代数限制码及其应用

Divesh Aggarwal, Nico Döttling, Jesko Dujmovic, Mohammad Hajiabadi, Giulio Malavolta, Maciej Obremski
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引用次数: 2

摘要

考虑以下问题:您有一个设备,它应该计算其输入的线性组合,这些输入来自某个有限域。然而,该设备可能出现故障并计算其输入的任意函数。是否有可能以这样一种方式对输入进行编码,即只有线性函数可以对编码进行评估?也就是说,学习编码的任意函数不会比线性组合揭示更多关于输入的信息。在这项工作中,我们引入了代数限制码(AR码)的概念,它将可能计算任何函数的对手限制为计算线性函数。我们的主要成果是一个信息理论结构的AR码,它将任何一类具有有限输出位的函数限制为线性函数。我们的建设依赖于一种没有提供给对手的种子。虽然它本身很有趣和自然,但我们展示了这个概念在密码学中的应用。特别地,我们展示了AR代码导致了第一个基于decision Diffie-Hellman假设的具有统计发送方安全性的rate-1无关传输的构造,以及第一个使密码学成为黑盒使用的构造。以前,这样的协议只能从LWE假设中知道,使用非黑盒加密技术。我们希望我们的AR代码的新概念能够在未来找到进一步的应用,例如,在不可延展性的背景下。
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Algebraic Restriction Codes and their Applications
Consider the following problem: You have a device that is supposed to compute a linear combination of its inputs, which are taken from some finite field. However, the device may be faulty and compute arbitrary functions of its inputs. Is it possible to encode the inputs in such a way that only linear functions can be evaluated over the encodings? I.e., learning an arbitrary function of the encodings will not reveal more information about the inputs than a linear combination. In this work, we introduce the notion of algebraic restriction codes (AR codes), which constrain adversaries who might compute any function to computing a linear function. Our main result is an information-theoretic construction AR codes that restrict any class of function with a bounded number of output bits to linear functions. Our construction relies on a seed which is not provided to the adversary. While interesting and natural on its own, we show an application of this notion in cryptography. In particular, we show that AR codes lead to the first construction of rate-1 oblivious transfer with statistical sender security from the Decisional Diffie–Hellman assumption, and the first-ever construction that makes black-box use of cryptography. Previously, such protocols were known only from the LWE assumption, using non-black-box cryptographic techniques. We expect our new notion of AR codes to find further applications, e.g., in the context of non-malleability, in the future.
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