Designs, Codes and Cryptography最新文献_第6页

Polynomial reduction from syndrome decoding problem to regular decoding problem

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-28 DOI: 10.1007/s10623-025-01567-2

Pavol Zajac

{"title":"Polynomial reduction from syndrome decoding problem to regular decoding problem","authors":"Pavol Zajac","doi":"10.1007/s10623-025-01567-2","DOIUrl":"https://doi.org/10.1007/s10623-025-01567-2","url":null,"abstract":"The regular decoding problem asks for (the existence of) regular solutions to a syndrome decoding problem (SDP). This problem has increased applications in post-quantum cryptography and cryptanalysis. Recently, Esser and Santini explored in depth the connection between the regular (RSD) and classical syndrome decoding problems. They have observed that while RSD to SDP reductions are known (in any parametric regime), a similar generic reduction from SDP to RSD is not known. In our contribution, we examine two different generic polynomial reductions from a syndrome decoding problem to a regular decoding problem instance. The first reduction is based on constructing a special parity check matrix that encodes weight counter progression inside the parity check matrix, which is then the input of the regular decoding oracle. The target regular decoding problem has a significantly longer code length, that depends linearly on the weight parameter of the original SDP. The second reduction is based on translating the SDP to a non-linear system of equations in the Multiple Right-Hand Sides form, and then applying RSD oracle to solve this system. The second reduction has better code length. The ratio between RSD and SDP code length of the second reduction can be bounded by a constant (less than 8).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"114 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143049911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Symmetric (15, 8, 4)-designs in terms of the geometry of binary simplex codes of dimension 4

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-24 DOI: 10.1007/s10623-025-01570-7

Mark Pankov, Krzysztof Petelczyc, Mariusz Żynel

引用次数: 0

Blocking sets of secant and tangent lines with respect to a quadric of $$text{ PG }(n,q)$$ 关于二次函数的正割线和切线的块集 $$text{ PG }(n,q)$$

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-17 DOI: 10.1007/s10623-024-01559-8

Bart De Bruyn, Puspendu Pradhan, Binod Kumar Sahoo

引用次数: 0

Efficient information-theoretic distributed point functions with general output groups 具有一般输出群的高效信息论分布点函数

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-16 DOI: 10.1007/s10623-024-01562-z

Junru Li, Pengzhen Ke, Liang Feng Zhang

{"title":"Efficient information-theoretic distributed point functions with general output groups","authors":"Junru Li, Pengzhen Ke, Liang Feng Zhang","doi":"10.1007/s10623-024-01562-z","DOIUrl":"https://doi.org/10.1007/s10623-024-01562-z","url":null,"abstract":"An n-server information-theoretic Distributed Point Function (DPF) allows a client to secret-share a point function (f_{alpha ,beta }(x)) with domain [N] and output group (mathbb {G}) among n servers such that each server learns no information about the function from its share (called a key) but can compute an additive share of (f_{alpha ,beta }(x)) for any x. DPFs with small key sizes and general output groups are preferred. In this paper, we propose a new transformation from share conversions to information-theoretic DPFs. By applying it to the share conversions from Efremenko’s PIR and Dvir–Gopi PIR, we obtain both an 8-server DPF with key size ( O(2^{10sqrt{log Nlog log N}}+log p)) and output group (mathbb {Z}_p) and a 4-server DPF with key size (O(tau cdot 2^{6sqrt{log Nlog log N}})) and output group (mathbb {Z}_{2^tau }). The former allows us to partially answer an open question by Boyle, Gilboa, Ishai, and Kolobov (ITC 2022) and the latter allows us to build the first DPFs that may take any finite Abelian groups as output groups. We also discuss how to further reduce the key sizes by using different PIRs, how to reduce the number of servers by resorting to statistical security or using nice integers, and how to obtain DPFs with t-security. We show the applications of the new DPFs by constructing new efficient PIR protocols with result verification.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"29 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142987796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rate-improved multi-permutation codes for correcting a single burst of stable deletions 用于校正单个稳定缺失的速率改进的多排列码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-16 DOI: 10.1007/s10623-025-01564-5

Xiang Wang, Fang-Wei Fu

引用次数: 0

Additive twisted codes: new distance bounds and infinite families of quantum codes 加性扭曲码：新的距离边界和量子码的无限族

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-16 DOI: 10.1007/s10623-024-01552-1

Reza Dastbasteh, Petr Lisoněk

引用次数: 0

On LCD skew group codes 液晶显示器上的偏斜组代码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-13 DOI: 10.1007/s10623-024-01561-0

Mohammed El Badry, Abdelfattah Haily, Ayoub Mounir

引用次数: 0

Designer of codes: a tribute to Jennifer Key 代码设计师：向Jennifer Key致敬

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-12 DOI: 10.1007/s10623-024-01517-4

Vassili C. Mavron, Harold N. Ward

引用次数: 0

Somewhat homomorphic encryption based on random codes 基于随机码的某种同态加密

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-06 DOI: 10.1007/s10623-024-01555-y

Carlos Aguilar-Melchor, Victor Dyseryn, Philippe Gaborit

{"title":"Somewhat homomorphic encryption based on random codes","authors":"Carlos Aguilar-Melchor, Victor Dyseryn, Philippe Gaborit","doi":"10.1007/s10623-024-01555-y","DOIUrl":"https://doi.org/10.1007/s10623-024-01555-y","url":null,"abstract":"We present a secret-key encryption scheme based on random rank metric ideal linear codes with a simple decryption circuit. It supports unlimited homomorphic additions and plaintext multiplications (i.e. the homomorphic multiplication of a clear plaintext with a ciphertext) as well as a fixed arbitrary number of homomorphic multiplications. We study a candidate bootstrapping algorithm that requires no multiplication but additions and plaintext multiplications only. This latter operation is therefore very efficient in our scheme, whereas bootstrapping is usually the main reason which penalizes the performance of other fully homomorphic encryption schemes. However, the security reduction of our scheme restricts the number of independent ciphertexts that can be published. In particular, this prevents to securely evaluate the bootstrapping algorithm as the number of ciphertexts in the key switching material is too large. Our scheme is nonetheless the first somewhat homomorphic encryption scheme based on random ideal codes and a first step towards full homomorphism. Random ideal codes give stronger security guarantees as opposed to existing constructions based on highly structured codes. We give concrete parameters for our scheme that shows that it achieves competitive sizes and performance, with a key size of 3.7 kB and a ciphertext size of 0.9 kB when a single multiplication is allowed.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"28 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142934919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Ternary isodual codes and 3-designs 三进制单码和3-设计

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-06 DOI: 10.1007/s10623-024-01558-9

Minjia Shi, Ruowen Liu, Dean Crnković, Patrick Solé, Andrea Švob

引用次数: 0