arXiv subjects

Paolo Santini

Publications and source records attributed to Paolo Santini.

At least 19 recordsLinked to original sources

arXiv2026

Design and Analysis of Quantum Dual-Containing CSS LDPC Codes based on Quasi-Dyadic Matrices

Quantum error correcting codes are essential to achieve fault-tolerant quantum computation. This work introduces two constructions of high-rate, dual-containing (DC) Calderbank--Shor--Steane low-density parity-check (LDPC) codes based on quasi-dyadic matrices. We characterize the automorphism group of such codes, investigate their minimum distance behavior, and provide several theoretical results on their cycle properties. Monte Carlo simulations under depolarizing and phenomenological noise show better finite-length logical error rates than the considered DC benchmark codes and competitive performance against several state-of-the-art quantum LDPC code families. Finally, we employ an automorphism-ensemble belief propagation decoder to improve their decoding performance.

cs.IT↗

arXiv2026

Efficient and Quantum-safe Internet Key Exchange Protocols for Satellite Communications

This paper studies cryptographic key exchange in satellite communications, which requires specific solutions because the satellite context presents unique challenges, particularly concerning onboard resource constraints and long transmission latency. We address these challenges by considering the Internet Key Exchange (IKE) protocol, which is widely used in terrestrial networks, and studying its applicability in the satellite context. This requires addressing two main issues: i) its efficiency in terms of the resources and bandwidth required to adapt to satellite terminals, and ii) its resistance even to attackers equipped with a quantum computer, in order to resist obsolescence and defend against harvest-now-decrypt-later attacks. We study these aspects from both a design and experimental point of view, defining and assessing some protocol variants characterized by low complexity and quantum resistance. To address the need to manage the transition from classic cryptographic primitives to post-quantum ones, we also consider the possibility of using hybrid cryptographic solutions that combine them both.

cs.CR↗

arXiv2026

The Power of Power Codes: New Classes of Easy Instances for the Linear Equivalence Problem

Given two linear codes, the Linear Equivalence Problem (LEP) asks to find (if it exists) a linear isometry between them; as a special case, we have the Permutation Equivalence Problem (PEP), in which isometries must be permutations. LEP and PEP have recently gained renewed interest as the security foundations for several post-quantum schemes, including LESS. A recent paper has introduced the use of the Schur product to solve PEP, identifying many new easy-to-solve instances. In this paper, we extend this result to LEP. In particular, we generalize the approach and rely on the more general notion of power codes. Combining it with Frobenius automorphisms and Hermitian hulls, we identify many classes of easy LEP instances. To the best of our knowledge, this is the first work exploiting algebraic weaknesses for LEP. Finally we show an improved reduction to PEP whenever the coefficients of the monomial matrix are in a subgroup of the multiplicative group of the finite field.

cs.CR↗

arXiv2026

Near-Codewords Aware Bit Flipping Decoding of QC-MDPC Codes

Bit-Flipping (BF) decoders are a family of decoders widely employed in post-quantum cryptographic schemes based on Quasi-Cyclic Moderate-Density Parity-Check (QC-MDPC) codes, such as BIKE. BF decoders suffer from trapping sets, corresponding to low-weight error patterns that likely lead to decoding failures. For QC-MDPC codes, the most relevant family of trapping sets is that of near-codewords, which are error patterns associated to low-weight syndromes. Indeed, recent works show that error patterns having a large overlap with near-codewords are the main culprits for decoding failures at very low Decoding Failure Rate (DFR) values. In this paper, we show that any BF decoder can be tweaked and made somehow aware of near-codewords, which means being able to recognize, and recover from, bad configurations due to near-codewords. We show that this modification results in minimal computational overhead. Through intensive numerical simulations, we evaluate the effectiveness of this approach on several BF decoders, considering both toy code parameters and BIKE parameters for NIST security category 1. Our results show drastic reductions in the DFR. We also find that, with this modification, a recently proposed BF variant called BF-Max outperforms the two decoders used by BIKE within the NIST competition.

cs.IT↗

arXiv2026

Vibrationally-mediated Dzyaloshinskii-Moriya interaction as the origin of Chirality-Induced Spin Selectivity in donor-acceptor molecules

