Wong et al. proposed a novel symmetric encryption scheme in which we can find the k-nearest neighbors from encrypted data and an encrypted query. Their scheme uses a pair of encryption functions that has an inner-product preserving property. Because of this property, the pair of encryption functions has been used in several encryption schemes involving ranked multi-keyword search as applications. On the other hand, Yao et al. pointed out that the pair of encryption functions is insecure when the attacker can get plaintext–ciphertext pairs. To prevent this attack, some countermeasures are given in the applications, e.g., randomizing plaintexts before encrypted. In this paper, we reanalyze the security of the inner-product preserving encryption functions. We first discuss the countermeasures against Yao et al.’s attack used in the applications. In particular, we show that one of them is ineffective. Next, we show that the first encryption function is breakable by the known plaintext attack by showing a concrete key-recovery procedure. Unlike Yao et al.’s attack, our attack does not use the second encryption function.

中文翻译：

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安全kNN的安全性分析和对加密数据的排名关键字搜索

Wong等。提出了一种新颖的对称加密方案，其中我们可以找到k-从加密数据和加密查询中获取邻居。他们的方案使用了一对具有内部产品保留属性的加密功能。由于此特性，该对加密功能已在涉及以排序多关键字搜索作为应用程序的几种加密方案中使用。另一方面，姚等。指出当攻击者可以获得明文-密文对时，加密功能对是不安全的。为了防止这种攻击，在应用程序中提供了一些对策，例如，在加密之前将纯文本随机化。在本文中，我们重新分析了保留内部产品加密功能的安全性。我们首先讨论针对应用中使用的Yao等人的攻击的对策。特别是，我们表明其中之一是无效的。下一个，通过显示具体的密钥恢复过程，我们证明了第一个加密功能可被已知的明文攻击破坏。与Yao等人的攻击不同，我们的攻击不使用第二加密功能。