Cyclic Equalizability of Words and Its Application to Card-Based Cryptography

• URL: http://arxiv.org/abs/2507.04916v1
• Date: Mon, 07 Jul 2025 12:03:36 GMT
• Title: Cyclic Equalizability of Words and Its Application to Card-Based Cryptography
• Abstract summary: We show that two binary words of equal length and equal Hamming weight are cyclically equalizable.<n>As applications of cyclic equalizability to card-based cryptography, we describe its applications to the information erasure problem and to single-cut full-open protocols.
• Score: 0.36832029288386137
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Card-based cryptography is a research area to implement cryptographic procedures using a deck of physical cards. In recent years, it has been found to be related to finite group theory and algebraic combinatorics, and is becoming more and more closely connected to the field of mathematics. In this paper, we discuss the relationship between card-based cryptography and combinatorics on words for the first time. In particular, we focus on cyclic equality of words. We say that a set of words are cyclically equalizable if they can be transformed to be cyclically equal by repeated simultaneous insertion of letters. The main result of this paper is to show that two binary words of equal length and equal Hamming weight are cyclically equalizable. As applications of cyclic equalizability to card-based cryptography, we describe its applications to the information erasure problem and to single-cut full-open protocols.

Related papers

• Does Syntax Matter? A Graph-Augmented Variational Topic Model for Computational Social Sciences [51.56484100374058]
  This paper introduces the Structural Contextual Probabilistic Topic Model ( SCPTM), an architecture that incorporates syntactic dependency relations into topic inference.<n>We evaluate seven topic modeling techniques across four corpora differing in register and discourse structure.<n>Results show that SCPTM's neural architecture yields substantial gains in document-topic alignment over generative baselines.
  arXiv  Detail & Related papers  (2026-09-07T17:39:06Z)
• 0-Cyclic Equalizability of Binary Words Characterized by Hamming Weight [0.0]
  Two binary words of equal length are 0-cyclically equalizable if and only if they have equal Hamming weight.<n>We encode a pair of binary words as a single word over the four-letter alphabet A, B, X, O.
  arXiv  Detail & Related papers  (2026-07-20T19:02:48Z)
• Ternary public-key cryptosystem [3.0860863056832826]
  We generalize the public-key cryptosystems to ternary algebraic structures.<n>We derive explicit ternary power and querelement formulas that enable correct decryption.
  arXiv  Detail & Related papers  (2026-06-05T20:45:41Z)
• Cyclic Equalizability Characterized by Parikh Vectors [0.0]
  Cyclic equalizability is a notion introduced by Shinagawa and Nuida in 2025.<n>We prove that two words are cyclically equalizable if and only if they have the same Parikh vector.
  arXiv  Detail & Related papers  (2026-04-21T14:22:19Z)
• Cryptographic transformations over polyadic rings [3.0860863056832826]
  cryptosystems rely on binary operations within groups, rings, or fields.<n>We propose a shift to polyadic rings, which generalize classical rings by allowing operations of higher arity.<n>We present two concrete encryption procedures that leverage this structure.
  arXiv  Detail & Related papers  (2025-12-14T07:15:55Z)
• Equilibrium SAT based PQC: New aegis against quantum computing [0.0]
  This paper introduces a novel public-key cryptography algorithm that generates ciphertexts by counting the number of elements in randomly extracted subsets from a multiset.<n>The advantages of the proposed algorithm are: first, it is significantly faster than other public-key algorithms; second, it does not require big numbers, making it executable on any devices; and third, it can be easily extended into a public-key cryptosystem using a single public key and multiple private keys while maintaining quantum resistance.
  arXiv  Detail & Related papers  (2025-12-02T10:05:06Z)
• Nonlocal Games Through Communication Complexity and Quantum Cryptography [0.0]
  This thesis explores foundational aspects of quantum information theory and quantum cryptography.<n>We aim to distinguish quantum correlations from non-signaling correlations by leveraging the principle of communication complexity.<n>We aim to construct an encryption scheme that prevents two distant parties from simultaneously obtaining information about a shared message.
  arXiv  Detail & Related papers  (2025-10-10T15:07:24Z)
• Singularity Cipher: A Topology-Driven Cryptographic Scheme Based on Visual Paradox and Klein Bottle Illusions [0.0]
  The Singularity Cipher integrates topological transformations and visual paradoxes to achieve multidimensional security.<n>The resulting binary data is encoded using perceptual illusions, such as the missing square paradox, to visually obscure the presence of encrypted content.<n>The paper formalizes the architecture, provides encryption and decryption algorithms, evaluates security properties, and compares the method against classical, post-quantum, and steganographic approaches.
  arXiv  Detail & Related papers  (2025-07-02T04:44:52Z)
• Topological Dictionary Learning [13.291627429657416]
  We introduce a novel dictionary learning algorithm for sparse signals defined over topological spaces, specifically, regular cell complexes.<n>The learning problem is cast to jointly infer the underlying cell complex and optimize the sparse signal representation.<n> Numerical results on both synthetic and real data show the effectiveness of the proposed procedure.
