arXiv subjects

Nikita Polyanskii

Publications and source records attributed to Nikita Polyanskii.

At least 19 recordsLinked to original sources

arXiv2026

Vantage: Availability-Graded Broadcast for Signature-Free BFT

Digital signatures make blocks and votes transferable evidence: one party can prove to another what a third party said. Authenticated channels convince only the direct receiver, so a proposer that references another party's block cannot prove to the voters who published it. High-throughput signature-free protocols therefore complete an availability vote or a reliable broadcast for every published data block before a proposer may reference it. We present Vantage, a partially synchronous Byzantine fault-tolerant protocol for $n \ge 3f+1$ parties, at most $f$ Byzantine, that uses only authenticated channels and collision-resistant hashing. Parties publish blocks on hash-linked author lanes; each view's proposer pairs a core manifest of lane prefixes that a quorum has acknowledged to it with an optimistic tip manifest of blocks it has just received. A new primitive, Availability-Graded Broadcast (AGB), makes the core irrevocable on a quorum of directly received acknowledgments while grading, rather than blocking on, the tip. A view that AGB leaves open or silent is decided by an on-demand instance of information-theoretic agreement. A block may thus be referenced in a proposal one message delay after publication, as in signed optimistic designs. Let $\delta$ be the message delay after global stabilization (GST). With all parties correct, a proposal commits within $2\delta$ of its send if all $n$ parties support it, and within $3\delta$ on the quorum path, so a block published in time for the next proposal is sequenced $3\delta$ to $4\delta$ after publication. Safety holds under asynchrony; liveness holds after GST. On an emulated ten-region WAN with 100 parties, Vantage has the lowest p50 latency among compared signed and signature-free protocols at every offered load up to its peak, and sequences 250k 512-byte transactions per second at median end-to-end latency below 500 ms.

cs.DC↗

arXiv2026

Improved Probabilistic Lower Bounds for Separable Matrices

This work focuses on non-adaptive combinatorial group testing, with a primary goal of efficiently identifying a set of at most $d$ defective elements among a given set of $n$ elements using the fewest possible tests. Non-adaptive combinatorial group testing often employs disjunctive matrices (DM) and separable matrices (SM). This paper discusses separable matrices and recently introduced list-decoding separable matrices (LDSM) with list size $n^{1/d}$, which allow for non-adaptive identification of defectives with the decoding complexity linear in the number of tests and the number of elements. In our study, we distinguish two subclasses of these matrices: matrices which can be used when the number of defectives $d$ is a priori known ($d$-SM and $(d, n^{1/d})$-LDSM), and matrices which can be used for any subset of at most $d$ defectives ($\bar{d}$-SM and $(\bar{d}, n^{1/d})$-LDSM). Our contribution lies in deriving new lower bounds on the rates of $d$-SM, $\bar{d}$-SM, $(d, n^{1/d})$-LDSM and $(\bar{d}, n^{1/d})$-LDSM for an arbitrary number $d \ge 3$ of defectives.

cs.IT↗

arXiv2025

Slipstream: Ebb-and-Flow Consensus on a DAG with Fast Confirmation for UTXO Transactions

This paper introduces Slipstream, a Byzantine Fault Tolerance (BFT) protocol where nodes concurrently propose blocks to be added to a Directed Acyclic Graph (DAG) and aim to agree on block ordering. Slipstream offers two types of block orderings: an optimistic ordering, which is live and secure in a sleepy model under up to 50% Byzantine nodes, and a final ordering, which is a prefix of the optimistic ordering and ensures safety and liveness in an eventual lock-step synchronous model under up to 33% Byzantine nodes. Additionally, Slipstream integrates a payment system that allows for fast UTXO transaction confirmation independently of block ordering. Transactions are confirmed in three rounds during synchrony, and unconfirmed double spends are resolved in a novel way using the DAG structure.

cs.DC↗

arXiv2025

SoK: DAG-based Consensus Protocols

This paper is a Systematization of Knowledge (SoK) on Directed Acyclic Graph (DAG)-based consensus protocols, analyzing their performance and trade-offs within the framework of consistency, availability, and partition tolerance inspired by the CAP theorem. We classify DAG-based consensus protocols into availability-focused and consistency-focused categories, exploring their design principles, core functionalities, and associated trade-offs. Furthermore, we examine key properties, attack vectors, and recent developments, providing insights into security, scalability, and fairness challenges. Finally, we identify research gaps and outline directions for advancing DAG-based consensus mechanisms.

