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首页> 外文期刊>IEEE Transactions on Information Theory >Dual Universality of Hash Functions and Its Applications to Quantum Cryptography
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Dual Universality of Hash Functions and Its Applications to Quantum Cryptography

机译：哈希函数的对偶通用性及其在量子密码学中的应用

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In this paper, we introduce the concept of dual universality of hash functions and present its applications to quantum cryptography. We begin by establishing the one-to-one correspondence between a linear function family ${cal F}$ and a code family ${cal C}$, and thereby defining $varepsilon $-almost dual ${rm universal}_{2}$ hash functions, as a generalization of the conventional ${rm universal}_{2}$ hash functions. Then, we show that this generalized (and thus broader) class of hash functions is in fact sufficient for the security of quantum cryptography. This result can be explained in two different formalisms. First, by noting its relation to the $delta $-biased family introduced by Dodis and Smith, we demonstrate that Renner's two-universal hashing lemma is generalized to our class of hash functions. Next, we prove that the proof technique by Shor and Preskill can be applied to quantum key distribution (QKD) systems that use our generalized class of hash functions for privacy amplification. While Shor–Preskill formalism requires an implementer of a QKD system to explicitly construct a linear code of the Calderbank–Shor–Steane (CSS) type, this result removes the existing difficulty of the construction of a linear code of CSS code by replacing it by the combination of an ordinary classical error correcting code and our proposed hash function. We also show that a similar result applies to the quantum wire-tap channel. Finally, we compare our results in the two formalisms and show that, in typical QKD scenarios, the Shor–Preskill-type- argument gives better security bounds in terms of the trace distance and Holevo information than the method based on the $delta $-biased family.
机译：在本文中，我们介绍了哈希函数的双重通用性的概念，并介绍了其在量子密码学中的应用。我们首先建立线性函数族 $ {cal F} $ 与代码族之间的一一对应关系 $ {cal C} $ ，从而定义 $ varepsilon $ -几乎双重对偶 $ {rm通用} _ {2} $ 哈希函数，作为常规 $ {rm通用} _ {2} $ 哈希函数的概括。然后，我们表明，这种广义的（因而更广泛的）哈希函数类别实际上足以保证量子密码学的安全性。这个结果可以用两种不同的形式主义来解释。首先，通过注意到其与Dodis和Smith引入的 $ delta $ 偏向族的关系，我们证明了Renner的两个通用哈希引理被推广到我们的哈希函数类中。接下来，我们证明Shor和Preskill的证明技术可以应用于使用我们的广义哈希函数类进行隐私放大的量子密钥分发（QKD）系统。尽管Shor-Preskill形式主义要求QKD系统的实现者显式构造Calderbank-Shor-Steane（CSS）类型的线性代码，但此结果通过将CSS替换为线性代码，从而消除了构建CSS线性代码的现有困难。普通的经典纠错码和我们提出的哈希函数的结合。我们还表明，类似的结果适用于量子窃听通道。最后，我们比较了两种形式主义的结果​​，结果表明，在典型的QKD方案中，Shor-Preskill-type-参数在跟踪距离和Holevo信息方面比基于 $ delta $ -有偏见的族。

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