The challenge of maintaining confidentiality of stored data in cloud is of utmost importance to realize the potential of cloud computing as an emerging storage solution service. Storing data in encrypted form may solve the problem, but exposes data to an adversary for each required computation. This repeated encryption decryption also diminishes the essence of cloud for storing encrypted database and huge computation power of cloud remains unused. Fully homomorphic encryption (FHE) is an effective scheme to support arbitrary operations directly on encrypted data, but has serious performance issues. In this paper, we have considered sorting on encrypted data, which is a frequently required database operation. We have investigated the feasibility of performing comparison as well as partition based sort on CPA resistant FHE data and highlight an important observation that time requirement of partition based sort on FHE data is no better than comparison based sort owing to the underlying security of the cryptosystem. We identify the recrypt operation, which is the denoising step of FHE as the main reason of costly timing requirement of such operations. We propose a FHE specific two stage sorting technique termed as $\sf {Lazy sort}$Lazysort with reduced recrypt operation, which proves to be better in terms of performance on FHE data in comparison to partition as well as comparison sort. Finally, we provide some multi-core implementation results to show that with proper implementation tricks performance of FHE computations can be improved further.

中文翻译：

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全同态加密云数据的排序：分区是否有效？

维护云中存储数据的机密性对于实现云计算作为新兴存储解决方案服务的潜力至关重要。以加密形式存储数据可能会解决问题，但每次所需的计算都会将数据暴露给对手。这种重复的加密解密也削弱了云存储加密数据库的本质，云的巨大计算能力没有得到利用。全同态加密（FHE）是一种支持直接对加密数据进行任意操作的有效方案，但存在严重的性能问题。在本文中，我们考虑了对加密数据进行排序，这是一项经常需要的数据库操作。我们已经研究了在抗 CPA 的 FHE 数据上执行比较和基于分区的排序的可行性，并强调了一个重要的观察结果，即由于密码系统的底层安全性，基于 FHE 数据的分区排序的时间要求并不比基于比较的排序好。我们确定重新加密操作，这是 FHE 的去噪步骤，是此类操作的时间要求昂贵的主要原因。我们提出了一种 FHE 特定的两阶段排序技术，称为$\sf {懒惰排序}$懒惰的种类减少了重新加密操作，与分区和比较排序相比，这证明在 FHE 数据的性能方面更好。最后，我们提供了一些多核实现结果，以表明通过适当的实现技巧可以进一步提高 FHE 计算的性能。