arXiv subjects

Paolo Santini

Publications and source records attributed to Paolo Santini.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2022

Optimization of a Reed-Solomon code-based protocol against blockchain data availability attacks

ASBK (named after the authors' initials) is a recent blockchain protocol tackling data availability attacks against light nodes, employing two-dimensional Reed-Solomon codes to encode the list of transactions and a random sampling phase where adversaries are forced to reveal information. In its original formulation, only codes with rate $1/4$ are considered, and a theoretical analysis requiring computationally demanding formulas is provided. This makes ASBK difficult to optimize in situations of practical interest. In this paper, we introduce a much simpler model for such a protocol, which additionally supports the use of codes with arbitrary rate. This makes blockchains implementing ASBK much easier to design and optimize. Furthermore, disposing of a clearer view of the protocol, some general features and considerations can be derived (e.g., nodes behaviour in largely participated networks). As a concrete application of our analysis, we consider relevant blockchain parameters and find network settings that minimize the amount of data downloaded by light nodes. Our results show that the protocol benefits from the use of codes defined over large finite fields, with code rates that may be even significantly different from the originally proposed ones.

cs.IT↗

arXiv2021

Counteracting dephasing in Molecular Nanomagnets by optimized qudit encodings

Molecular Nanomagnets may enable the implementation of qudit-based quantum error-correction codes which exploit the many spin levels naturally embedded in a single molecule, a promising step towards scalable quantum processors. To fully realize the potential of this approach, a microscopic understanding of the errors corrupting the quantum information encoded in a molecular qudit is essential, together with the development of tailor-made quantum error correction strategies. We address these central points by first studying dephasing effects on the molecular spin qudit produced by the interaction with surrounding nuclear spins, which are the dominant source of errors at low temperatures. Numerical quantum error correction codes are then constructed, by means of a systematic optimisation procedure based on simulations of the coupled system-bath dynamics, that provide a striking enhancement of the coherence time of the molecular computational unit. The sequence of pulses needed for the experimental implementation of the codes is finally proposed.

quant-ph↗

arXiv2021

Cryptanalysis of a code-based full-time signature

We present an attack against a code-based signature scheme based on the Lyubashevsky protocol that was recently proposed by Song, Huang, Mu, Wu and Wang (SHMWW). The private key in the SHMWW scheme contains columns coming in part from an identity matrix and in part from a random matrix. The existence of two types of columns leads to a strong bias in the distribution of set bits in produced signatures. Our attack exploits such a bias to recover the private key from a bunch of collected signatures. We provide a theoretical analysis of the attack along with experimental evaluations, and we show that as few as 10 signatures are enough to be collected for successfully recovering the private key. As for previous attempts of adapting Lyubashevsky's protocol to the case of code-based cryptography, the SHMWW scheme is thus proved unable to provide acceptable security. This confirms that devising secure code-based signature schemes with efficiency comparable to that of other post-quantum solutions (e.g., based on lattices) is still a challenging task.

cs.CR↗

arXiv2021

Information set decoding of Lee-metric codes over finite rings

Information set decoding (ISD) algorithms are the best known procedures to solve the decoding problem for general linear codes. These algorithms are hence used for codes without a visible structure, or for which efficient decoders exploiting the code structure are not known. Classically, ISD algorithms have been studied for codes in the Hamming metric. In this paper we switch from the Hamming metric to the Lee metric, and study ISD algorithms and their complexity for codes measured with the Lee metric over finite rings.

cs.CR↗

arXiv2021

A New Path to Code-based Signatures via Identification Schemes with Restricted Errors

In this paper we introduce a variant of the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries of the searched vector are defined over a subset of the underlying finite field. We prove the NP-completeness of R-SDP, via a reduction from the classical SDP, and describe algorithms which solve such new problem. We study the properties of random codes under this new decoding perspective, in the fashion of traditional coding theory results, and assess the complexity of solving a random R-SDP instance. As a concrete application, we describe how Zero-Knowledge Identification (ZK-ID) schemes based on SDP can be tweaked to rely on R-SDP, and show that this leads to compact public keys as well as significantly reduced communication costs. Thus, these schemes offer an improved basis for the construction of code-based digital signature schemes derived from identification schemes through the well-know Fiat-Shamir transformation.

cs.CR↗

arXiv2021

Unravelling the Spin Dynamics of Molecular Nanomagnets with Four-Dimensional Inelastic Neutron Scattering

