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An Authentication Code over Galois Rings with Optimal Impersonation and Substitution Probabilities

Juan Ku-Cauich, Guillermo Morales-Luna, Horacio Tapia-Recillas
2018 Mathematical and Computational Applications  
Two new systematic authentication codes based on the Gray map over a Galois ring are introduced. The first introduced code attains optimal impersonation and substitution probabilities.  ...  The second code improves space sizes, but it does not attain optimal probabilities. Additionally, it is conditioned to the existence of a special class of bent maps on Galois rings.  ...  In this section, a systematic authentication code is constructed using a resilient function on a Galois ring and the Gray map on this ring. Let p > 2 be a prime number, r, , m ∈ Z + , and q = p .  ... 
doi:10.3390/mca23030046 fatcat:oe7z4mm54bhaxg7chyyjiuo3om

Authentication codes based on resilient Boolean maps

Juan Carlos Ku-Cauich, Guillermo Morales-Luna
2015 Designs, Codes and Cryptography  
We introduce new constructions of systematic authentication codes over finite fields and Galois rings.  ...  Being the finite fields special cases of Galois rings, the first code introduced for Galois rings apply also at finite fields.  ...  Let us now introduce an useful class of maps for systematic authentication codes. At [4] there was introduced a class of bent maps over Galois rings of characteristic p 2 .  ... 
doi:10.1007/s10623-015-0121-3 fatcat:udvts5rgrncydcathmkd2hqaxa

Universal Hash Functions from Exponential Sums over Finite Fields and Galois Rings [chapter]

Tor Helleseth, Thomas Johansson
1996 Lecture Notes in Computer Science  
In t#liis 1)apcr ncw families of stmngly universal hash funct,ions, or equivalently, authentication codes, are proposed.  ...  Their parameters are derived from bounds on exponential sums over finite fields and Galois rings. This is the first tirnr hash families based upon such exponential sums have 1)een considered.  ...  We will next show that using the theory of exponential sums over Galois rings we can also construct universal hash families. 5 Some preliminaries on Galois rings are giveri below.  ... 
doi:10.1007/3-540-68697-5_3 fatcat:q7fpbgmcfvevndenxmodnujcrm

New constructions of systematic authentication codes from three classes of cyclic codes

Yunwen Liu, Longjiang Qu, Chao Li
2018 Advances in Mathematics of Communications  
Our results show that these new authentication codes are better than some of the authentication codes in the literature.  ...  Wang, we present new systematic authentication codes based on these cyclic codes. In this paper, we study three special classes of cyclic codes and their authentication codes.  ...  A generic construction of authentication codes. In [7] , a generic construction of authentication codes using the error-correcting codes was presented.  ... 
doi:10.3934/amc.2018001 fatcat:mtfvbmob2nhfbbvgv4pdxmxbru

Optimal Algebraic Manipulation Detection Codes in the Constant-Error Model [chapter]

Ronald Cramer, Carles Padró, Chaoping Xing
2015 Lecture Notes in Computer Science  
Algebraic manipulation detection (AMD) codes, introduced at EUROCRYPT 2008, may, in some sense, be viewed as keyless combinatorial authentication codes that provide security in the presence of an oblivious  ...  There is an explicit construction of AMD codes based on cyclic codes (Theorem 3.6).  ...  Best Previous Constructions The following definition of systematic AMD code was introduced in [5, 6] .  ... 
doi:10.1007/978-3-662-46494-6_20 fatcat:ejbiyj4uzre7ze6vdkyqg7eooi

On the Minimum Number of Multiplications Necessary for Universal Hash Functions [chapter]

Mridul Nandi
2015 Lecture Notes in Computer Science  
The Toeplitz construction and d independent invocations of PDP are d-block hash outputs which require d × n 2 multiplications.  ...  Let d ≥ 1 be an integer and R1 be a finite ring whose elements are called block.  ...  Acknowledgement This work was supported by the Centre of Excellence in Cryptology, Indian Statistical Institute, Kolkata.  ... 
doi:10.1007/978-3-662-46706-0_25 fatcat:5dzfpc4ndrc3fpwcznggqyvp2y

Constructions of difference covering arrays

Jianxing Yin
2003 Journal of combinatorial theory. Series A  
The result is also useful in encoding systematic authentication codes, as well as in software testing and data compression problems. t0 ; d h1 d À1 t1 ; y; d hðqÀ1Þ d À1 tðqÀ1Þ g $ Research supported in  ...  It is well known that a ðq; k; 1Þ difference matrix does not exist, whenever q 2 ðmod 4Þ and kX3: Thus, we have nXq þ 1 for these values of k and q: In this article, several constructive techniques for  ...  Infinitely many new systematic authentication codes are produced using these existing difference covering arrays.  ... 
doi:10.1016/j.jcta.2003.09.005 fatcat:qe3trf4sffbfbaepaao7oe5gzm

Algebraic Coding Theory for Networks, Storage, and Security (Dagstuhl Seminar 18511)

