Journal of Mathematical Cryptology最新文献_第2页

DLP in semigroups: Algorithms and lower bounds 半群中的DLP：算法和下界

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2022-01-01 DOI: 10.1515/jmc-2021-0049

Jiao Han, Jincheng Zhuang

引用次数: 1

The mF mode of authenticated encryption with associated data 使用关联数据进行身份验证加密的mF模式

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2022-01-01 DOI: 10.1515/jmc-2020-0054

Bishwajit Chakraborty, M. Nandi

{"title":"The mF mode of authenticated encryption with associated data","authors":"Bishwajit Chakraborty, M. Nandi","doi":"10.1515/jmc-2020-0054","DOIUrl":"https://doi.org/10.1515/jmc-2020-0054","url":null,"abstract":"Abstract In recent years, the demand for lightweight cryptographic protocols has grown immensely. To fulfill this necessity, the National Institute of Standards and Technology (NIST) has initiated a standardization process for lightweight cryptographic encryption. NIST’s call for proposal demands that the scheme should have one primary member that has a key length of 128 bits, and it should be secure up to 2 50 − 1 {2}^{50}-1 byte queries and 2 112 {2}^{112} computations. In this article, we propose a tweakable block cipher (TBC)-based authenticated encryption with associated data (AEAD) scheme, which we call mF {mathsf{mF}} . We provide authenticated encryption security analysis for mF {mathsf{mF}} under some weaker security assumptions (stated in the article) on the underlying TBC. We instantiate a TBC using block cipher and show that the TBC achieves these weaker securities, provided the key update function has high periodicity. mixFeed {mathsf{mixFeed}} is a round 2 candidate in the aforementioned lightweight cryptographic standardization competition. When we replace the key update function with the key scheduling function of Advanced Encryption Standard (AES), the mF {mathsf{mF}} mode reduces to mixFeed {mathsf{mixFeed}} . Recently, the low periodicity of AES key schedule is shown. Exploiting this feature, a practical attack on mixFeed {mathsf{mixFeed}} is reported. We have shown that multiplication by primitive element satisfies the high periodicity property, and we have a secure instantiation of mF {mathsf{mF}} , a secure variant of mixFeed {mathsf{mixFeed}} .","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"16 1","pages":"73 - 97"},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48034522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Pseudo-free families and cryptographic primitives 伪自由族和密码原语

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2022-01-01 DOI: 10.1515/jmc-2020-0055

M. Anokhin

{"title":"Pseudo-free families and cryptographic primitives","authors":"M. Anokhin","doi":"10.1515/jmc-2020-0055","DOIUrl":"https://doi.org/10.1515/jmc-2020-0055","url":null,"abstract":"Abstract In this article, we study the connections between pseudo-free families of computational Ω Omega -algebras (in appropriate varieties of Ω Omega -algebras for suitable finite sets Ω Omega of finitary operation symbols) and certain standard cryptographic primitives. We restrict ourselves to families ( H d ∣ d ∈ D ) left({H}_{d}hspace{0.33em}| hspace{0.33em}din D) of computational Ω Omega -algebras (where D ⊆ { 0 , 1 } ∗ Dsubseteq {left{0,1right}}^{ast } ) such that for every d ∈ D din D , each element of H d {H}_{d} is represented by a unique bit string of the length polynomial in the length of d d . Very loosely speaking, our main results are as follows: (i) pseudo-free families of computational mono-unary algebras with one to one fundamental operation (in the variety of all mono-unary algebras) exist if and only if one-way families of permutations exist; (ii) for any m ≥ 2 mge 2 , pseudo-free families of computational m m -unary algebras with one to one fundamental operations (in the variety of all m m -unary algebras) exist if and only if claw resistant families of m m -tuples of permutations exist; (iii) for a certain Ω Omega and a certain variety V {mathfrak{V}} of Ω Omega -algebras, the existence of pseudo-free families of computational Ω Omega -algebras in V {mathfrak{V}} implies the existence of families of trapdoor permutations.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"16 1","pages":"114 - 140"},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44040424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Integer polynomial recovery from outputs and its application to cryptanalysis of a protocol for secure sorting 从输出中恢复整数多项式及其在安全排序协议密码分析中的应用

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2022-01-01 DOI: 10.1515/jmc-2021-0054

S. Vivek, Shyam Murthy, D. Kumaraswamy

{"title":"Integer polynomial recovery from outputs and its application to cryptanalysis of a protocol for secure sorting","authors":"S. Vivek, Shyam Murthy, D. Kumaraswamy","doi":"10.1515/jmc-2021-0054","DOIUrl":"https://doi.org/10.1515/jmc-2021-0054","url":null,"abstract":"Abstract We investigate the problem of recovering integer inputs (up to an affine scaling) when given only the integer monotonic polynomial outputs. Given n n integer outputs of a degree- d d integer monotonic polynomial whose coefficients and inputs are integers within known bounds and n ≫ d ngg d , we give an algorithm to recover the polynomial and the integer inputs (up to an affine scaling). A heuristic expected time complexity analysis of our method shows that it is exponential in the size of the degree of the polynomial but polynomial in the size of the polynomial coefficients. We conduct experiments with real-world data as well as randomly chosen parameters and demonstrate the effectiveness of our algorithm over a wide range of parameters. Using only the polynomial evaluations at specific integer points, the apparent hardness of recovering the input data served as the basis of security of a recent protocol proposed by Kesarwani et al. for secure k k -nearest neighbor computation on encrypted data that involved secure sorting. The protocol uses the outputs of randomly chosen monotonic integer polynomial to hide its inputs except to only reveal the ordering of input data. By using our integer polynomial recovery algorithm, we show that we can recover the polynomial and the inputs within a few seconds, thereby demonstrating an attack on the protocol of Kesarwani et al.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"16 1","pages":"251 - 277"},"PeriodicalIF":1.2,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44952054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Application of automorphic forms to lattice problems 自同构形式在格问题中的应用

