On the Information-Theoretic Security of Combinatorial All-or-Nothing Transforms
On the Information-Theoretic Security of Combinatorial All-or-Nothing Transforms
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DOI：
10.1109/tit.2022.3174008
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发表时间：
2022-02
影响因子：
2.5
通讯作者：
Yujie Gu;Sonata Akao;Navid Nasr Esfahani;Ying Miao;K. Sakurai
中科院分区：
文献类型：
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作者：
Yujie Gu;Sonata Akao;Navid Nasr Esfahani;Ying Miao;K. Sakurai
全或无转换（AONTs）是Rivest提出的一种用于加密数据以防止暴力攻击的消息预处理技术，在密码学和信息安全领域有着广泛的应用。随后，Stinson介绍了无条件安全aont及其组合表征。非正式地说，组合AONT是一个具有无偏要求的数组，其安全性通常取决于输入$s$元组的先验概率分布。最近，Esfahani和Stinson证明了组合AONT在所有输入$s$元组均为等概率条件下具有完全的安全性，在所有输入$s$元组均为非零概率条件下具有弱安全性。本文旨在探讨组合$(t,s,v)$ - aont的完全安全性与弱安全性之间的差距。具体地说，我们考虑一个典型的场景，即所有$s$输入都独立地（但不一定相同）取值，并量化关于任何$t$输入$\mathcal {X}$的信息量$H(\mathcal {X}|\mathcal {Y})$，而任何$s-t$输出$\mathcal {Y}$没有透露。特别地，我们利用信息理论技术建立了组合AONTs $H(\mathcal {X}|\mathcal {Y})$的一般下界和上界，并证明了在某些情况下可以得到所导出的下界。在此基础上，进一步讨论了组合非对称aont的安全性。
All-or-nothing transforms (AONTs) were proposed by Rivest as a message preprocessing technique for encrypting data to protect against brute-force attacks, and have numerous applications in cryptography and information security. Later the unconditionally secure AONTs and their combinatorial characterization were introduced by Stinson. Informally, a combinatorial AONT is an array with the unbiased requirements and its security properties in general depend on the prior probability distribution on the inputs $s$ -tuples. Recently, it was shown by Esfahani and Stinson that a combinatorial AONT has perfect security provided that all the inputs $s$ -tuples are equiprobable, and has weak security provided that all the inputs $s$ -tuples are with non-zero probability. This paper aims to explore on the gap between perfect security and weak security for combinatorial $(t,s,v)$ -AONTs. Concretely, we consider the typical scenario that all the $s$ inputs take values independently (but not necessarily identically) and quantify the amount of information $H(\mathcal {X}|\mathcal {Y})$ about any $t$ inputs $\mathcal {X}$ that is not revealed by any $s-t$ outputs $\mathcal {Y}$ . In particular, we establish the general lower and upper bounds on $H(\mathcal {X}|\mathcal {Y})$ for combinatorial AONTs using information-theoretic techniques, and also show that the derived bounds can be attained in certain cases. Furthermore, the discussions are extended for the security properties of combinatorial asymmetric AONTs.