Codes, Designs, Cryptography and Optimization, 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 31 May 2025 | Viewed by 573

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Department of Applied Mathematics I, University of Seville, 41012 Sevilla, Spain
Interests: discrete mathematics; graph theory; combinatorics; computational geometry; Latin squares
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Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to publish original research articles covering recent advances in any of the areas included in coding theory, cryptography, combinatorial design, and combinatorial optimization, with particular emphasis on establishing new synergies among them and new applications to other fields and to the real world, including algebraic geometry, artificial intelligence, communication networks, computer science, hardware and software design, design of experiments, logistics, machine learning, and scheduling or transportation networks, among others.

Potential topics of this Special Issue include, but are not limited to, the following:

  • Algebraic coding theory;
  • Algorithm design and analysis;
  • Block design theory;
  • Computational complexity;
  • Discrete structures: enumeration and classification;
  • Error-correcting and error-detecting codes;
  • Finite geometry;
  • Graph theory;
  • Modeling combinatorial optimization problems;
  • Network design and analysis;
  • Orthogonal arrays;
  • Pseudorandom sequences;
  • Quantum cryptography;
  • Quasigroup theory;
  • Secret sharing schemes.

Dr. Raúl M. Falcón
Guest Editor

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Keywords

  • association schemes
  • block design
  • cryptosystems
  • difference sets
  • Hadamard matrices
  • Latin squares
  • lattices
  • matroids
  • networks
  • orthogonal arrays

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Published Papers (1 paper)

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Research

41 pages, 477 KiB  
Article
Linear-Time Polynomial Holographic Interactive Oracle Proofs with Logarithmic-Time Verification for Rank-1 Constraint System from Lookup Protocol
by Shuangjun Zhang
Mathematics 2025, 13(8), 1309; https://doi.org/10.3390/math13081309 - 16 Apr 2025
Viewed by 230
Abstract
Modern SNARKs are constructed using polynomial Interactive Oracle Proofs (IOPs) and polynomial commitments. In this work, we introduce a novel polynomial holographic IOP for the NP-Complete language Rank-1 Constraint System (R1CS), where holographic IOP means that the proof system supports preprocessing. Our [...] Read more.
Modern SNARKs are constructed using polynomial Interactive Oracle Proofs (IOPs) and polynomial commitments. In this work, we introduce a novel polynomial holographic IOP for the NP-Complete language Rank-1 Constraint System (R1CS), where holographic IOP means that the proof system supports preprocessing. Our construction achieves linear-time proving, logarithmic-time verification, and constant query complexity. For an R1CS instance with size O(N) over a sufficiently large finite field, the prover’s time is O(N), the verifier’s time is O(log N), and the query complexity is O(1). By combining our polynomial holographic IOP with the recent polynomial commitment scheme Orion, we obtain a transparent SNARK for R1CS with remarkable performance: the prover’s time is O(N), the verifier’s time is O(log2N), and the proof size is O(log2N). The core technique in our construction is the classical SumCheck protocol, which enables us to efficiently check whether an n-variate polynomial sums to a specific value on a given domain, such as {0, 1}n. Additionally, we showcase how to achieve holography from the lookup protocol, which allows us to efficiently verify that all elements in a vector are contained in another vector. We introduce a new polynomial IOP for the lookup relation with a linear-time prover. Full article
(This article belongs to the Special Issue Codes, Designs, Cryptography and Optimization, 3rd Edition)
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