Chirality-induced spin selectivity (CISS) was recently observed in photo-excited donor-chiral bridge-acceptor molecules, but a predictive theory able to explain available experiments is still lacking. Here we show that low-energy torsional modes modulating hopping and spin-orbit coupling give rise to a Dzyaloshinskii-Moriya interaction between the transferred electron and the one sitting on the donor, producing high spin polarization for perfectly realistic parameters. Our model introduces a low energy scale in the spin dynamics which explains the magnetic field dependence observed in EPR measurements and predicts a non-trivial temperature dependence, as demonstrated by numerical simulations. The present theory lays the foundations for future test-bed experiments and for the design of applications in spintronics and quantum technologies.

cond-mat.mes-hall↗

arXiv2026

Raman relaxation in Yb(III) molecular qubits: non-trivial correlations between spin-phonon coupling and molecular structure

The coordination complexes of Yb(III) exhibit some of the longest spin coherence times among 4f compounds, making them a promising platform for molecular quantum technologies. While spin-phonon relaxation remains a limiting factor for coherence times even at low temperature, its control through chemical design has the potential to push these spin qubits prototypes beyond current limits. With the aim of providing insights on how to chemically control spin-phonon relaxation, we here present a full ab initio study of spin-phonon dynamics for three Yb(III) molecules exhibiting minimal chemical differences, yet quantitatively different spin relaxation times. Results show that low-temperature relaxation is governed by Raman processes triggered by a small group of largely delocalized low-energy phonons. The analysis of these contributions highlights that the modulation of spin-phonon coupling by molecular structure modifications beyond the first coordination shell are highly non-trivial in nature and hard to rationalize in simple chemical terms. These findings call for a conceptual step change from the attempt to use simple magneto-structural correlations to interpret the effect of molecular structural modifications on spin-phonon relaxation, and present predictive first-principles frameworks as a potential driving force of future chemical design strategies

cond-mat.mtrl-sci↗

arXiv2026

Implementation and transition to post-quantum cryptography of the Minimal IKE protocol

This paper concerns the Minimal Internet Key Exchange (IKE) protocol, which has received little attention to date, despite its potential to make the best-known IKE protocol sufficiently lightweight to be also applied in contexts where it is currently prohibitive, due to its large footprint. First, we introduce and describe Colibri, an efficient, open-source implementation of the Minimal IKE protocol, which allows us to quantitatively assess its real advantages in terms of lightness. Then we introduce a post-quantum variant of the Minimal IKE protocol, which is essential to make it contemporary, and assess it through Colibri. We demonstrate that the protocol performance remains excellent even in such a more challenging context, making it suitable for deploying pervasive and quantum-resistant virtual private networks.

cs.CR↗

arXiv2026

An Efficient Algorithm to Sample Quantum Low-Density Parity-Check Codes

In this paper, we present an efficient algorithm to sample random sparse matrices to be used as check matrices for quantum Low-Density Parity-Check (LDPC) codes. To ease the treatment, we mainly describe our algorithm as a technique to sample a dual-containing binary LDPC code, hence, a sparse matrix $\mathbf H\in\mathbb F_2^{r\times n}$ such that $\mathbf H\mathbf H^\top = \mathbf 0$. However, as we show, the algorithm can be easily generalized to sample dual-containing LDPC codes over non binary finite fields as well as more general quantum stabilizer LDPC codes. While several constructions already exist, all of them are somewhat algebraic as they impose some specific property (e.g., the matrix being quasi-cyclic). Instead, our algorithm is purely combinatorial as we do not require anything apart from the rows of $\mathbf H$ being sparse enough. In this sense, we can think of our algorithm as a way to sample sparse, self-orthogonal matrices that are as random as possible. Our algorithm is conceptually very simple and, as a key ingredient, uses Information Set Decoding (ISD) to sample the rows of $\mathbf H$, one at a time. The use of ISD is fundamental as, without it, efficient sampling would not be feasible. We give a theoretical characterization of our algorithm, determining which ranges of parameters can be sampled as well as the expected computational complexity. Numerical simulations and benchmarks confirm the feasibility and efficiency of our approach.