cs.DC↗

arXiv2025

Fairness Notions in DAG-based DLTs

This paper investigates the issue of fairness in Distributed Ledger Technology (DLT), specifically focusing on the shortcomings observed in current blockchain systems due to Miner Extractable Value (MEV) phenomena and systemic centralization. We explore the potential of Directed Acyclic Graphs (DAGs) as a solution to address or mitigate these fairness concerns. Our objective is to gain a comprehensive understanding of fairness in DAG-based DLTs by examining its different aspects and measurement metrics. We aim to establish a shared knowledge base that facilitates accurate fairness assessment and allows for an evaluation of whether DAG-based DLTs offer a more equitable design. We describe the various dimensions of fairness and conduct a comparative analysis to examine how they relate to different components of DLTs. This analysis serves as a catalyst for further research, encouraging the development of cryptographic systems that promote fairness.

cs.CR↗

arXiv2025

Combinatorial Group Testing in Presence of Deletions

The study in group testing aims to develop strategies to identify a small set of defective items among a large population using a few pooled tests. The established techniques have been highly beneficial in a broad spectrum of applications ranging from channel communication to identifying COVID-19-infected individuals efficiently. Despite significant research on group testing and its variants since the 1940s, testing strategies robust to deletion noise have yet to be studied. Many practical systems exhibit deletion errors, for instance, in wireless communication and data storage systems. Such deletions of test outcomes lead to asynchrony between the tests, which the current group testing strategies cannot handle. In this work, we initiate the study of non-adaptive group testing strategies resilient to deletion noise. We characterize the necessary and sufficient conditions to successfully identify the defective items even after the adversarial deletion of certain test outputs. We also provide constructions of testing matrices along with an efficient recovery algorithm.

cs.IT↗

arXiv2024

Deterministic Bounds in Committee Selection: Enhancing Decentralization and Scalability in Distributed Ledgers

Consensus plays a crucial role in distributed ledger systems, impacting both scalability and decentralization. Many blockchain systems use a weighted lottery based on a scarce resource such as a stake, storage, memory, or computing power to select a committee whose members drive the consensus and are responsible for adding new information to the ledger. Therefore, ensuring a robust and fair committee selection process is essential for maintaining security, efficiency, and decentralization. There are two main approaches to randomized committee selection. In one approach, each validator candidate locally checks whether they are elected to the committee and reveals their proof during the consensus phase. In contrast, in the second approach, a sortition algorithm decides a fixed-sized committee that is globally verified. This paper focuses on the latter approach, with cryptographic sortition as a method for fair committee selection that guarantees a constant committee size. Our goal is to develop deterministic guarantees that strengthen decentralization. We introduce novel methods that provide deterministic bounds on the influence of adversaries within the committee, as evidenced by numerical experiments. This approach overcomes the limitations of existing protocols that only offer probabilistic guarantees, often providing large committees that are impractical for many quorum-based applications like atomic broadcast and randomness beacon protocols.

cs.DC↗

arXiv2024

On Codes for the Noisy Substring Channel

We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems, interest in this channel has renewed in recent years. In contrast to existing literature, we consider a noisy channel model where information is subject to noise before its substrings are sampled, motivated by in-vivo storage. We study two separate noise models, substitutions or deletions. In both cases, we examine families of codes which may be utilized for error-correction and present combinatorial bounds on their sizes. Through a generalization of the concept of repeat-free strings, we show that the added required redundancy due to this imperfect observation assumption is sublinear, either when the fraction of errors in the observed substring length is sufficiently small, or when that length is sufficiently long. This suggests that no asymptotic cost in rate is incurred by this channel model in these cases. Moreover, we develop an efficient encoder for such constrained strings in some cases. Finally, we show how a similar encoder can be used to avoid formation of secondary-structures in coded DNA strands, even when accounting for imperfect structures.

cs.IT↗

arXiv2023

Reality-based UTXO Ledger

The Unspent Transaction Output (UTXO) model is commonly used in the field of Distributed Ledger Technology (DLT) to transfer value between participants. One of its advantages is that it allows parallel processing of transactions, as independent transactions can be added in any order. This property of order invariance and parallelisability has potential benefits in terms of scalability. However, since the UTXO Ledger is an append-only data structure, this advantage is compromised through the presence of conflicting transactions. We propose an extended UTXO Ledger model that optimistically updates the ledger and keeps track of the dependencies of the possible conflicts. In the presence of a conflict resolution mechanism, we propose a method to reduce the extended ledger back to a consistent UTXO Ledger.

