arXiv subjects

Alessio Meneghetti

Publications and source records attributed to Alessio Meneghetti.

At least 19 recordsLinked to original sources

arXiv2024

Quadratic Modelings of Syndrome Decoding

This paper presents enhanced reductions of the bounded-weight and exact-weight Syndrome Decoding Problem (SDP) to a system of quadratic equations. Over $\mathbb{F}_2$, we improve on a previous work and study the degree of regularity of the modeling of the exact weight SDP. Additionally, we introduce a novel technique that transforms SDP instances over $\mathbb{F}_q$ into systems of polynomial equations and thoroughly investigate the dimension of their varieties. Experimental results are provided to evaluate the complexity of solving SDP instances using our models through Gr\"obner bases techniques.

cs.CR↗

arXiv2024

A class of locally recoverable codes over finite chain rings

Locally recoverable codes deal with the task of reconstructing a lost symbol by relying on a portion of the remaining coordinates smaller than an information set. We consider the case of codes over finite chain rings, generalizing known results and bounds for codes over fields. In particular, we propose a new family of locally recoverable codes by extending a construction proposed in 2014 by Tamo and Barg, and we discuss its optimality.

cs.IT↗

arXiv2022

The weight distribution of codes over finite chain rings

In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code. Thanks to these relations we are able to compute the full weight distribution of codes with small Singleton defects, such as MDS, MDR and AMDR codes.

cs.IT↗

arXiv2022

Cob: a consensus layer enabling sustainable sharding-based consensus protocols

In this paper we explore a context of application of Cob, a recently introduced Byzantine Fault Tolerant consensus protocol. Cob proves to be a leaderless consensus protocol which carries out the consensus process in parallel on each component of a list of events to be observed and recorded. We show how Cob can be used to define a consensus layer for scalable and sustainable blockchains. This layer is used to design consensus protocols based on sharding as a mean to achieve scalability, and on the fragmentation of time in time-slots (which get assigned to nodes that are instructed to create new blocks) as a mean to reduce the amount of computation and communication necessary for the maintenance of the distributed ledger. We explain why Cob is a viable candidate to implement such consensus layer through the introduction of an auxiliary blockchain that we name Synchronization Chain.

cs.DC↗

arXiv2022

Multidimensional Byzantine Agreement in a Synchronous Setting

In this paper we will present the Multidimensional Byzantine Agreement (MBA) Protocol, a leaderless Byzantine agreement protocol defined for complete and synchronous networks that allows a network of nodes to reach consensus on a vector of relevant information regarding a set of observed events. The consensus process is carried out in parallel on each component, and the output is a vector whose components are either values with wide agreement in the network (even if no individual node agrees on every value) or a special value $\bot$ that signals irreconcilable disagreement. The MBA Protocol is probabilistic and its execution halts with probability 1, and the number of steps necessary to halt follows a Bernoulli-like distribution. The design combines a Multidimensional Graded Consensus and a Multidimensional Binary Byzantine Agreement, the generalization to the multidimensional case of two protocols by Micali and Feldman. We prove the correctness and security of the protocol assuming a synchronous network where less than a third of the nodes are malicious.

cs.DC↗

arXiv2022

Cob: a Leaderless Protocol for Parallel Byzantine Agreement in Incomplete Networks

In this paper we extend the \emph{Multidimensional Byzantine Agreement (MBA) Protocol}, a {leaderless} Byzantine agreement for lists of arbitrary values, into a protocol suitable for wide gossiping networks: \emph{Cob}. This generalization allows the consensus process to be run by an incomplete network of nodes provided with (non-synchronized) same-speed clocks. Not all nodes are active in every step, so the network size does not hamper the efficiency, as long as the gossiping broadcast delivers the messages to every node in reasonable time. These network assumptions model more closely real-life communication channels, so the Cob protocol may be applicable to a variety of practical problems, such as blockchain platforms implementing sharding. Cob has the same Bernoulli-like distribution that upper-bounds the number of steps as the MBA protocol. We prove its correctness and security assuming a supermajority of honest nodes in the network, and compare its performance with Algorand.

