Designs, Codes and Cryptography最新文献

Weak colourings of Kirkman triple systems 柯克曼三元系的弱着色

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-01 DOI: 10.1007/s10623-025-01635-7

Andrea C. Burgess, Nicholas J. Cavenagh, Peter Danziger, David A. Pike

{"title":"Weak colourings of Kirkman triple systems","authors":"Andrea C. Burgess, Nicholas J. Cavenagh, Peter Danziger, David A. Pike","doi":"10.1007/s10623-025-01635-7","DOIUrl":"https://doi.org/10.1007/s10623-025-01635-7","url":null,"abstract":"A (delta )-colouring of the point set of a block design is said to be weak if no block is monochromatic. The chromatic number (chi (S)) of a block design S is the smallest integer (delta ) such that S has a weak (delta )-colouring. It has previously been shown that any Steiner triple system has chromatic number at least 3 and that for each (vequiv 1) or (3pmod {6}) there exists a Steiner triple system on v points that has chromatic number 3. Moreover, for each integer (delta geqslant 3) there exist infinitely many Steiner triple systems with chromatic number (delta ). We consider colourings of the subclass of Steiner triple systems which are resolvable. A Kirkman triple system consists of a resolvable Steiner triple system together with a partition of its blocks into parallel classes. We show that for each (vequiv 3pmod {6}) there exists a Kirkman triple system on v points with chromatic number 3. We also show that for each integer (delta geqslant 3), there exist infinitely many Kirkman triple systems with chromatic number (delta ). We close with several open problems.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"26 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143893852","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

Lattice codes for CRYSTALS-Kyber 晶格代码为CRYSTALS-Kyber

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-05-01 DOI: 10.1007/s10623-025-01640-w

Shuiyin Liu, Amin Sakzad

{"title":"Lattice codes for CRYSTALS-Kyber","authors":"Shuiyin Liu, Amin Sakzad","doi":"10.1007/s10623-025-01640-w","DOIUrl":"https://doi.org/10.1007/s10623-025-01640-w","url":null,"abstract":"This paper describes a constant-time lattice encoder for the National Institute of Standards and Technology (NIST) recommended post-quantum encryption algorithm: Kyber. The first main contribution of this paper is to refine the analysis of Kyber decoding noise and prove that Kyber decoding noise can be bounded by a sphere. This result shows that the Kyber encoding problem is essentially a sphere packing in a hypercube. The original Kyber encoder uses the integer lattice for sphere packing purposes, which is far from optimal. Our second main contribution is to construct optimal lattice codes to ensure denser packing and a lower decryption failure rate (DFR). Given the same ciphertext size as the original Kyber, the proposed lattice encoder enjoys a larger decoding radius, and is able to encode much more information bits. This way we achieve a decrease of the communication cost by up to (32.6%), and a reduction of the DFR by a factor of up to (2^{85}). Given the same plaintext size as the original Kyber, e.g., 256 bits, we propose a bit-interleaved coded modulation (BICM) approach, which combines a BCH code and the proposed lattice encoder. The proposed BICM scheme significantly reduces the DFR of Kyber, thus enabling further compression of the ciphertext. Compared with the original Kyber encoder, the communication cost is reduced by (24.49%), while the DFR is decreased by a factor of (2^{39}). The proposed encoding scheme is a constant-time algorithm, thus resistant against the timing side-channel attacks.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"114 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143893779","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

Rational transformations over finite fields that are never irreducible 有限域上从不不可约的有理变换

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-24 DOI: 10.1007/s10623-025-01591-2

Max Schulz

引用次数: 0

Permutations minimizing the number of collinear triples 排列最小化共线三元组的数量

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-23 DOI: 10.1007/s10623-025-01632-w

Joshua Cooper, Jack Hyatt

引用次数: 0

Coding properties and automorphism groups of two classes of twisted generalized Reed–Solomon codes 两类扭曲广义里德-所罗门码的编码特性和自形群

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-19 DOI: 10.1007/s10623-025-01630-y

Xue Jia, Qin Yue, Huan Sun

引用次数: 0

Understanding the new distinguisher of alternant codes at degree 2 了解 2 级交替编码的新区分度

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-19 DOI: 10.1007/s10623-025-01626-8