cs.DC↗

arXiv2023

Codes for the Z-channel

This paper is a collection of results on combinatorial properties of codes for the Z-channel. A Z-channel with error fraction $τ$ takes as input a length-$n$ binary codeword and injects in an adversarial manner up to $nτ$ asymmetric errors, i.e., errors that only zero out bits but do not flip $0$'s to $1$'s. It is known that the largest $(L-1)$-list-decodable code for the Z-channel with error fraction $τ$ has exponential size (in $n$) if $τ$ is less than a critical value that we call the $(L-1)$-list-decoding Plotkin point and has constant size if $τ$ is larger than the threshold. The $(L-1)$-list-decoding Plotkin point is known to be $ L^{-\frac{1}{L-1}} - L^{-\frac{L}{L-1}} $, which equals $1/4$ for unique-decoding with $ L-1=1 $. In this paper, we derive various results for the size of the largest codes above and below the list-decoding Plotkin point. In particular, we show that the largest $(L-1)$-list-decodable code $ε$-above the Plotkin point, {for any given sufficiently small positive constant $ ε>0 $,} has size $Θ_L(ε^{-3/2})$ for any $L-1\ge1$. We also devise upper and lower bounds on the exponential size of codes below the list-decoding Plotkin point.

cs.IT↗

arXiv2023

Codes Correcting a Single Long Duplication Error

We consider the problem of constructing a code capable of correcting a single long tandem duplication error of variable length. As the main contribution of this paper, we present a $q$-ary efficiently encodable code of length $n+1$ and redundancy $1$ that can correct a single duplication of length at least $K=4\cdot\lceil \log_q n\rceil +1$. The complexity of encoding is $O(\frac{n^2}{\log n})$ and the complexity of decoding is $O(n)$. We also present a $q$-ary non-efficient code of length $n+1$ correcting single long duplication of length at least $K = \lceil \log_q n\rceil +ϕ(n)$, where $ϕ(n)\rightarrow{\infty}$ as $n\rightarrow{\infty}$. This code has redundancy less than $1$ for sufficiently large $n$. Moreover, we show that in the class of codes correcting a single long duplication with redundancy $1$, the value $K$ in our constructions is order-optimal.

cs.IT↗

arXiv2022

Tangle 2.0 Leaderless Nakamoto Consensus on the Heaviest DAG

We introduce the theoretical foundations of the Tangle 2.0, a probabilistic leaderless consensus protocol based on a directed acyclic graph (DAG) called the Tangle. The Tangle naturally succeeds the blockchain as its next evolutionary step as it offers features suited to establish more efficient and scalable distributed ledger solutions. Consensus is no longer found in the longest chain but on the heaviest DAG, where PoW is replaced by a stake- or reputation-based weight function. The DAG structure and the underlying Reality-based UTXO Ledger allow parallel validation of transactions without the need for total ordering. Moreover, it enables the removal of the intermediary of miners and validators, allowing a pure two-step process that follows the \emph{propose-vote} paradigm at the node level and not at the validator level. We propose a framework to analyse liveness and safety under different communication and adversary models. This allows providing impossibility results in some edge cases and in the asynchronous communication model. We provide formal proof of the security of the protocol assuming a common random coin.

cs.DC↗

arXiv2022

Signature Codes for a Noisy Adder Multiple Access Channel

In this work, we consider $q$-ary signature codes of length $k$ and size $n$ for a noisy adder multiple access channel. A signature code in this model has the property that any subset of codewords can be uniquely reconstructed based on any vector that is obtained from the sum (over integers) of these codewords. We show that there exists an algorithm to construct a signature code of length $k = \frac{2n\log{3}}{(1-2τ)\left(\log{n} + (q-1)\log{\fracπ{2}}\right)} +\mathcal{O}\left(\frac{n}{\log{n}(q+\log{n})}\right)$ capable of correcting $τk$ errors at the channel output, where $0\le τ< \frac{q-1}{2q}$. Furthermore, we present an explicit construction of signature codewords with polynomial complexity being able to correct up to $\left( \frac{q-1}{8q} - ε\right)k$ errors for a codeword length $k = \mathcal{O} \left ( \frac{n}{\log \log n} \right )$, where $ε$ is a small non-negative number. Moreover, we prove several non-existence results (converse bounds) for $q$-ary signature codes enabling error correction.

cs.IT↗

arXiv2022

Quadratic-Curve-Lifted Reed-Solomon Codes

Lifted codes are a class of evaluation codes attracting more attention due to good locality and intermediate availability. In this work we introduce and study quadratic-curve-lifted Reed-Solomon (QC-LRS) codes, where the codeword symbols whose coordinates are on a quadratic curve form a codeword of a Reed-Solomon code. We first develop a necessary and sufficient condition on the monomials which form a basis the code. Based on the condition, we give upper and lower bounds on the dimension and show that the asymptotic rate of a QC-LRS code over $\mathbb{F}_q$ with local redundancy $r$ is $1-Θ(q/r)^{-0.2284}$. Moreover, we provide analytical results on the minimum distance of this class of codes and compare QC-LRS codes with lifted Reed-Solomon codes by simulations in terms of the local recovery capability against erasures. For short lengths, QC-LRS codes have better performance in local recovery for erasures than LRS codes of the same dimension.