Molecular Nanomagnets have attracted the attention of the scientific community since the rich physics behind their magnetic behaviour make them ideal test-beds for fundamental concepts in quantum mechanics. Sophisticated experiments and targeted research activities have also unveiled their potential for several technological applications. Inelastic neutron scattering is a powerful and widely used technique to investigate the properties of these systems. The new generation of spectrometers, equipped with arrays of position-sensitive detectors, enable to efficiently measure the neutron cross-sections as a function of energy and of the three component of the momentum transfer vector Q, in vast portions of the reciprocal space. Exploiting these capabilities together with the availability of sufficiently large single-crystal samples of MNMs, it is now possible to obtain an unprecedented insight into the coherent spin dynamics of these molecular clusters. This is witnessed by several recent results, that we present in this review. By using the benchmark system Cr$_8$, it has been demonstrated that the richness of the four-dimensional inelastic neutrons scattering technique enables to extract dynamical correlation functions directly from the data. This technique has been also applied to the archetypical single-molecule magnet Mn$_{12}$ to unambiguously characterise its Spin Hamiltonian as well as to portray the entanglement between molecular qubits in (Cr$_7$Ni)$_2$.

cond-mat.mes-hall↗

arXiv2020

Constructing Clock-Transition-Based Two-Qubit Gates from Dimers of Molecular Nanomagnets

A good qubit must have a coherence time long enough for gate operations to be performed. Avoided level crossings allow for clock transitions in which coherence is enhanced by the insensitivity of the transition to fluctuations in external fields. Because of this insensitivity, it is not obvious how to effectively couple qubits together while retaining clock-transition behavior. Here we present a scheme for using a heterodimer of two coupled molecular nanomagnets, each with a clock transition at zero magnetic field, in which all of the gate operations needed to implement one- and two-qubit gates can be implemented with pulsed radio-frequency radiation. We show that given realistic coupling strengths between the nanomagnets in the dimer, good gate fidelities ($\sim$99.4\%) can be achieved. We identify the primary sources of error in implementing gates and discuss how these may be mitigated, and investigate the range of coherence times necessary for such a system to be a viable platform for implementing quantum computing protocols.

quant-ph↗

arXiv2020

Analysis of the error correction capability of LDPC and MDPC codes under parallel bit-flipping decoding and application to cryptography

Iterative decoders used for decoding low-density parity-check (LDPC) and moderate-density parity-check (MDPC) codes are not characterized by a deterministic decoding radius and their error rate performance is usually assessed through intensive Monte Carlo simulations. However, several applications, like code-based cryptography, need guaranteed low values of the error rate, which are infeasible to assess through simulations, thus requiring the development of theoretical models for the error rate of these codes under iterative decoding. Some models of this type already exist, but become computationally intractable for parameters of practical interest. Other approaches approximate the code ensemble behaviour through some assumptions, which may not hold true for a specific code. We propose a theoretical analysis of the error correction capability of LDPC and MDPC codes that allows deriving tight bounds on the error rate at the output of parallel bit-flipping decoders. Special attention is devoted to the case of codes with small girth; moreover, single-iteration decoding is investigated through a rigorous approach, which does not require any assumption and hence results in a guaranteed error correction capability for any single code. We show an example of application of the new bound to the context of code-based cryptography, where guaranteed error rates are needed to achieve some strong security levels.

cs.IT↗

arXiv2019

A Code-specific Conservative Model for the Failure Rate of Bit-flipping Decoding of LDPC Codes with Cryptographic Applications

Characterizing the decoding failure rate of iteratively decoded Low- and Moderate-Density Parity Check (LDPC/MDPC) codes is paramount to build cryptosystems based on them, able to achieve indistinguishability under adaptive chosen ciphertext attacks. In this paper, we provide a statistical worst-case analysis of our proposed iterative decoder obtained through a simple modification of the classic in-place bit-flipping decoder. This worst case analysis allows both to derive the worst-case behaviour of an LDPC/MDPC code picked among the family with the same length, rate and number of parity checks, and a code-specific bound on the decoding failure rate. The former result allows us to build a code-based cryptosystem enjoying the $δ$-correctness property required by IND-CCA2 constructions, while the latter result allows us to discard code instances which may have a decoding failure rate significantly different from the average one (i.e., representing weak keys), should they be picked during the key generation procedure.

cs.CR↗

arXiv2019

First-principles many-body models for electron transport through molecular nanomagnets

Impressive advances in the field of molecular spintronics allow one to study electron transport through individual magnetic molecules embedded between metallic leads in the purely quantum regime of single electron tunneling. Besides fundamental interest, this experimental setup, in which a single molecule is manipulated by electronic means, provides the elementary units of possible forthcoming technological applications, ranging from spin valves to transistors and qubits for quantum information processing. Theoretically, while for weakly correlated molecular junctions established first-principles techniques do enable the system-specific description of transport phenomena, methods of similar power and flexibility are still lacking for junctions involving strongly correlated molecular nanomagnets. Here we propose an efficient scheme based on the ab initio construction of material-specific Hubbard models and on the master-equation formalism. We apply this approach to a representative case, the Ni$_2$ molecular spin dimer, in the regime of weak molecule-electrode coupling, the one relevant for quantum-information applications. Our approach allows us to study in a realistic setting many-body effects such as current suppression and negative differential conductance. We think that this method has the potential for becoming a very useful tool for describing transport phenomena in strongly correlated molecules.