  arXiv  Detail & Related papers  (2025-03-14T14:56:23Z)
• The Evolution of Cryptography through Number Theory [55.2480439325792]
  cryptography began around 100 years ago, its roots trace back to ancient civilizations like Mesopotamia and Egypt.<n>This paper explores the link between early information hiding techniques and modern cryptographic algorithms like RSA.
  arXiv  Detail & Related papers  (2024-11-11T16:27:57Z)
• Structured Analysis and Comparison of Alphabets in Historical Handwritten Ciphers [3.423211639513232]
  We propose the CSI metric, a novel way of comparing pairs of ciphered documents. We assess their effectiveness in an unsupervised clustering scenario utilising visual features, including SIFT, pre-trained learnt embeddings, and OCR descriptors.
  arXiv  Detail & Related papers  (2024-10-29T10:12:16Z)
• On the use of dynamical systems in cryptography [0.0]
  This paper provides a new algorithm that can be used to attack -- and hence test the security of -- stream ciphers based on the iteration of a chaotic map of the interval. The second is to cast discrete dynamical systems problems in a modern cryptographic and complexity theoretic language, so that researchers working in chaos-based cryptography can begin designing cryptographic protocols.
  arXiv  Detail & Related papers  (2024-05-05T19:59:49Z)
• CipherSniffer: Classifying Cipher Types [0.0]
  We frame the decryption task as a classification problem. We first create a dataset of transpositions, substitutions, text reversals, word reversals, sentence shifts, and unencrypted text.
  arXiv  Detail & Related papers  (2023-06-13T20:18:24Z)
• Linear-Time Modeling of Linguistic Structure: An Order-Theoretic Perspective [97.57162770792182]
  Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. We show that these exhaustive comparisons can be avoided, and, moreover, the complexity can be reduced to linear by casting the relation between tokens as a partial order over the string. Our method predicts real numbers for each token in a string in parallel and sorts the tokens accordingly, resulting in total orders of the tokens in the string.
  arXiv  Detail & Related papers  (2023-05-24T11:47:35Z)
• Boosting word frequencies in authorship attribution [0.0]
  I introduce a simple method of computing relative word frequencies for authorship attribution and similar stylometric tasks. The notion of relevant words includes synonyms and, usually, a few dozen other words in some ways semantically similar to a word in question. The proposed method outperforms classical most-frequent-word approaches substantially.
  arXiv  Detail & Related papers  (2022-11-02T17:11:35Z)
• FastKASSIM: A Fast Tree Kernel-Based Syntactic Similarity Metric [48.66580267438049]
  We present FastKASSIM, a metric for utterance- and document-level syntactic similarity. It pairs and averages the most similar dependency parse trees between a pair of documents based on tree kernels. It runs up to to 5.2 times faster than our baseline method over the documents in the r/ChangeMyView corpus.
  arXiv  Detail & Related papers  (2022-03-15T22:33:26Z)
• Deep Keyphrase Completion [59.0413813332449]
  Keyphrase provides accurate information of document content that is highly compact, concise, full of meanings, and widely used for discourse comprehension, organization, and text retrieval. We propose textitkeyphrase completion (KPC) to generate more keyphrases for document (e.g. scientific publication) taking advantage of document content along with a very limited number of known keyphrases. We name it textitdeep keyphrase completion (DKPC) since it attempts to capture the deep semantic meaning of the document content together with known keyphrases via a deep learning framework
  arXiv  Detail & Related papers  (2021-10-29T07:15:35Z)
• Keyphrase Extraction with Dynamic Graph Convolutional Networks and Diversified Inference [50.768682650658384]
  Keyphrase extraction (KE) aims to summarize a set of phrases that accurately express a concept or a topic covered in a given document. Recent Sequence-to-Sequence (Seq2Seq) based generative framework is widely used in KE task, and it has obtained competitive performance on various benchmarks. In this paper, we propose to adopt the Dynamic Graph Convolutional Networks (DGCN) to solve the above two problems simultaneously.
  arXiv  Detail & Related papers  (2020-10-24T08:11:23Z)
• Pairwise Learning for Name Disambiguation in Large-Scale Heterogeneous Academic Networks [81.00481125272098]
  We introduce Multi-view Attention-based Pairwise Recurrent Neural Network (MA-PairRNN) to solve the name disambiguation problem. MA-PairRNN combines heterogeneous graph embedding learning and pairwise similarity learning into a framework. Results on two real-world datasets demonstrate that our framework has a significant and consistent improvement of performance on the name disambiguation task.
  arXiv  Detail & Related papers  (2020-08-30T06:08:20Z)
• Exclusive Hierarchical Decoding for Deep Keyphrase Generation [63.357895318562214]
  Keyphrase generation (KG) aims to summarize the main ideas of a document into a set of keyphrases. Previous work in this setting employs a sequential decoding process to generate keyphrases. We propose an exclusive hierarchical decoding framework that includes a hierarchical decoding process and either a soft or a hard exclusion mechanism.
  arXiv  Detail & Related papers  (2020-04-18T02:58:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.