资源受限信道中的局部可译码码
On Locally Decodable Codes in Resource Bounded Channels
摘要：
局部可解码码（LDC）的构造具有两个不期望的特性之一：低速率或高局部性（消息长度的多项式）。在编码器/解码器已经交换了密码密钥并且信道是概率多项式时间（PPT）算法的设置中，可以绕过这些障碍并且设计具有恒定速率和小局部性的LDC。然而，编码器/解码器已经交换了密码密钥的假设通常是禁止的。因此，我们考虑在信道相对于一些资源（例如，空间或（顺序）时间。给定一个明确的功能$f$的信道不能计算，我们展示了如何编码器可以发送一个随机的秘密密钥的本地解码器使用$f(\cdot)$和一个随机的甲骨文$H(\cdot)$。这允许从Ostrovsky、Pandey和Sahai的私钥LDC构造（ICALP，2007）进行引导，从而回答了Guruswami和Smith（FOCS 2010）提出的一个开放性问题，即这种引导技术是否可以应用于比PPT算法更弱的信道模型中的LDC。具体来说，在随机预言机模型中，我们展示了如何构建显式的恒定速率最不发达国家与当地的polylog的安全参数对各种资源受限的渠道。
英文摘要：
Constructions of locally decodable codes (LDCs) have one of two undesirable properties: low rate or high locality (polynomial in the length of the message). In settings where the encoder/decoder have already exchanged cryptographic keys and the channel is a probabilistic polynomial time (PPT) algorithm, it is possible to circumvent these barriers and design LDCs with constant rate and small locality. However, the assumption that the encoder/decoder have exchanged cryptographic keys is often prohibitive. We thus consider the problem of designing explicit and efficient LDCs in settings where the channel is slightly more constrained than the encoder/decoder with respect to some resource e.g., space or (sequential) time. Given an explicit function $f$ that the channel cannot compute, we show how the encoder can transmit a random secret key to the local decoder using $f(\cdot)$ and a random oracle $H(\cdot)$. This allows bootstrap from the private key LDC construction of Ostrovsky, Pandey and Sahai (ICALP, 2007), thereby answering an open question posed by Guruswami and Smith (FOCS 2010) of whether such bootstrapping techniques may apply to LDCs in weaker channel models than just PPT algorithms. Specifically, in the random oracle model we show how to construct explicit constant rate LDCs with locality of polylog in the security parameter against various resource constrained channels.
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