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Towards Fully Homomorphic Encryption From Gentry-Peikert-Vaikuntanathan Scheme

机译:从Gentry-Peikert-Vaikuntanathan方案转向完全同态加密

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Despite the convenience brought by cloud computing, internet users, meanwhile, are faced with risks of data theft, tampering, forgery, etc. Fully homomorphic encryption (FHE) has the ability to deal with the ciphertext directly, which can solve the problem of data security in cloud computing. Therefore, fully homomorphic encryption (FHE) has been widely used in cloud computing as well as multiparty computing, functional encryption and private information retrieval, etc. However, previous FHE schemes are based on standard (ring) learning with errors (LWE) assumption and the most typical schemes were created by Braker-ski (CRYPTO2012) and Gentry-Sahai-Waters (GSW) (CRYPTO2013). Moreover, inspired by the work of Li et al. at ICPADS2016, they made use of Brakerski's scale-invariant technology and constructed a new FHE scheme with errorless key switching under Dual-First-is-errorless LWE (Dual-Ferr.LWE) problem. Hence, armed with Li et al.'s work, in this paper, we use Gentry-Peikert-Vaikuntanathan's scheme (i.e., under dual LWE assumption) as building block to construct a FHE scheme. Lastly, under the assumption of decisional learning with errors (LWE), we prove that our scheme is CPA (chosen-plaintext-attack) secure.
机译:尽管云计算带来了便利,但互联网用户同时面临着数据被盗,篡改,伪造等风险。全同态加密(FHE)具有直接处理密文的能力,可以解决数据问题。云计算中的安全性。因此,完全同态加密(FHE)已被广泛用于云计算以及多方计算,功能加密和私有信息检索等。但是,以前的FHE方案基于错误的标准(ring)学习(LWE)假设和最典型的方案是由Braker-ski(CRYPTO2012)和Gentry-Sahai-Waters(GSW)(CRYPTO2013)创建的。此外,受到李等人工作的启发。在ICPADS2016上,他们利用了Brakerski的尺度不变技术,构建了一种新的FHE方案,该方案具有在双重优先无错误LWE(Dual-Ferr.LWE)问题下进行无误密钥切换的功能。因此,根据Li等人的工作,在本文中,我们使用Gentry-Peikert-Vaikuntanathan的方案(即在双重LWE假设下)作为构建FHE方案的基础。最后,在带有错误的决策学习(LWE)的假设下,我们证明了我们的方案是CPA(选择明文攻击)的安全性。

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