Finite Fields and Their Applications最新文献_第3页

On hyperelliptic Jacobians with complex multiplication by Q(−2+2) 关于 Q(-2+2) 复乘法的超椭圆雅各比

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-10-07 DOI: 10.1016/j.ffa.2024.102512

Tomasz Jędrzejak

引用次数: 0

Erasure list-decodable codes and Turán hypercube problems 可擦除列表解码和图兰超立方问题

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-10-02 DOI: 10.1016/j.ffa.2024.102513

Noga Alon

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Linear codes with few weights over finite fields 有限域上权重较少的线性编码

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-09-27 DOI: 10.1016/j.ffa.2024.102509

Yan Wang , Jiayi Fan , Nian Li , Fangyuan Liu

引用次数: 0

The explicit values of the UBCT, the LBCT and the DBCT of the inverse function 反函数的 UBCT、LBCT 和 DBCT 的显式值

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-09-17 DOI: 10.1016/j.ffa.2024.102508

Yuying Man , Nian Li , Zhen Liu , Xiangyong Zeng

{"title":"The explicit values of the UBCT, the LBCT and the DBCT of the inverse function","authors":"Yuying Man , Nian Li , Zhen Liu , Xiangyong Zeng","doi":"10.1016/j.ffa.2024.102508","DOIUrl":"10.1016/j.ffa.2024.102508","url":null,"abstract":"<div>Substitution boxes (S-boxes) play a significant role in ensuring the resistance of block ciphers against various attacks. The Upper Boomerang Connectivity Table (UBCT), the Lower Boomerang Connectivity Table (LBCT) and the Double Boomerang Connectivity Table (DBCT) of a given S-box are crucial tools to analyze its security concerning specific attacks. However, there are currently no research results on determining these tables of a function. The inverse function is crucial for constructing S-boxes of block ciphers with good cryptographic properties in symmetric cryptography. Therefore, extensive research has been conducted on the inverse function, exploring various properties related to standard attacks. Thanks to the recent advances in boomerang cryptanalysis, particularly the introduction of concepts such as UBCT, LBCT, and DBCT, this paper aims to further investigate the properties of the inverse function <math><mi>F</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup><mo>−</mo><mn>2</mn></mrow></msup></math> over <math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></mrow></msub></math> for arbitrary n. As a consequence, by carrying out certain finer manipulations of solving specific equations over <math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></mrow></msub></math>, we give all entries of the UBCT, LBCT of <math><mi>F</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> over <math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></mrow></msub></math> for arbitrary n. Besides, based on the results of the UBCT and LBCT for the inverse function, we determine that <math><mi>F</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> is hard when n is odd. Furthermore, we completely compute all entries of the DBCT of <math><mi>F</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> over <math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></mrow></msub></math> for arbitrary n. Additionally, we provide the precise number of elements with a given entry by means of the values of some Kloosterman sums. Further, we determine the double boomerang uniformity of <math><mi>F</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> over <math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi></mrow></msup></mrow></msub></math> for arbitrary n. Our in-depth analysis of the DBCT of <math><mi>F</mi><mo>(</mo><mi>x</mi><mo>)</mo></math> contributes to a better evaluation of the S-box's resistance against boomerang attacks.</div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Oriented supersingular elliptic curves and Eichler orders of prime level 有向超星椭圆曲线和素级艾希勒阶

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-09-17 DOI: 10.1016/j.ffa.2024.102501

Guanju Xiao , Zijian Zhou , Longjiang Qu

引用次数: 0

On the duality of cyclic codes of length ps over Fpm[u]〈u3〉论Fpm[u]〈u3〉上长度为ps的循环码的对偶性

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-09-04 DOI: 10.1016/j.ffa.2024.102500

Ahmad Erfanian , Roghaye Mohammadi Hesari

引用次数: 0

Denniston partial difference sets exist in the odd prime case 奇素数情况下存在丹尼斯顿偏差集

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-09-03 DOI: 10.1016/j.ffa.2024.102499

James A. Davis , Sophie Huczynska , Laura Johnson , John Polhill

引用次数: 0

The resultant method in higher dimensions 高维度结果法

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-30 DOI: 10.1016/j.ffa.2024.102493

N. Harrach , L. Storme , P. Sziklai , M. Takáts

引用次数: 0

A note on (2,2)-isogenies via theta coordinates 通过 Theta 坐标的 (2,2)-isogenies 注释

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-30 DOI: 10.1016/j.ffa.2024.102496

Jianming Lin , Saiyu Wang , Chang-An Zhao

{"title":"A note on (2,2)-isogenies via theta coordinates","authors":"Jianming Lin , Saiyu Wang , Chang-An Zhao","doi":"10.1016/j.ffa.2024.102496","DOIUrl":"10.1016/j.ffa.2024.102496","url":null,"abstract":"<div>In this paper, we revisit the algorithm for computing chains of <math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>-isogenies between products of elliptic curves via theta coordinates proposed by Dartois et al. For each fundamental block of this algorithm, we provide an explicit inversion-free version. Besides, we exploit the technique of x-only ladder to speed up the computation of gluing isogeny. Finally, we present a mixed optimal strategy, which combines the inversion-elimination tool with the original methods together to execute a chain of <math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>-isogenies.We make a cost analysis and present a concrete comparison between ours and the previously known methods for inversion elimination. Furthermore, we implement the mixed optimal strategy for benchmark. The results show that when computing <math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>-isogeny chains with lengths of 126, 208 and 632, compared to Dartois, Maino, Pope and Robert's latest implementation, utilizing our techniques can reduce 9.7%, 9.5% and 9.6% multiplications over the base field <math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math>, respectively. Therefore, even for the updated version that employs their inversion-free algorithms, our tools still possess an advantage.</div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Achromatic colorings of polarity graphs 极性图的消色性着色

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-08-30 DOI: 10.1016/j.ffa.2024.102497

Vladislav Taranchuk , Craig Timmons

引用次数: 0