On the Security Properties of Combinatorial All-or-nothing Transforms
On the Security Properties of Combinatorial All-or-nothing Transforms
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DOI：
10.1109/isit50566.2022.9834366
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
Yujie Gu;Sonata Akao;Navid Nasr Esfahani;Ying Miao;K. Sakurai
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文献类型：
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作者：
Yujie Gu;Sonata Akao;Navid Nasr Esfahani;Ying Miao;K. Sakurai
全有或全无变换(AONT)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中有许多应用。后来，Stinson提出了无条件安全的AONT及其组合刻画。非正式地，组合AONT是具有无偏要求的阵列，其安全性质一般取决于输入S元组上的先验概率分布。最近，Esfahani和Stinson证明了，如果所有的输入S元组都是等概率的，那么一个组合AONT是完全安全的；如果所有的输入S元组都是非零概率的，那么它是弱安全的。本文旨在探讨组合(t，S，v)-AONTs的完全安全性和弱安全性之间的差距。具体地说，我们考虑这样的典型场景：所有S输入独立取值(但不一定相同)，并且量化关于任何S−t输出$\数学{Y}$\t输入$\数学{X}$的信息量$H(\数学{X}\中\数学{Y})$。特别地，我们用信息论的方法建立了组合AONTs的$H(数学{X}中数学{Y})$的一般上下界，并证明了在某些情况下这些上下界是可以得到的。
All-or-nothing transforms (AONT) were proposed by Rivest as a message preprocessing technique for encrypting data to protect against brute-force attacks, and have many applications in cryptography and information security. Later the unconditionally secure AONT 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 $H(\mathcal{X}\mid \mathcal{Y})$ 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 $H(\mathcal{X}\mid \mathcal{Y})$ for combinatorial AONTs using information-theoretic techniques, and also show that the derived bounds can be attained in certain cases.