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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. [ABSTRACT FROM AUTHOR]

In this paper we 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 ⊥ 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 presented by Micali et al. (SIAM J Comput 26(4):873–933, 1997; Byzantine agreement, made trivial, 2016). We prove the correctness and security of the protocol assuming a synchronous network where less than a third of the nodes are malicious. [ABSTRACT FROM AUTHOR]

A quantum random number generator (QRNG) based on a silicon nanocrystals (Si-NCs) light emitting device (LED) coupled with a silicon single photon avalanche photodiode (Si-SPAD) is presented. A simple setup is used for the generation of random bits. The modeled approach assures a negligible bias on datasets of [ABSTRACT FROM AUTHOR]

Most bounds on the size of codes hold for any code, whether linear or not. Notably, the Griesmer bound holds only in the linear case and so optimal linear codes are not necessarily optimal codes. In this paper, we identify code parameters $(q,d,k)$ , namely, field size, minimum distance, and combinatorial dimension, for which the Griesmer bound also holds in the (systematic) nonlinear case. Moreover, we show that the Griesmer bound does not necessarily hold for a systematic code by explicit construction of a family of optimal systematic binary codes. On the other hand, we are able to provide some versions of the Griesmer bound holding for all the systematic codes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Blockchain-based platforms utilise cryptographic protocols to enforce the correct behaviour of users, as well as to guarantee a sufficient level of protection against malicious adversaries. Cryptography is, however, an ever-evolving discipline, and any breakthrough would have immediate consequences on the security of blockchain-based applications. A possible threat currently under investigation is given by the development of quantum computers, since several wide-adopted cryptographic protocols have been proved to be unsafe against quantum-capable adversaries. In this work, we propose a novel approach for the management of cryptographic primitives in smart-contract-based ledgers, discussing how it fits in both a (partially) permissioned and a fully permissionless setting. The cryptographic protocols are managed in a flexible manner via a set of smart-contracts defined on the ledger itself, in this way the choice of algorithms and parameters can change quickly. Among the advantages of this approach, we remark how it allows designing an adaptive post-quantum-based blockchain that keeps up with ongoing technological advances. In general, the introduction of new features and the application of fixes to a blockchain cause forks in the chain, which may cause major disruptions. The use of smart contracts in blockchain management allows to avoid this problem, dynamically introducing new protocols or deprecating old ones without compromising previous data. The Cryptographic Kernel approach has been adopted by Quadrans, an open-source, public, decentralised smart-contract-based blockchain with a specific focus on the needs of industry, complex supply chains, and IOT devices. [ABSTRACT FROM AUTHOR]

Blockchain technology has attracted a lot of research interest in the last few years. Originally, their consensus algorithm was Hashcash, which is an instance of the so-called Proof-of-Work. Nowadays, there are several competing consensus algorithms, not necessarily PoW. In this paper, we propose an alternative proof of work algorithm which is based on the solution of consecutive discrete logarithm problems over the point group of elliptic curves. At the same time, we sketch a blockchain scheme, whose consensus is reached via our algorithm. 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. [ABSTRACT FROM AUTHOR]

Abstract A quantum random generator based on photon detection is here presented. The system consists of a photon source, typically a commercial LED, coupled with a detector with single photon detection capability. The detector is composed of a Single-Photon Avalanche Diode (SPAD) and a time stamp circuit, which samples the arrival time of impinging photons within a predefined temporal window. The proposed implementation optimizes the area, allowing embedding all circuitry into a single pixel, and increases the efficiency of random bit extraction. Moreover, the adopted fast pre-charge mode of the SPAD quenching circuit reduces the afterpulsing probability, and hence possible undesirable correlation in the resulting random bit sequence. Thanks to the implemented random bit extraction, experimental results show that the pixel has a flat behavior for a significant range of light intensity, which makes the pixel robust against variations of external PVT parameters. The maximum achievable bit rate has been measured equal to 1 Mbps, while random sequences are shown to pass NIST tests without any post-processing. [ABSTRACT FROM AUTHOR]