cond-mat.str-el↗

arXiv2019

Analysis of reaction and timing attacks against cryptosystems based on sparse parity-check codes

In this paper we study reaction and timing attacks against cryptosystems based on sparse parity-check codes, which encompass low-density parity-check (LDPC) codes and moderate-density parity-check (MDPC) codes. We show that the feasibility of these attacks is not strictly associated to the quasi-cyclic (QC) structure of the code but is related to the intrinsically probabilistic decoding of any sparse parity-check code. So, these attacks not only work against QC codes, but can be generalized to broader classes of codes. We provide a novel algorithm that, in the case of a QC code, allows recovering a larger amount of information than that retrievable through existing attacks and we use this algorithm to characterize new side-channel information leakages. We devise a theoretical model for the decoder that describes and justifies our results. Numerical simulations are provided that confirm the effectiveness of our approach.

cs.IT↗

arXiv2019

Cryptanalysis of a One-Time Code-Based Digital Signature Scheme

We consider a one-time digital signature scheme recently proposed by Persichetti and show that a successful key recovery attack can be mounted with limited complexity. The attack we propose exploits a single signature intercepted by the attacker, and relies on a statistical analysis performed over such a signature, followed by information set decoding. We assess the attack complexity and show that a full recovery of the secret key can be performed with a work factor that is far below the claimed security level. The efficiency of the attack is motivated by the sparsity of the signature, which leads to a significant information leakage about the secret key.

cs.CR↗

arXiv2018

Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes

Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are promising post-quantum candidates to replace quantum vulnerable classical alternatives. However, a new type of attacks based on Bob's reactions have recently been introduced and appear to significantly reduce the length of the life of any keypair used in these systems. In this paper we estimate the complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based variants of the McEliece cryptosystem. We also show how the structure of the secret key and, in particular, the secret code rate affect the complexity of these attacks. It follows from our results that QC-LDPC code-based systems can indeed withstand reaction attacks, on condition that some specific decoding algorithms are used and the secret code has a sufficiently high rate.

cs.CR↗

arXiv2018

Design and Implementation of a Digital Signature Scheme Based on Low-density Generator Matrix Codes

In this paper we consider a post-quantum digital signature scheme based on low-density generator matrix codes and propose efficient algorithmic solutions for its implementation. We also review all known attacks against this scheme and derive closed-form estimates of their complexity when running over both classical and quantum computers. Based on these estimates, we propose new parametrization for the considered system to achieve given pre-quantum and post-quantum security levels. Finally, we provide and discuss performance benchmarks obtained through a suitably developed and publicly available reference implementation of the considered system.

cs.CR↗

arXiv2018

Hindering reaction attacks by using monomial codes in the McEliece cryptosystem

In this paper we study recent reaction attacks against QC-LDPC and QC-MDPC code-based cryptosystems, which allow an opponent to recover the private parity-check matrix through its distance spectrum by observing a sufficiently high number of decryption failures. We consider a special class of codes, known as monomial codes, to form private keys with the desirable property of having a unique and complete distance spectrum. We verify that for these codes the problem of recovering the secret key from the distance spectrum is equivalent to that of finding cliques in a graph, and use this equivalence to prove that current reaction attacks are not applicable when codes of this type are used in the McEliece cryptosystem.

cs.IT↗

arXiv2018

LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes

This work presents a new code-based key encapsulation mechanism (KEM) called LEDAkem. It is built on the Niederreiter cryptosystem and relies on quasi-cyclic low-density parity-check codes as secret codes, providing high decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known statistical attacks, and takes advantage of a new decoding algorithm that provides faster decoding than the classical bit-flipping decoder commonly adopted in this kind of systems. The main attacks against LEDAkem are investigated, taking into account quantum speedups. Some instances of LEDAkem are designed to achieve different security levels against classical and quantum computers. Some performance figures obtained through an efficient C99 implementation of LEDAkem are provided.

cs.CR↗

arXiv2017

Superadiabatic driving of a three-level quantum system

We study superadiabatic quantum control of a three-level quantum system whose energy spectrum exhibits multiple avoided crossings. In particular, we investigate the possibility of treating the full control task in terms of independent two-level Landau-Zener problems. We first show that the time profiles of the elements of the full control Hamiltonian are characterized by peaks centered around the crossing times. These peaks decay algebraically for large times. In principle, such a power-law scaling invalidates the hypothesis of perfect separability. Nonetheless, we address the problem from a pragmatic point of view by studying the fidelity obtained through separate control as a function of the intercrossing separation. This procedure may be a good approach to achieve approximate adiabatic driving of a specific instantaneous eigenstate in realistic implementations.

quant-ph↗