Some new classes of 2-fold optimal or perfect splitting authentication codes

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• 作者：Miao Liang ; Lijun Ji ; Jingcai Zhang
• 关键词：Splitting t ; designs ; Restricted strong partially balanced t ; designs ; Splitting authentication codes
• 刊名：Cryptography and Communications
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：9
• 期：3
• 页码：407-430
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Data Structures, Cryptology and Information Theory; Coding and Information Theory; Communications Engineering, Networks; Information and Communication, Circuits; Mathematics of Computing;
• 出版者：Springer US
• ISSN：1936-2455
• 卷排序：9

文摘

Optimal restricted strong partially balanced t-design can be used to construct splitting authentication codes which achieve combinatorial lower bounds or information-theoretic lower bounds. In this paper, we investigate the existence of optimal restricted strong partially balanced 2-designs ORSPBD (v, k×c,1), and show that there exists an ORSPBD (v,2×c,1) for any positive integer v≡ v₀ (mod 2c2) and \(v_{0}\in \{1\leq x\leq 2c^{2}:\ \gcd (x,c)=1\ \text {or} \ \gcd (x,c)=c \} \setminus \)\(\{c^{2}+1\leq x\leq (c+1)^{2} :\gcd (x,c)=1\ \text {and}\ \gcd (x,2)=2\}\). Furthermore, we determine the existence of an ORSPBD (v,k×c,1) for any integer v≥kc with (k,c)=(2,4), (2,5), (3,2) or for any even integer v≥kc with (k,c)=(4,2). As their applications, we obtain six new infinite classes of 2-fold optimal or perfect c-splitting authentication codes.