Eimear Byrne, Martin Bossert, Antonia Wachter-Zeh, Michael Wagner
2019 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 18511 "Algebraic Coding Theory for Networks, Storage, and Security".  ...  The ever increasing traffic in networks and the growth of distributed storage systems require advanced techniques based on algebraic coding to meet user demand.  ...  When constructing a code, we may be interested in minimizing the number of nodes used. Note that a minimal length code serving a given set of requests does not always have the minimum length.  ... 
doi:10.4230/dagrep.8.12.49 dblp:journals/dagstuhl-reports/ByrneBW18 fatcat:qmcdjxigx5ahxe3jpnmns4v6ka

Combinatorial Designs for Authentication and Secrecy Codes

Michael Huber
2008 Foundations and Trends in Communications and Information Theory  
Douglas Stinson, University of Waterloo, for an inspiring conversation on this topic. I am also indebted to the Editor-in-Chief Prof.  ...  We also mention that there are various other constructions of different types of authentication codes, using, e.g., algebraic curves [228] , Galois rings [168] , rational normal curves [170] , generalized  ...  [106] ): (i) Construction of multi-fold secure splitting authentication codes: Using Theorem 3.36, this asks for systematically constructing t-(v, b, l = cu, 1) splitting design for t > 2.  ... 
doi:10.1561/0100000044 fatcat:i2ykqtz3zrbnpahelbybq7qlxu

A Survey of Wearable Devices Pairing Based on Biometric Signals [article]

Jafar Pourbemany, Ye Zhu, Riccardo Bettati
2021 arXiv   pre-print
A wide range of approaches has been proposed to address autonomous pairing in wearable devices.  ...  We review the steps needed for generating a common key and provide a survey of existing techniques utilized in each step.  ...  BCH codes form a class of cyclic error-correcting codes constructed using polynomials over a finite field (also called Galois field).  ... 
arXiv:2107.11685v1 fatcat:hgbpauqvzrfnpgnrfraugjtf4u

A class of three-weight linear codes and their complete weight enumerators

Shudi Yang, Zheng-An Yao, Chang-An Zhao
2016 Cryptography and Communications  
The results show that they are linear codes with three weights and suitable for the constructions of authentication codes and secret sharing schemes.  ...  Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications.  ...  We also mention that the complete weight enumerators, presented in Theorems 1, 2 and 3, can be applied to construct systematic authentication codes.  ... 
doi:10.1007/s12095-016-0187-4 fatcat:2k7ebyhxa5bxfjugws4umkm3xe

A secure and robust scheme for sharing confidential information in IoT systems

Lake Bu, Mihailo Isakov, Michel A. Kinsy
2018 Ad hoc networks  
- specifically, all the compromised devices can be identified, the confidentiality of information is kept, and authenticity of the secret can be guaranteed.  ...  can only be retrieved collaboratively by groups of devices; and (2) it ensures the privacy and integrity of the information, even when attackers hijack a large number of devices and use them in concert  ...  HMAC, keyed-hashing for message authentication code, is the most often used technique for authentication today.  ... 
doi:10.1016/j.adhoc.2018.09.007 fatcat:bapxnyfknrakjlyupm4qsvwclq

A Unified Approach to MPC with Preprocessing Using OT [chapter]

Tore Kasper Frederiksen, Marcel Keller, Emmanuela Orsini, Peter Scholl
2015 Lecture Notes in Computer Science  
This work describes new protocols for generating multiplication triples in fields of characteristic two using OT extensions.  ...  Before this work, TinyOT, which works on binary circuits, was the only protocol in this family using OT extensions.  ...  However, remember that we work on elements which are codewords of some systematic linear error correcting code, C.  ... 
doi:10.1007/978-3-662-48797-6_29 fatcat:hz4dap2sznculjmehnkchii3kq

Machine Learning of Physical Unclonable Functions using Helper Data

Emanuele Strieder, Christoph Frisch, Michael Pehl
2021 Transactions on Cryptographic Hardware and Embedded Systems  
This work, however, reveals a pitfall in these constructions: When using state-of-the-art helper data algorithms to correct noisy PUF responses, an attacker can exploit the publicly accessible helper data  ...  The analysis reveals that especially the frequently used repetition code is vulnerable: For a SUM-PUF in combination with a repetition code, e.g., already the observation of 800 challenges and helper data  ...  Acknowledgements This work was partly funded by the German Ministry of Education, Research and Technology through the project SecForCARs (grant number 16KIS0795).  ... 
doi:10.46586/tches.v2021.i2.1-36 fatcat:5alolkueozghfp6tasykm2pf6y

Post-Quantum Cryptography [chapter]

Qijun Gu, Pascal Paillier, Tanja Lange, Edlyn Teske, Darrel Hankerson, Alfred Menezes, David Zhang, Feng Yue, Wangmeng Zuo, Jean-Jacques Quisquater, Gildas Avoine, Gerald Brose (+73 others)
2011 Encyclopedia of Cryptography and Security  
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective  ...  We hope that it serves as an introduction to the field, as an overview of the state of the art, and as an encouragement for many more scientists to join us in investigating post-quantum cryptography.  ...  Acknowledgements We thank Phong Nguyen and Markus Rückert for helpful discussions on the practical security of lattice-based cryptography.  ... 
doi:10.1007/978-1-4419-5906-5_386 fatcat:ucdkilta7zc3voq7nqctmjkcr4
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