Designs, Codes and Cryptography最新文献_第8页

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

RYDE: a digital signature scheme based on rank syndrome decoding problem with MPC-in-the-Head paradigm RYDE：一个基于MPC-in-the-Head范式的秩证解码问题的数字签名方案

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-04 DOI: 10.1007/s10623-024-01544-1

Loïc Bidoux, Jesús-Javier Chi-Domínguez, Thibauld Feneuil, Philippe Gaborit, Antoine Joux, Matthieu Rivain, Adrien Vinçotte

{"title":"RYDE: a digital signature scheme based on rank syndrome decoding problem with MPC-in-the-Head paradigm","authors":"Loïc Bidoux, Jesús-Javier Chi-Domínguez, Thibauld Feneuil, Philippe Gaborit, Antoine Joux, Matthieu Rivain, Adrien Vinçotte","doi":"10.1007/s10623-024-01544-1","DOIUrl":"https://doi.org/10.1007/s10623-024-01544-1","url":null,"abstract":"We present a signature scheme based on the syndrome decoding (SD) problem in rank metric. It is a construction from Multi-Party Computation (MPC), using a MPC protocol which is a slight improvement of the linearized polynomial protocol used in Feneuil (Cryptology ePrint Archive, Report 2022/1512, 2022), allowing to obtain a zero-knowledge proof thanks to the MPCitH (MPC-in-the-Head) paradigm. We design two different zero-knowledge proofs exploiting this paradigm: the first, which reaches the lower communication costs, relies on additive secret sharing and uses the hypercube technique (Aguilar-Melchor et al., in: Cryptology ePrint Archive, Report 2022/1645, 2022); and the second relies on low-threshold linear secret sharing as proposed in Feneuil (Cryptology ePrint Archive, Report 2022/1512, 2022). These proofs of knowledge are transformed to signature schemes thanks to the Fiat–Shamir transform (Fiat and Shamir, in: International Cryptology Conference (CRYPTO), 1986) and the resulting schemes have signatures of size less than 6 kB. These performances prompted us to propose this signature scheme to the post-quantum cryptography standardization process organized by NIST.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"12 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142924654","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

Fully selective opening secure IBE from LWE 完全选择性打开安全IBE从LWE

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-03 DOI: 10.1007/s10623-024-01560-1

Dingding Jia, Haiyang Xue, Bao Li

引用次数: 0

Quantum sieving for code-based cryptanalysis and its limitations for ISD 基于码的密码分析的量子筛分及其在ISD中的局限性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-01-02 DOI: 10.1007/s10623-024-01545-0

Lynn Engelberts, Simona Etinski, Johanna Loyer

{"title":"Quantum sieving for code-based cryptanalysis and its limitations for ISD","authors":"Lynn Engelberts, Simona Etinski, Johanna Loyer","doi":"10.1007/s10623-024-01545-0","DOIUrl":"https://doi.org/10.1007/s10623-024-01545-0","url":null,"abstract":"Sieving using near-neighbor search techniques is a well-known method in lattice-based cryptanalysis, yielding the current best runtime for the shortest vector problem in both the classical and quantum setting. Recently, sieving has also become an important tool in code-based cryptanalysis. Specifically, a variant of the information-set decoding (ISD) framework, commonly used for attacking cryptographically relevant instances of the decoding problem, has been introduced that involves a sieving subroutine. The resulting sieving-based ISD framework yields complexities close to the best-performing classical algorithms for the decoding problem. It is therefore natural to ask how well quantum versions perform. In this work, we introduce the first quantum algorithms for code sieving by designing quantum variants of the aforementioned sieving subroutine. In particular, using quantum-walk techniques, we provide a speed-up over classical code sieving and over a variant using Grover’s algorithm. Our quantum-walk algorithm exploits the structure of the underlying search problem by adding a layer of locality sensitive filtering, inspired by a quantum-walk algorithm for lattice sieving. We complement our asymptotic analysis of the quantum algorithms with numerical results, and observe that our quantum speed-ups for code sieving behave similarly as those observed in lattice sieving. In addition, we show that a natural quantum analog of the sieving-based ISD framework does not provide any speed-up over the first quantum ISD algorithm. Our analysis highlights that the framework should be adapted in order to outperform state-of-the-art quantum ISD algorithms.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"20 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142916896","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

Divisible design graphs from the symplectic graph 辛图的可分设计图

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-29 DOI: 10.1007/s10623-024-01557-w

Bart De Bruyn, Sergey Goryainov, Willem H. Haemers, Leonid Shalaginov

{"title":"Divisible design graphs from the symplectic graph","authors":"Bart De Bruyn, Sergey Goryainov, Willem H. Haemers, Leonid Shalaginov","doi":"10.1007/s10623-024-01557-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01557-w","url":null,"abstract":"A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a (group) divisible design. Divisible design graphs were introduced in 2011 as a generalization of ((v,k,lambda ))-graphs. Here we describe four new infinite families that can be obtained from the symplectic strongly regular graph Sp(2e, q) (q odd, (ege 2)) by modifying the set of edges. To achieve this we need two kinds of spreads in (PG(2e-1,q)) with respect to the associated symplectic form: the symplectic spread consisting of totally isotropic subspaces and, when (e=2), a special spread that consists of lines which are not totally isotropic and which is closed under the action of the associated symplectic polarity. Existence of symplectic spreads is known, but the construction of a special spread for every odd prime power q is a main result of this paper. We also show an equivalence between special spreads of Sp(4, q) and certain nice point sets in the projective space (operatorname {PG}(4,q)). We have included relevant background from finite geometry, and when (q=3,5) and 7 we worked out all possible special spreads.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"25 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887802","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

The set of pure gaps at several rational places in function fields 函数域中若干有理位上的纯间隙集

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-28 DOI: 10.1007/s10623-024-01556-x

Alonso S. Castellanos, Erik A. R. Mendoza, Guilherme Tizziotti

引用次数: 0

The weight hierarchies of three classes of linear codes 三类线性码的权重层次

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-27 DOI: 10.1007/s10623-024-01553-0

Wei Lu, Qingyao Wang, Xiaoqiang Wang, Dabin Zheng

引用次数: 0

Fault attacks on multi-prime RSA signatures 针对RSA多素数签名的故障攻击

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-27 DOI: 10.1007/s10623-024-01554-z

Chunzhi Zhao, Jinzheng Cao, Junqi Zhang, Qingfeng Cheng

引用次数: 0

Several families of negacyclic BCH codes and their duals 几个负环BCH码族及其对偶

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-27 DOI: 10.1007/s10623-024-01551-2

Zhonghua Sun, Xinyue Liu

引用次数: 0