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Three Constructions of Authentication Codes with Perfect Secrecy

Cunsheng Ding, Xiaojian Tian
2004 Designs, Codes and Cryptography  
In this paper, we present three algebraic constructions of authentication codes with secrecy. The first and the third class are optimal.  ...  Some of the codes in the second class are optimal, and others in the second class are asymptotically optimal. All authentication codes in the three classes provide perfect secrecy.  ...  Acknowledgments The authors thank the referee for his constructive comments and suggestions that greatly improved this paper.  ... 
doi:10.1023/b:desi.0000036248.82691.11 fatcat:3dij7uf6h5g6bn4lvxcilkbdjq

Constructing Optimal Authentication Codes with Perfect Multi-fold Secrecy [article]

Michael Huber
2009 arXiv   pre-print
We establish a construction of optimal authentication codes achieving perfect multi-fold secrecy by means of combinatorial designs.  ...  As an application, we present the first infinite class of optimal codes that provide two-fold security against spoofing attacks and at the same time perfect two- fold secrecy.  ...  The author gratefully acknowledges support of his work by the Deutsche Forschungsgemeinschaft (DFG) via a Heisenberg grant (Hu954/4) and a Heinz Maier-Leibnitz Prize grant (Hu954/5).  ... 
arXiv:0912.0597v1 fatcat:rpcgjbbxlrd37c25h3acync6mu

Authentication and secrecy codes for equiprobable source probability distributions

Michael Huber
2009 2009 IEEE International Symposium on Information Theory  
In particular, we construct an infinite class of optimal authentication codes which are multiple-fold secure against spoofing and simultaneously achieve perfect secrecy.  ...  Almost all of these appear to be the first authentication codes with these properties.  ...  The author gratefully acknowledges support of his work by the Deutsche Forschungsgemeinschaft (DFG) via a Heisenberg grant (Hu954/4) and a Heinz Maier-Leibnitz Prize grant (Hu954/5).  ... 
doi:10.1109/isit.2009.5206028 dblp:conf/isit/Huber09 fatcat:sgaw3d3vabdkjppr2rdzf6itaq

Authentication codes and bipartite graphs

Rongquan Feng, Lei Hu, Jin Ho Kwak
2008 European journal of combinatorics (Print)  
As a result, some (optimal) minimal authentication codes with perfect secrecy are constructed from association schemes, from finite groups or from known authentication codes no matter whether the known  ...  By using such a characterization, two necessary and sufficient conditions for a minimal authentication code with perfect secrecy are derived.  ...  AC(q 2s(ν−s) , q s(2ν−s) , q s(2ν−s) ) with perfect secrecy. The probabilities of a successful impersonation and of a successful substitution attack of it are P I = 1/q s 2 and P S = 1/q s .  ... 
doi:10.1016/j.ejc.2007.06.013 fatcat:3nbhx2zyg5d5roaplorpyhd3lq

Information Theoretic Authentication and Secrecy Codes in the Splitting Model [article]

Michael Huber
2011 arXiv   pre-print
In this paper, we establish a construction method for optimal splitting authentication codes with perfect secrecy in the more general case when the number of keys may differ from the number of messages  ...  Ogata-Kurosawa-Stinson-Saido (2004) have constructed optimal splitting authentication codes achieving perfect secrecy for the special case when the number of keys equals the number of messages.  ...  Ogata-Kurosawa-Stinson-Saido [6] have constructed optimal splitting authentication codes with perfect secrecy for the special case when the number of keys equals the number of messages.  ... 
arXiv:1112.0038v1 fatcat:shqgcgirszawlhq6k3ukcu72tu

Systematic Authentication Codes From Highly Nonlinear Functions

C. Ding, H. Niederreiter
2004 IEEE Transactions on Information Theory  
Recently, highly nonlinear functions have been successfully employed to construct authentication codes with and without secrecy.  ...  In this paper, we construct four classes of systematic authentication codes from perfect nonlinear functions and almost-perfect nonlinear functions.  ...  ACKNOWLEDGMENT The authors wish to thank the referees for their constructive comments and suggestions that improved both the quality and readability of this paper.  ... 
doi:10.1109/tit.2004.834788 fatcat:qle4f43h4rdbdahtrxfpsfmltm

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.  ...  Optimal authentication codes with perfect secrecy: further examples.  ...  Authentication Codes with Secrecy We study now codes that offer both authenticity and secrecy. For authentication codes without secrecy, there exist numerous constructions for quite some time.  ... 
doi:10.1561/0100000044 fatcat:i2ykqtz3zrbnpahelbybq7qlxu

On the equivalence of authentication codes and robust (2,2)-threshold schemes [article]