cs.IT↗

arXiv2025

Triplet Loss Based Quantum Encoding for Class Separability

An efficient and data-driven encoding scheme is proposed to enhance the performance of variational quantum classifiers. This encoding is specially designed for complex datasets like images and seeks to help the classification task by producing input states that form well-separated clusters in the Hilbert space according to their classification labels. The encoding circuit is trained using a triplet loss function inspired by classical facial recognition algorithms, and class separability is measured via average trace distances between the encoded density matrices. Benchmark tests performed on various binary classification tasks on MNIST and MedMNIST datasets demonstrate considerable improvement over amplitude encoding with the same VQC structure while requiring a much lower circuit depth.

quant-ph↗

arXiv2025

BF-Max: an Efficient Bit Flipping Decoder with Predictable Decoding Failure Rate

The Bit-Flipping (BF) decoder, thanks to its very low computational complexity, is widely employed in post-quantum cryptographic schemes based on Moderate Density Parity Check codes in which, ultimately, decryption boils down to syndrome decoding. In such a setting, for security concerns, one must guarantee that the Decoding Failure Rate (DFR) is negligible. Such a condition, however, is very difficult to guarantee, because simulations are of little help and the decoder performance is difficult to model theoretically. In this paper, we introduce a new version of the BF decoder, that we call BF-Max, characterized by the fact that in each iteration only one bit (the least reliable) is flipped. When the number of iterations is equal to the number of errors to be corrected, we are able to develop a theoretical characterization of the DFR that tightly matches with numerical simulations. We also show how BF-Max can be implemented efficiently, achieving low complexity and making it inherently constant time. With our modeling, we are able to accurately predict values of DFR that are remarkably lower than those estimated by applying other approaches.

cs.IT↗

arXiv2025

Mitigating decoherence in molecular spin qudits

Molecular nanomagnets are quantum spin systems potentially serving as qudits for future quantum technologies thanks to their many accessible low-energy states. At low temperatures, the primary source of error in these systems is pure dephasing, caused by their interactions with the bath of surrounding nuclear spins degrees of freedom. Most importantly, as the system's dimensionality grows going from qubits to qudits, the control and mitigation of decoherence becomes more challenging. Here we analyze the characteristics of pure dephasing in molecular qudits under spin-echo sequences. We use a realistic description of their interaction with the bath, whose non-Markovian dynamics is accurately computed by the cluster correlation expansion technique. First, we demonstrate a necessary and sufficient condition to prevent the decay of coherence with time, also introducing a parameter to quantify the deviation from such ideal condition. We illustrate this with two paradigmatic systems: a single giant spin and a composite antiferromagnetic spin system. We then advance a proposal for optimized nanomagnets, identifying key ingredients for engineering robust qudits for quantum technologies.

quant-ph↗

arXiv2023

Proof-of-concept Quantum Simulator based on Molecular Spin Qudits

The use of $d$-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Molecular Nanomagnets are ideal spin systems to realize these large-dimensional qudits. Indeed, their Hamiltonian can be engineered to an unparalleled extent and can yield a spectrum with many low-energy states. In particular, in the last decade intense theoretical, experimental and synthesis efforts have been devoted to develop quantum simulators based on Molecular Nanomagnets. However, this remarkable potential is practically unexpressed, because no quantum simulation has ever been experimentally demonstrated with these systems. Here we show the first prototype quantum simulator based on an ensemble of molecular qudits and a radiofrequency broadband spectrometer. To demonstrate the operativity of the device, we have simulated quantum tunneling of the magnetization and the transverse-field Ising model, representative of two different classes of problems. These results represent an important step towards the actual use of molecular spin qudits in quantum technologies.

quant-ph↗

arXiv2023

Generic Decoding of Restricted Errors

Several recently proposed code-based cryptosystems base their security on a slightly generalized version of the classical (syndrome) decoding problem. Namely, in the so-called restricted (syndrome) decoding problem, the error values stem from a restricted set. In this paper, we propose new generic decoders, that are inspired by subset sum solvers and tailored to the new setting. The introduced algorithms take the restricted structure of the error set into account in order to utilize the representation technique efficiently. This leads to a considerable decrease in the security levels of recently published code-based cryptosystems.

