arXiv subjects

Michał Wroński

Publications and source records attributed to Michał Wroński.

4 recordsLinked to original sources

arXiv2026

A Bipartite Quantum Key Distribution Protocol Based on Indefinite Causal Order

We propose a bipartite quantum key distribution (QKD) protocol based on causal nonseparability: the presence of a resource -- a process matrix -- that does not correspond to any definite causal order between two parties. In our protocol, Alice and Bob perform local operations arranged in a ``causal-order guessing game,'' whereby each round yields an 85.35\% probability of matching bits when the communication is undisturbed. This raw matching probability (or equivalently, a $\sim14.65\%$ error rate) is amenable to standard forward error-correction strategies. We further discuss the practical construction of the QKD protocol using indefinite causal order, where several different scenarios are deeply analyzed.

quant-ph↗

arXiv2026

Privacy for Quantum Annealing. Attack on Spin Reversal Transformations in the case of cryptanalysis

This paper demonstrates that applying spin reversal transformations (SRT), commonly known as a sufficient method for privacy enhancement in problems solved using quantum annealing, does not guarantee privacy for all possible cases. We show how to recover the original problem from the Ising problem obtained using SRT when the resulting problem in Ising form represents the algebraic attack on the $E_0$ stream cipher. A small example illustrates how to retrieve the original problem from that transformed by SRT. Moreover, we show that our method is efficient also for full-scale problems.

cs.CR↗

arXiv2024

Transformation of the discrete logarithm problem over $\mathbb F_{2^n}$ to the QUBO problem using normal bases

Quantum computations are very important branch of modern cryptology. According to the number of working physical qubits available in general-purpose quantum computers and in quantum annealers, there is no coincidence, that nowadays quantum annealers allow to solve larger problems. In this paper we focus on solving discrete logarithm problem (DLP) over binary fields using quantum annealing. It is worth to note, that however solving DLP over prime fields using quantum annealing has been considered before, no author, until now, has considered DLP over binary fields using quantum annealing. Therefore, in this paper, we aim to bridge this gap. We present a polynomial transformation of the discrete logarithm problem over binary fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem, using approximately $3n^2$ logical variables for the binary field $\mathbb{F}_{2^n}$. In our estimations, we assume the existence of an optimal normal base of II type in the given fields. Such a QUBO instance can then be solved using quantum annealing.

cs.CR↗

arXiv2022

High-degree compression functions on alternative models of elliptic curves and their applications

This paper presents method for obtaining high-degree compression functions using natural symmetries in a given model of an elliptic curve. Such symmetries may be found using symmetry of involution $[-1]$ and symmetry of translation morphism $τ_T=P+T$, where $T$ is the $n$-torsion point which naturally belongs to the $E(\mathbb K)$ for a given elliptic curve model. We will study alternative models of elliptic curves with points of order $2$ and $4$, and specifically Huff's curves and the Hessian family of elliptic curves (like Hessian, twisted Hessian and generalized Hessian curves) with a point of order $3$. We bring up some known compression functions on those models and present new ones as well. For (almost) every presented compression function, differential addition and point doubling formulas are shown. As in the case of high-degree compression functions manual investigation of differential addition and doubling formulas is very difficult, we came up with a Magma program which relies on the Gröbner basis. We prove that if for a model $E$ of an elliptic curve exists an isomorphism $ϕ:E \to E_M$, where $E_M$ is the Montgomery curve and for any $P \in E(\mathbb K)$ holds that $ϕ(P)=(ϕ_x(P), ϕ_y(P))$, then for a model $E$ one may find compression function of degree $2$. Moreover, one may find, defined for this compression function, differential addition and doubling formulas of the same efficiency as Montgomery's. However, it seems that for the family of elliptic curves having a natural point of order $3$, compression functions of the same efficiency do not exist.

cs.CR↗