cs.DC↗

arXiv2022

A Provably-Unforgeable Threshold EdDSA with an Offline Recovery Party

A $(t,n)$-threshold signature scheme enables distributed signing among $n$ players such that any subset of size at least $t$ can sign, whereas any subset with fewer players cannot. The goal is to produce threshold digital signatures that are compatible with an existing centralized signature scheme. Starting from the threshold scheme for the ECDSA signature due to Battagliola et al., we present the first protocol that supports EdDSA multi-party signatures with an offline participant during the key-generation phase, without relying on a trusted third party. Under standard assumptions we prove our scheme secure against adaptive malicious adversaries. Furthermore we show how our security notion can be strengthen when considering a rushing adversary. We discuss the resiliency of the recovery in the presence of a malicious party. Using a classical game-based argument, we prove that if there is an adversary capable of forging the scheme with non-negligible probability, then we can build a forger for the centralized EdDSA scheme with non-negligible probability.

cs.CR↗

arXiv2021

Vanishing ideals of binary Hamming spheres

We consider the simplified Algebraic Normal Form (sANF) of Boolean functions vanishing on Hamming spheres centred at zero and the associated sANF vector. We show that this vector is periodic, leading to an efficient computation of the sANF and to specific formulas for particular cases. Moreover, we explicitly provide a connection to the binary M{ö}bius transform of the elementary symmetric functions. We conclude by presenting a method based on polynomial evaluation to bound the minimum distance of binary nonlinear codes. The same method can be used to compute the minimum distance and the weight distribution of binary linear codes.

math.AC↗

arXiv2021

Security issues of CFS-like digital signature algorithms

We analyse the security of some variants of the CFS code-based digital signature scheme. We show how the adoption of some code-based hash-functions to improve the efficiency of CFS leads to the ability of an attacker to produce a forgery compatible to the rightful user's public key.

cs.CR↗

arXiv2021

A formula on the weight distribution of linear codes with applications to AMDS codes

The determination of the weight distribution of linear codes has been a fascinating problem since the very beginning of coding theory. There has been a lot of research on weight enumerators of special cases, such as self-dual codes and codes with small Singleton's defect. We propose a new set of linear relations that must be satisfied by the coefficients of the weight distribution. From these relations we are able to derive known identities (in an easier way) for interesting cases, such as extremal codes, Hermitian codes, MDS and NMDS codes. Moreover, we are able to present for the first time the weight distribution of AMDS codes. We also discuss the link between our results and the Pless equations.

math.CO↗

arXiv2021

On the equivalence of two post-quantum cryptographic families

The Maximum Likelihood Decoding Problem (MLD) is known to be NP-hard and its complexity is strictly related to the security of some post-quantum cryptosystems, that is, the so-called code-based primitives. Analogously, the Multivariate Quadratic System Problem (MQ) is NP-hard and its complexity is necessary for the security of the so-called multivariate-based primitives. In this paper we present a closed formula for a polynomial-time reduction from any instance of MLD to an instance of MQ, and viceversa. We also show a polynomial-time isomorphism between MQ and MLD, thus demonstrating the direct link between the two post-quantum cryptographic families.

cs.CC↗

arXiv2021

A survey on NIST PQ signatures

Shor's shockingly fast quantum algorithm for solving the period-finding problem is a threat for the most common public-key primitives, as it can be efficiently applied to solve both the Integer Factorisation Problem and the Discrete Logarithm Problem. In other words, many once-secure protocols have to be replaced by still-secure alternatives. Instead of relying, for example, on the RSA protocol, the Diffie-Hellman key-exchange or the (Elliptic Curve) Digital Signature Algorithm, many researchers moved their attention to the design and analysis of primitives which are yet to be broken by quantum algorithms. The urgency of the threat imposed by quantum computers led the U.S. National Institute of Standards and Technology (NIST) to open calls for both Post-Quantum Public-Keys Exchange Algorithms and Post-Quantum Digital Signature Algorithms. In this brief survey we focus on the round 3 finalists and alternate candidates for Digital Signatures: CRYSTALS-DILITHIUM, FALCON, Rainbow, SPHINCS+, GeMSS, Picnic.

