The theory of Markowitz portfolio has had enormous value and extensive applications in finance since it came into being. With the advent of the Big-Data era and the increasingly complicated financial market, the resource consumption of computing portfolio investments is significantly increasing. Cloud computing offers a good platform to efficiently compute large-scale portfolio investments, in particular, for resource-limited investors. In this paper, a Markowitz model (MM) is taken into consideration for outsourcing to a public cloud in a privacy-conscious way. As in general computation outsourcing, outsourcing MM inevitably faces four issues, namely, input/output privacy, correctness, verification, and substantial computation gain for investors; it has consistent complexity with the original methods when the cloud solves the encrypted version. However, the proposed cloud-assisted privacy-conscious MM employs location-scrambling and value-alteration encryption operations, which can protect the MM’s input/output privacy well. Moreover, the correctness of solving MM over an encrypted domain in the cloud side can be demonstrated and the results returned by the cloud can be verified. Furthermore, both theoretical and experimental analyses validate that the investor can obtain a huge amount of computational gain, and the cloud complexity consistent with that of the original case when solving the encrypted version.

自建立以来，马科维兹组合理论在金融领域就具有巨大的价值和广泛的应用。随着大数据时代的到来以及金融市场日益复杂，计算证券投资的资源消耗正在大大增加。云计算提供了一个很好的平台，可以有效地计算大规模的证券投资，尤其是对于资源有限的投资者。在本文中，考虑了Markowitz模型（MM），以注重隐私的方式外包给公共云。像一般的计算外包一样，MM外包不可避免地面临四个问题，即输入/输出隐私，正确性，验证以及为投资者带来可观的计算收益。当云解决加密版本时，它与原始方法具有一致的复杂性。但是，提出的云辅助隐私意识MM采用位置加扰和值变更加密操作，可以很好地保护MM的输入/输出隐私。此外，可以证明在云侧在加密域上求解MM的正确性，并可以验证云返回的结果。此外，理论和实验分析都证明投资者可以获得大量的计算收益，并且在求解加密版本时，云的复杂性与原始情况一致。可以证明在云端通过加密域解决MM的正确性，并可以验证云返回的结果。此外，理论和实验分析都证明投资者可以获得大量的计算收益，并且在求解加密版本时，云的复杂性与原始情况一致。可以证明在云端通过加密域解决MM的正确性，并可以验证云返回的结果。此外，理论和实验分析都证明投资者可以获得大量的计算收益，并且在求解加密版本时，云的复杂性与原始情况一致。