arXiv subjects

Russell W. F. Lai

Publications and source records attributed to Russell W. F. Lai.

5 recordsLinked to original sources

arXiv2026

Algorithms for Sampling Self-Orthogonal and Totally Self-Orthogonal Codes in Odd Characteristic

We give an algorithm that samples uniformly random linear codes of any hull dimension and type over finite fields of odd characteristic, implying the first algorithm for sampling uniformly random self-orthogonal codes of any rate, including self-dual codes. Our algorithm is a re-visitation of the algorithm given by Albrecht, Benčina and Lai (EC'25), using the mass formulae proven by Li, Shi and Ling (IEEE Trans. Inf. Theory 71(1)). This allows us to instantiate code-based cryptographic schemes that rely on the hardness of Permutation Code Equivalence (PCE) on `random' self-dual codes for security and that were previously unable to sample them. Building on the observation by Bardet, Otmani and Saeed-Taha (ISIT'19) that Euclidean orthogonality is insufficient when considering PCE over finite extension fields due to non-trivial Galois automorphisms, we study the behaviour of what we call total orthogonality, that is orthogonality with respect to all induced Galois geometries simultaneously. We characterise total orthogonality of vectors and codes, and give an algorithm that samples linear codes with a total hull of a prescribed dimension; a subcode that acts as the hull in all Galois geometries of the ambient space. The algorithm incurs a rate decrease by a factor equal to the extension degree, however, we argue why this may be necessary in the context of PCE and explore how it limits the practicality of our algorithm. We consider the notion of Galois type of a linear code when Galois hulls are symmetric and show that all linear codes have constant Hermitian type.

cs.IT↗

arXiv2024

On Defeating Graph Analysis of Anonymous Transactions

In a ring-signature-based anonymous cryptocurrency, signers of a transaction are hidden among a set of potential signers, called a ring, whose size is much smaller than the number of all users. The ring-membership relations specified by the sets of transactions thus induce bipartite transaction graphs, whose distribution is in turn induced by the ring sampler underlying the cryptocurrency. Since efficient graph analysis could be performed on transaction graphs to potentially deanonymise signers, it is crucial to understand the resistance of (the transaction graphs induced by) a ring sampler against graph analysis. Of particular interest is the class of partitioning ring samplers. Although previous works showed that they provide almost optimal local anonymity, their resistance against global, e.g. graph-based, attacks were unclear. In this work, we analyse transaction graphs induced by partitioning ring samplers. Specifically, we show (partly analytically and partly empirically) that, somewhat surprisingly, by setting the ring size to be at least logarithmic in the number of users, a graph-analysing adversary is no better than the one that performs random guessing in deanonymisation up to constant factor of 2.

cs.CR↗

arXiv2022

Multichannel Optimal Tree-Decodable Codes are Not Always Optimal Prefix Codes

The theory of multichannel prefix codes aims to generalize the classical theory of prefix codes. Although single- and two-channel prefix codes always have decoding trees, the same cannot be said when there are more than two channels. One question is of theoretical interest: Do there exist optimal tree-decodable codes that are not optimal prefix codes? Existing literature, which focused on generalizing single-channel results, covered little about non-tree-decodable prefix codes since they have no single-channel counterparts. In this work, we study the fundamental reason behind the non-tree-decodability of prefix codes. By investigating the simplest non-tree-decodable structure, we obtain a general sufficient condition on the channel alphabets for the existence of optimal tree-decodable codes that are not optimal prefix codes.

cs.IT↗

arXiv2021

On Multi-Channel Huffman Codes for Asymmetric-Alphabet Channels

Zero-error single-channel source coding has been studied extensively over the past decades. Its natural multi-channel generalization is however not well investigated. While the special case with multiple symmetric-alphabet channels was studied a decade ago, codes in such setting have no advantage over single-channel codes in data compression, making them worthless in most applications. With essentially no development since the last decade, in this paper, we break the stalemate by showing that it is possible to beat single-channel source codes in terms of compression assuming asymmetric-alphabet channels. We present the multi-channel analog of several classical results in single-channel source coding, such as that a multi-channel Huffman code is an optimal tree-decodable code. We also show some evidences that finding an efficient construction of multi-channel Huffman codes may be hard. Nevertheless, we propose a suboptimal code construction whose redundancy is guaranteed to be no larger than that of an optimal single-channel source code.

cs.IT↗

arXiv2019

Decision Procedure for the Existence of Two-Channel Prefix-Free Codes

The Kraft inequality gives a necessary and sufficient condition for the existence of a single channel prefix-free code. However, the multichannel Kraft inequality does not imply the existence of a multichannel prefix-free code in general. It is natural to ask whatever there exists an efficient decision procedure for the existence of multichannel prefix-free codes. In this paper, we tackle the two-channel case of the above problem by relating it to a constrained rectangle packing problem. Although a general rectangle packing problem is NP-complete, the extra imposed constraints allow us to propose an algorithm which can solve the problem efficiently.

cs.IT↗