Maura B. Paterson, Douglas R. Stinson
2019 arXiv   pre-print
Our new equivalences motivate the consideration of a certain "key-substitution attack." We study this attack and analyze it in the setting of "dual authentication codes."  ...  We also show how this viewpoint provides a nice way to prove properties and generalizations of some known constructions.  ...  If a splitting BIBD is equitably ordered, then it yields an authentication code with perfect secrecy, from Theorem 1.3.  ... 
arXiv:1910.05572v1 fatcat:arelq77mebglflmctuzdhpu3za

On the equivalence of authentication codes and robust (2, 2)-threshold schemes

Maura B. Paterson, Douglas R. Stinson
2020 Journal of Mathematical Cryptology  
Our new equivalences motivate the consideration of a certain "key-substitution attack." We study this attack and analyze it in the setting of "dual authentication codes."  ...  We also show how this viewpoint provides a nice way to prove properties and generalizations of some known constructions.  ...  If a splitting BIBD is equitably ordered, then it yields an authentication code with perfect secrecy, from Theorem 2.3.  ... 
doi:10.1515/jmc-2019-0048 fatcat:u5naphsuozfdpmt5j2myq2m42i

Perfect secrecy systems immune to spoofing attacks

Michael Huber
2012 International Journal of Information Security  
We obtain this way novel perfect secrecy systems with immunity to spoofing in the verification oracle model.  ...  Moreover, we construct, by means of t-designs for large values of t, the first near-optimal systems that are 5- and 6-fold secure as well as further systems with a feasible number of keys that are 7-fold  ...  This is known as an authentication system (or authentication code, A-code).  ... 
doi:10.1007/s10207-012-0166-5 fatcat:lqo2dwpshzdojmij4gp345qdhy

Bounds and Constructions for Authentication - Secrecy Codes with Splitting [chapter]

Marijke De Soete
1990 Lecture Notes in Computer Science  
In this paper we give some new bounds and constructions for authentication/secrecy codes with splitting.  ...  It is the aim to deal with codes having unconditional security, which means that the security is independent of the computing power. .4nalogously to the theory of unconditional secrecy due t o Shannon  ...  [14] , we define an optimal L-code t o be a code which achieves perfect L-fold secrecy, which is (L -1)-fold secure against spoofing and which meets equality in the foregoing formula. 3 Constructions  ... 
doi:10.1007/0-387-34799-2_24 fatcat:utrmbkrprvcsth7tfutrhw7ayy

Authentication codes in plaintext and chosen-content attacks [chapter]

R. Safavi-Naini, L. Tombak
1995 Lecture Notes in Computer Science  
We study authentication codes (A-codes) where it is assumed that the enemy has access to the content of the intercepted cryptogram. This is similar to plaintext attack in secrecy systems.  ...  We will obtain information theoretic bounds, define perfect protection and obtain lower bounds on the number of encoding rules for codes with perfect protection against chosen-content impersonation and  ...  Theorem 3 leads to a construction of A-codes, with perfect protection against plaintext attack.  ... 
doi:10.1007/bfb0053441 fatcat:wbusjiol4veu3bcgf6djulscs4

Authentication codes in plaintext and chosen-content attacks

R. Safavi-Naini, L. Tombak
1996 Designs, Codes and Cryptography  
We study authentication codes (A-codes) where it is assumed that the enemy has access to the content of the intercepted cryptogram. This is similar to plaintext attack in secrecy systems.  ...  We will obtain information theoretic bounds, define perfect protection and obtain lower bounds on the number of encoding rules for codes with perfect protection against chosen-content impersonation and  ...  Theorem 3 leads to a construction of A-codes, with perfect protection against plaintext attack.  ... 
doi:10.1007/bf00125077 fatcat:eekbrdw3mjc3vjn5eahvt7mn6m

A Construction for Authentication/secrecy Codes from 3-homogeneous Permutation Groups

D.R. Stinson, L. Teirlinck
1990 European journal of combinatorics (Print)  
We construct an infinite family of codes which provide perfect secrecy even if the same encoding rule is used three times in succession; and provide optimal protection against deception by an opponent  ...  In this paper, we construct codes which provide both secrecy and authentication using 3-homogeneous groups.  ...  The research of the first author was supported by NSERC grant A9287, and the research of the second author was supported by NSA grant MDA 904-88-H-2005.  ... 
doi:10.1016/s0195-6698(13)80058-3 fatcat:kgivz7qezfgsvhutmj7ygouy4u

Three constructions of authentication/secrecy codes

Cunsheng Ding, Arto Salomaa, Patrick Solé, Xiaojian Tian
2005 Journal of Pure and Applied Algebra  
In this paper, we present three algebraic constructions of authentication codes with secrecy. The codes have simple algebraic structures and are easy to implement.  ...  They are asymptotically optimal with respect to certain bounds.  ...  Acknowledgements The authors thank the referee for her/his constructive suggestions and comments that improved the quality and presentation of this paper.  ... 
doi:10.1016/j.jpaa.2004.08.008 fatcat:rf7cbi54nrgqtkmx73rjbzndga
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