Message-Restriction-Free Commitment Scheme Based on?Lattice Assumption
Message-Restriction-Free Commitment Scheme Based on?Lattice Assumption
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基于格假设的消息无限制承诺方案
DOI：
10.1007/978-3-030-93206-0_7
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Miyaji Atsuko
中科院分区：
文献类型：
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作者：
Miyaji Hideaki;Wang Yuntao;Miyaji Atsuko
承诺方案是一种基本协议，也是基本密码任务（如零知识识别）的重要组成部分。近年来，基于格的密码学因其潜在的后量子密码学而受到广泛的研究。因此，研究了基于格假设的承诺方案的实际应用。通常，许多应用程序需要提交任意向量，而不仅仅是短向量。为了发送如此大的消息，承诺方案的关键挑战之一是增加消息字符串的大小。到目前为止，已经进行了各种现有的研究来扩大消息字符串的大小。Baum等人构建了承诺方案，该方案允许在2018年发送大消息。然而，消息字符串可用的域仍然被用于非消息目的。的承诺计划，我们提出了一个承诺计划，可以发送一个更大的消息大小比鲍姆等人。的消息字符串大小。证明了承诺方案的隐藏性是基于决策背包问题的困难性，绑定性是基于模小整数解问题的困难性.我们还展示了如何通过设置适当的参数来实现一个统计隐藏的承诺方案。
A commitment scheme is a fundamental protocol and an essential component of basic cryptographic tasks, such as zero-knowledge identification. In recent years, lattice-based cryptography has been intensively studied owing to its potential to be promising post-quantum cryptography. Therefore, the commitment schemes based on lattice assumption have been studied for practical applications. Typically, many applications require to commit arbitrary vectors rather than only short ones. In order to send such large messages, one of a crucial challenges of commitment schemes is to increase the size of a message string. Various existing studies have been done to enlarge the size of a message string so far. Baum et al. constructed the commitment scheme, which can allow sending large message size in 2018. However, the domain available for message string is still being used for non-message purposes.In this paper, by improving Baum et al.’s commitment scheme, we propose a commitment scheme that can send a larger message size than Baum et al.’s message string size. Furthermore, we prove that the hiding property of our commitment scheme is based on the hardness of the decisional knapsack problem, and the binding property is based on the hardness of the module small-integer solution problem. We also show how to achieve a statistically hiding commitment scheme by setting appropriate parameters.