancy is a multiple of $p_1p_2$ and not of $q$, so the small-error premise of the proof cannot remove it, and at the reported parameters a single error coefficient refutes the identity while satisfying that premise. The centered binomial $B_2$ separates the coefficient laws at total variation distance $3/8$, and at the reported dimension that distance between the induced polynomial laws is exponentially close to one.

cs.CR↗

arXiv2020

Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell--Yan scattering

We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations of the surface and use them to provide an explicit Shioda--Inose structure. Moreover, we point out the physical relevance of our results.

math.AG↗

arXiv2019

The generalized Fermat equation with exponents 2, 3, n

We study the Generalized Fermat Equation $x^2 + y^3 = z^p$, to be solved in coprime integers, where $p \ge 7$ is prime. Using modularity and level lowering techniques, the problem can be reduced to the determination of the sets of rational points satisfying certain 2-adic and 3-adic conditions on a finite set of twists of the modular curve $X(p)$. We first develop new local criteria to decide if two elliptic curves with certain types of potentially good reduction at 2 and 3 can have symplectically or anti-symplectically isomorphic $p$-torsion modules. Using these criteria we produce the minimal list of twists of $X(p)$ that have to be considered, based on local information at 2 and 3; this list depends on $p \bmod 24$. Recent results on mod $p$ representations with image in the normalizer of a split Cartan subgroup allow us to reduce the list further in some cases. Our second main result is the complete solution of the equation when $p = 11$, which previously was the smallest unresolved $p$. One relevant new ingredient is the use of the `Selmer group Chabauty' method introduced by the third author in recent work, applied in an Elliptic Curve Chabauty context, to determine relevant points on $X_0(11)$ defined over certain number fields of degree 12. This result is conditional on GRH, which is needed to show correctness of the computation of the class groups of five specific number fields of degree 36. We also give some partial results for the case $p = 13$.

math.NT↗

arXiv2017

On a certain hypergeometric motive of weight 2 and rank 3

We study a family of hypergeometric motives $H(α,β|t)$ attached to a pair of tuples $α=(1/4,1/2,3/4)$, $β=(0,0,0)$. To each such motive we can attach a system of $\ell$--adic realisations with the trace of geometric Frobenius given by the evaluation of the finite field analogue of complex hypergeometric function. Geometry of elliptic fibrations makes it possible to to realise the motive $H(α,β|t)$ as a pure Chow motive attached to a suitable K3 surface $V_{t}$.

math.NT↗

arXiv2009

Infinite family of elliptic curves of rank at least 4

We investigate $\mathbb{Q}$-ranks of the elliptic curve $E_t$: $y^2+txy=x^3+tx^2-x+1$ where $t$ is a rational parameter. We prove that for infinitely many values of $t$ the rank of $E_t(\mathbb{Q})$ is at least 4.

math.NT↗