论文标题
针对量子对手的水印
Watermarking PRFs against Quantum Adversaries
论文作者
论文摘要
我们启动针对量子对手的软件水印研究。量子对手作为海盗软件生成量子状态，该软件可能会从经典标记的软件中删除嵌入式消息。从量子海盗软件中提取嵌入式消息很困难，因为测量可能会不可逆地改变量子状态。 在这项工作中，我们为量子对手定义了安全的水印（针对量子对手的不足性）。我们还提供了两个水印PRF，如下所示。 - 我们从学习错误（LWE）问题的量子硬度（LWE）问题中构建了针对量子对手的私人提取的水印PRF。标记和提取算法分别使用公共参数和私人提取密钥。即使对手有（公共参数和）访问提取甲骨文，这是返回查询量子电路的提取结果，即使对手具有（公共参数和）访问，因此PRF的水印也是不明显的。 - 我们构建了一个可公开提取的水印PRF，以抵抗无法区分性混淆（IO）和LWE问题的量子硬度。标记和提取算法分别使用公共参数和公共提取密钥。即使对手有提取密钥（和公共参数），水印PRF也是不明显的。 我们开发了一种量子提取技术，以从量子状态中提取信息（经典字符串）而不会太多破坏状态。我们还介绍了无提取的水印PRF作为关键的构建块的概念，以通过将工具与我们的量子提取技术相结合来实现上述结果。
We initiate the study of software watermarking against quantum adversaries. A quantum adversary generates a quantum state as a pirate software that potentially removes an embedded message from a classical marked software. Extracting an embedded message from quantum pirate software is difficult since measurement could irreversibly alter the quantum state. In this work, we define secure watermarking PRFs for quantum adversaries (unremovability against quantum adversaries). We also present two watermarking PRFs as follows. - We construct a privately extractable watermarking PRF against quantum adversaries from the quantum hardness of the learning with errors (LWE) problem. The marking and extraction algorithms use a public parameter and a private extraction key, respectively. The watermarking PRF is unremovable even if adversaries have (the public parameter and) access to the extraction oracle, which returns a result of extraction for a queried quantum circuit. - We construct a publicly extractable watermarking PRF against quantum adversaries from indistinguishability obfuscation (IO) and the quantum hardness of the LWE problem. The marking and extraction algorithms use a public parameter and a public extraction key, respectively. The watermarking PRF is unremovable even if adversaries have the extraction key (and the public parameter). We develop a quantum extraction technique to extract information (a classical string) from a quantum state without destroying the state too much. We also introduce the notion of extraction-less watermarking PRFs as a crucial building block to achieve the results above by combining the tool with our quantum extraction technique.