cs.CR↗

arXiv2020

Threshold ECDSA with an Offline Recovery Party

A $(t,n)-$ threshold signature scheme enables distributed signing among $n$ players such that any subgroup of size $t$ can sign, whereas any group with fewer players cannot. Our goal is to produce signatures that are compatible with an existing centralized signature scheme: the key generation and signature algorithm are replaced by a communication protocol between the parties, but the verification algorithm remains identical to that of a signature issued using the centralized algorithm. Starting from the threshold schemes for the ECDSA signature due to R. Gennaro and S. Goldfeder, we present the first protocol that supports multiparty signatures with an offline participant during the Key Generation Phase, without relying on a trusted third party. Following well-established approaches, we prove our scheme secure against adaptive malicious adversaries.

cs.CR↗

arXiv2020

Characterisation of the parameters of maximum weight spectrum codes according to their spread

We introduce the concept of spread of a code, and we specialize it to the case of maximum weight spectrum (MWS) codes. We classify two newly-defined sub-families of MWS codes according to their weight distributions, and completely describe their fundamental parameters. We focus on one of these families, the strictly compact MWS codes, proving their optimality as MWS codes and linking them to known codes.

math.CO↗

arXiv2020

A new ECDLP-based PoW model

We lay the foundations for a blockchain scheme, whose consensus is reached via a proof of work algorithm based on the solution of consecutive discrete logarithm problems over the point group of elliptic curves. In the considered architecture, the curves are pseudorandomly determined by block creators, chosen to be cryptographically secure and changed every epoch. Given the current state of the chain and a prescribed set of transactions, the curve selection is fully rigid, therefore trust is needed neither in miners nor in the scheme proposers.

cs.CR↗

arXiv2019

Two-tier blockchain timestamped notarization with incremental security

Digital notarization is one of the most promising services offered by modern blockchain-based solutions. We present a digital notary design with incremental security and cost reduced with respect to current solutions. A client of the service receives evidence in three steps. In the first step, evidence is received almost immediately, but a lot of trust is required. In the second step, less trust is required, but evidence is received seconds later. Finally, in the third step evidence is received within minutes via a public blockchain.

cs.CR↗

arXiv2019

A survey on efficient parallelization of blockchain-based smart contracts

The main problem faced by smart contract platforms is the amount of time and computational power required to reach consensus. In a classical blockchain model, each operation is in fact performed by each node, both to update the status and to validate the results of the calculations performed by others. In this short survey we sketch some state-of-the-art approaches to obtain an efficient and scalable computation of smart contracts. Particular emphasis is given to sharding, a promising method that allows parallelization and therefore a more efficient management of the computational resources of the network.

cs.CR↗

arXiv2018

Type-Preserving Matrices and Security of Block Ciphers

We provide a new property, called Non-Type-Preserving, for a mixing layer which guarantees protection against algebraic attacks based on the imprimitivity of the group generated by the round functions. Our main result is to present necessary and sufficient conditions on the structure of the binary matrix associated to the mixing layer, so that it has this property. Then we show how several families of linear maps are Non-Type-Preserving, including the mixing layers of AES, GOST and PRESENT. Finally we prove that the group generated by the round functions of an SPN cipher with addition modulo a power of 2 as key mixing function is primitive if its mixing layer satisfies this property. Moreover we generalise the definition of a GOST-like cipher using a Non-Type-Preserving matrix as mixing layer and we show, under the only assumption of invertibility of the S-Boxes, that the corresponding group is primitive.

math.GR↗