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2022-01-01 DOI: 10.1515/jmc-2021-0045

Samed Düzlü, Julian Krämer

引用次数: 0

A Ring-LWE-based digital signature inspired by Lindner–Peikert scheme 受Lindner–Peikert方案启发的基于Ring LWE的数字签名

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2022-01-01 DOI: 10.1515/jmc-2021-0013

J. Sharafi, H. Daghigh

引用次数: 1

A code-based hybrid signcryption scheme 基于代码的混合签名加密方案

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2021-12-14 DOI: 10.36227/techrxiv.17283899.v1

Jean Belo Klamti, M. Hasan

{"title":"A code-based hybrid signcryption scheme","authors":"Jean Belo Klamti, M. Hasan","doi":"10.36227/techrxiv.17283899.v1","DOIUrl":"https://doi.org/10.36227/techrxiv.17283899.v1","url":null,"abstract":"Abstract A key encapsulation mechanism ( KEM {mathsf{KEM}} ) that takes as input an arbitrary string, i.e., a tag, is known as tag- KEM {mathsf{KEM}} , while a scheme that combines signature and encryption is called signcryption. In this article, we present a code-based signcryption tag- KEM {mathsf{KEM}} scheme. We utilize a code-based signature and an IND - CCA2 {mathsf{IND}}hspace{0.1em}text{-}hspace{0.1em}{mathsf{CCA2}} (adaptive chosen ciphertext attack) secure version of McEliece’s encryption scheme. The proposed scheme uses an equivalent subcode as a public code for the receiver, making the NP-completeness of the subcode equivalence problem be one of our main security assumptions. We then base the signcryption tag- KEM {mathsf{KEM}} to design a code-based hybrid signcryption scheme. A hybrid scheme deploys asymmetric- as well as symmetric-key encryption. We give security analyses of both our schemes in the standard model and prove that they are secure against IND - CCA2 {mathsf{IND}}hspace{0.1em}text{-}hspace{0.1em}{mathsf{CCA2}} (indistinguishability under adaptive chosen ciphertext attack) and SUF - CMA {mathsf{SUF}}hspace{0.1em}text{-}hspace{0.1em}{mathsf{CMA}} (strong existential unforgeability under chosen message attack).","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"17 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2021-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43908328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the efficiency of a general attack against the MOBS cryptosystem 关于对MOBS密码系统的一般攻击的有效性

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2021-11-10 DOI: 10.1515/jmc-2021-0050

Christopher Battarbee, Delaram Kahrobaei, Dylan Tailor, S. F. Shahandashti

引用次数: 4

On the confusion coefficient of Boolean functions 关于布尔函数的混淆系数

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2021-08-05 DOI: 10.1515/jmc-2021-0012

Yu Zhou, Jianyong Hu, Xudong Miao, Yu Han, Fuzhong Zhang

引用次数: 2

A deterministic algorithm for the discrete logarithm problem in a semigroup 半群中离散对数问题的一种确定性算法

IF 1.2

Journal of Mathematical Cryptology Pub Date : 2021-01-27 DOI: 10.1515/jmc-2021-0022

Simran Tinani, J. Rosenthal

{"title":"A deterministic algorithm for the discrete logarithm problem in a semigroup","authors":"Simran Tinani, J. Rosenthal","doi":"10.1515/jmc-2021-0022","DOIUrl":"https://doi.org/10.1515/jmc-2021-0022","url":null,"abstract":"Abstract The discrete logarithm problem (DLP) in a finite group is the basis for many protocols in cryptography. The best general algorithms which solve this problem have a time complexity of O ( N log N ) Oleft(sqrt{N}log N) and a space complexity of O ( N ) Oleft(sqrt{N}) , where N N is the order of the group. (If N N is unknown, a simple modification would achieve a time complexity of O ( N ( log N ) 2 ) Oleft(sqrt{N}{left(log N)}^{2}) .) These algorithms require the inversion of some group elements or rely on finding collisions and the existence of inverses, and thus do not adapt to work in the general semigroup setting. For semigroups, probabilistic algorithms with similar time complexity have been proposed. The main result of this article is a deterministic algorithm for solving the DLP in a semigroup. Specifically, let x x be an element in a semigroup having finite order N x {N}_{x} . The article provides an algorithm, which, given any element y ∈ ⟨ x ⟩ yin langle xrangle , provides all natural numbers m m with x m = y {x}^{m}=y , and has time complexity O ( N x ( log N x ) 2 ) Oleft(sqrt{{N}_{x}}{left(log {N}_{x})}^{2}) steps. The article also gives an analysis of the success rates of the existing probabilistic algorithms, which were so far only conjectured or stated loosely.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":"16 1","pages":"141 - 155"},"PeriodicalIF":1.2,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43508095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0