Axel Lemoine, Rocco Mora, Jean-Pierre Tillich

{"title":"Understanding the new distinguisher of alternant codes at degree 2","authors":"Axel Lemoine, Rocco Mora, Jean-Pierre Tillich","doi":"10.1007/s10623-025-01626-8","DOIUrl":"https://doi.org/10.1007/s10623-025-01626-8","url":null,"abstract":"Distinguishing Goppa codes or alternant codes from generic linear codes (Faugère et al. in Proceedings of the IEEE Information Theory Workshop—ITW 2011, Paraty, Brasil, October 2011, pp. 282–286, 2011) has been shown to be a first step before being able to attack McEliece cryptosystem based on those codes (Bardet et al. in IEEE Trans Inf Theory 70(6):4492–4511, 2024). Whereas the distinguisher of Faugère et al. (2011) is only able to distinguish Goppa codes or alternant codes of rate very close to 1, in Couvreur et al. (in: Guo and Steinfeld (eds) Advances in Cryptology—ASIACRYPT 2023—29th International Conference on the Theory and Application of Cryptology and Information Security, Guangzhou, China, December 4–8, 2023, Proceedings, Part IV, Volume 14441 of LNCS, pp. 3–38, Springer, 2023) a much more powerful (and more general) distinguisher was proposed. It is based on computing the Hilbert series ({{{,textrm{HF},}}(d),;d in mathbb {N}}) of a Pfaffian modeling. The distinguisher of Faugère et al. (2011) can be interpreted as computing ({{,textrm{HF},}}(1)). Computing ({{,textrm{HF},}}(2)) still gives a polynomial time distinguisher for alternant or Goppa codes and is apparently able to distinguish Goppa or alternant codes in a much broader regime of rates as the one of Faugère et al. (2011). However, the scope of this distinguisher was unclear. We give here a formula for ({{,textrm{HF},}}(2)) corresponding to generic alternant codes when the field size q satisfies (q geqslant r), where r is the degree of the alternant code. We also show that this expression for ({{,textrm{HF},}}(2)) provides a lower bound in general. The value of ({{,textrm{HF},}}(2)) corresponding to random linear codes is known and this yields a precise description of the new regime of rates that can be distinguished by this new method. This shows that the new distinguisher improves significantly upon the one given in Faugère et al. (2011).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"17 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143849751","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

New upper bounds for wide-sense frameproof codes 宽义防帧码的新上界

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-18 DOI: 10.1007/s10623-025-01631-x

Chengyu Sun, Xin Wang

引用次数: 0

Knot theory and error-correcting codes 结理论与纠错码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-18 DOI: 10.1007/s10623-025-01615-x

Altan B. Kılıç, Anne Nijsten, Ruud Pellikaan, Alberto Ravagnani

引用次数: 0

Utilizing two subfields to accelerate individual logarithm computation in extended tower number field sieve 利用两个子域加速扩展塔数场筛中单个对数的计算

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-10 DOI: 10.1007/s10623-025-01590-3

Yuqing Zhu, Chang Lv, Jiqiang Liu

{"title":"Utilizing two subfields to accelerate individual logarithm computation in extended tower number field sieve","authors":"Yuqing Zhu, Chang Lv, Jiqiang Liu","doi":"10.1007/s10623-025-01590-3","DOIUrl":"https://doi.org/10.1007/s10623-025-01590-3","url":null,"abstract":"The hardness of discrete logarithm problem (DLP) over finite fields forms the security foundation of many cryptographic schemes. When the characteristic is not small, the state-of-the-art algorithms for solving the DLP are the number field sieve (NFS) and its variants. NFS first computes the logarithms of the factor base, which consists of elements of small norms. Then, for a target element, its logarithm is calculated by establishing a relation with the factor base. Although computing the factor-base elements is the most time-consuming part of NFS, it can be performed only once and treated as pre-computation for a fixed finite field when multiple logarithms need to be computed. In this paper, we present a method for accelerating individual logarithm computation by utilizing two subfields. We focus on the case where the extension degree of the finite field is a multiple of 6 within the extended tower number field sieve framework. Our method allows for the construction of an element with a lower degree, while maintaining the same coefficient bound compared to Guillevic’s method, which uses only one subfield. Consequently, the element derived from our approach enjoys a smaller norm, which will improve the efficiency in individual logarithm computation.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"26 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143819557","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 geometry of covering codes in the sum–rank metric 和秩度量中覆盖码的几何形状

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2025-04-09 DOI: 10.1007/s10623-025-01628-6

Matteo Bonini, Martino Borello, Eimear Byrne

引用次数: 0