cs.IT↗

arXiv2022

Two-stage coding over the Z-channel

In this paper, we discuss two-stage encoding algorithms capable of correcting a fraction of asymmetric errors. Suppose that the encoder transmits $n$ binary symbols $(x_1,\ldots,x_n)$ one-by-one over the Z-channel, in which a 1 is received only if a 1 is transmitted. At some designated moment, say $n_1$, the encoder uses noiseless feedback and adjusts further encoding strategy based on the partial output of the channel $(y_1,\ldots,y_{n_1})$. The goal is to transmit error-free as much information as possible under the assumption that the total number of errors inflicted by the Z-channel is limited by $τn$, $0<τ<1$. We propose an encoding strategy that uses a list-decodable code at the first stage and a high-error low-rate code at the second stage. This strategy and our converse result yield that there is a sharp transition at $τ=\max\limits_{0<w<1}\frac{w + w^3}{1+4w^3}\approx 0.44$ from positive rate to zero rate for two-stage encoding strategies. As side results, we derive bounds on the size of list-decodable codes for the Z-channel and prove that for a fraction $1/4+ε$ of asymmetric errors, an error-correcting code contains at most $O(ε^{-3/2})$ codewords.

cs.IT↗

arXiv2022

Feedback Insertion-Deletion Codes

In this paper, a new problem of transmitting information over the adversarial insertion-deletion channel with feedback is introduced. Suppose that the encoder transmits $n$ binary symbols one-by-one over a channel, in which some symbols can be deleted and some additional symbols can be inserted. After each transmission, the encoder is notified about the insertions or deletions that have occurred within the previous transmission and the encoding strategy can be adapted accordingly. The goal is to design an encoder that is able to transmit error-free as much information as possible under the assumption that the total number of deletions and insertions is limited by $τn$, $0<τ<1$. We show how this problem can be reduced to the problem of transmitting messages over the substitution channel. Thereby, the maximal asymptotic rate of feedback insertion-deletion codes is completely established. The maximal asymptotic rate for the adversarial substitution channel has been partially determined by Berlekamp and later finished by Zigangirov. However, the analysis of the lower bound by Zigangirov is quite complicated. We revisit Zigangirov's result and present a more elaborate version of his proof.

cs.IT↗

arXiv2021

Lifted Reed-Solomon Codes and Lifted Multiplicity Codes

Lifted Reed-Solomon and multiplicity codes are classes of codes, constructed from specific sets of $m$-variate polynomials. These codes allow for the design of high-rate codes that can recover every codeword or information symbol from many disjoint sets. Recently, the underlying approaches have been combined for the bi-variate case to construct lifted multiplicity codes, a generalization of lifted codes that can offer further rate improvements. We continue the study of these codes by first establishing new lower bounds on the rate of lifted Reed-Solomon codes for any number of variables $m$, which improve upon the known bounds for any $m\ge 4$. Next, we use these results to provide lower bounds on the rate and distance of lifted multiplicity codes obtained from polynomials in an arbitrary number of variables, which improve upon the known results for any $m\ge 3$. Specifically, we investigate a subcode of a lifted multiplicity code formed by the linear span of $m$-variate monomials whose restriction to an arbitrary line in $\mathbb{F}_q^m$ is equivalent to a low-degree univariate polynomial. We find the tight asymptotic behavior of the fraction of such monomials when the number of variables $m$ is fixed and the alphabet size $q=2^\ell$ is large. Using these results, we give a new explicit construction of batch codes utilizing lifted Reed-Solomon codes. For some parameter regimes, these codes have a better trade-off between parameters than previously known batch codes. Further, we show that lifted multiplicity codes have a better trade-off between redundancy and the number of disjoint recovering sets for every codeword or information symbol than previously known constructions, thereby providing the best known PIR codes for some parameter regimes. Additionally, we present a new local self-correction algorithm for lifted multiplicity codes.

cs.IT↗

arXiv2021

Almost Affinely Disjoint Subspaces

In this work, we introduce a natural notion concerning finite vector spaces. A family of $k$-dimensional subspaces of $\mathbb{F}_q^n$, which forms a partial spread, is called almost affinely disjoint if any $(k+1)$-dimensional subspace containing a subspace from the family non-trivially intersects with only a few subspaces from the family. The central question discussed in the paper is the polynomial growth (in $q$) of the maximal cardinality of these families given the parameters $k$ and $n$. For the cases $k=1$ and $k=2$, optimal families are constructed. For other settings, we find lower and upper bounds on the polynomial growth. Additionally, some connections with problems in coding theory are shown.

math.CO↗