cs.CR↗

arXiv2022

A Novel Attack to the Permuted Kernel Problem

The Permuted Kernel Problem (PKP) asks to find a permutation of a given vector belonging to the kernel of a given matrix. The PKP is at the basis of PKP-DSS, a post-quantum signature scheme deriving from the identification scheme proposed by Shamir in 1989. The most efficient solver for PKP is due to a recent paper by Koussa et al. In this paper we propose an improvement of such an algorithm, which we achieve by considering an additional collision search step applied on kernel equations involving a small number of coordinates. We study the conditions for such equations to exist from a coding theory perspective, and we describe how to efficiently find them with methods borrowed from coding theory, such as information set decoding. We assess the complexity of the resulting algorithm and show that it outperforms previous approaches in several cases. We also show that, taking the new solver into account, the security level of some instances of PKP-DSS turns out to be slightly overestimated.

cs.CR↗

arXiv2022

Implementation of Ethereum Accounts and Transactions on Embedded IoT Devices

The growing interest in Internet of Things (IoT) and Industrial IoT (IIoT) poses the challenge of finding robust solutions for the certification and notarization of data produced and collected by embedded devices. The blockchain and distributed ledger technologies represent a promising solution to address these issues, but rise other questions, for example regarding their practical feasibility. In fact, IoT devices have limited resources and, consequently, may not be able to easily perform all the operations required to participate in a blockchain. In this paper we propose a minimal architecture to allow IoT devices performing data certification and notarization on the Ethereum blockchain. We develop a hardware-software platform through which a lightweight device (e.g., an IoT sensor), holding a secret key and the associated public address, produces signed transactions, which are then submitted to the blockchain network. This guarantees data integrity and authenticity and, on the other hand, minimizes the computational burden on the lightweight device. To show the practicality of the proposed approach, we report and discuss the results of benchmarks performed on ARM Cortex-M4 hardware architectures, sending transactions over the Ropsten testnet. Our results show that all the necessary operations can be performed with small latency, thus proving that an IoT device can directly interact with the blockchain, without apparent bottlenecks.

cs.CR↗

arXiv2022

SPANSE: combining sparsity with density for efficient one-time code-based digital signatures

The use of codes defined by sparse characteristic matrices, like QC-LDPC and QC-MDPC codes, has become an established solution to design secure and efficient code-based public-key encryption schemes, as also witnessed by the ongoing NIST post-quantum cryptography standardization process. However, similar approaches have been less fortunate in the context of code-based digital signatures, since no secure and efficient signature scheme based on these codes is available to date. The main limitation of previous attempts in this line of research has been the use of sparse signatures, which produces some leakage of information about the private key. In this paper, we propose a new code-based digital signature scheme that overcomes such a problem by publishing signatures that are abnormally dense, rather than sparse. This eliminates the possibility of deducing information from the sparsity of signatures, and follows a recent trend in code-based cryptography exploiting the hardness of the decoding problem for large-weight vectors, instead of its classical version based on small-weight vectors. In this study we focus on one-time use and provide some preliminary instances of the new scheme, showing that it achieves very fast signature generation and verification with reasonably small public keys.

cs.CR↗

arXiv2022

Analysis of a blockchain protocol based on LDPC codes

In a blockchain Data Availability Attack (DAA), a malicious node publishes a block header but withholds part of the block, which contains invalid transactions. Honest full nodes, which can download and store the full blockchain, are aware that some data are not available but they have no formal way to prove it to light nodes, i.e., nodes that have limited resources and are not able to access the whole blockchain data. A common solution to counter these attacks exploits linear error correcting codes to encode the block content. A recent protocol, called SPAR, employs coded Merkle trees and low-density parity-check codes to counter DAAs. In this paper, we show that the protocol is less secure than claimed, owing to a redefinition of the adversarial success probability. As a consequence we show that, for some realistic choices of the parameters, the total amount of data downloaded by light nodes is larger than that obtainable with competitor solutions.

cs.CR↗

arXiv2022

On the Hardness of the Lee Syndrome Decoding Problem

In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric. We first prove that the decisional version of the problem is NP-complete, by a reduction from the $3$-dimensional matching problem. Then, we study the complexity of solving the problem, by translating the best known solvers in the Hamming metric over finite fields to the Lee metric over finite rings, as well as proposing some novel solutions. For the analyzed algorithms, we assess the computational complexity in the asymptotic regime and compare it to the corresponding algorithms in the Hamming metric.

cs.IT↗