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Lattice-based completely non-malleable public-key encryption in the standard model

机译：标准模型中基于格的完全不可恶意的公钥加密

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摘要

An encryption scheme is non-malleable if giving an encryption of a message to an adversary does not increase its chances of producing an encryption of a related message (under a given public key). Fischlin introduced a stronger notion, known as complete non-malleability, which requires attackers to have negligible advantage, even if they are allowed to transform the public key under which the related message is encrypted. Ventre and Visconti later proposed a comparison-based definition of this security notion, which is more in line with the well-studied definitions proposed by Bellare et al. The authors also provide additional feasibility results by proposing two constructions of completely non-malleable schemes, one in the common reference string model using non-interactive zero-knowledge proofs, and another using interactive encryption schemes. Therefore, the only previously known completely non-malleable (and non-interactive) scheme in the standard model, is quite inefficient as it relies on generic NIZK approach. They left the existence of efficient schemes in the common reference string model as an open problem. Recently, two efficient public-key encryption schemes have been proposed by Libert and Yung, and Barbosa and Farshim, both of them are based on pairing identity-based encryption. At ACISP 2011, Sepahi et al. proposed a method to achieve completely non-malleable encryption in the public-key setting using lattices but there is no security proof for the proposed scheme. In this paper we review the mentioned scheme and provide its security proof in the standard model. Our study shows that Sepahi's scheme will remain secure even for post-quantum world since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best known classical (i.e., non-quantum) algorithms.
机译：如果将消息加密给对手不会增加其对相关消息进行加密的机会（在给定的公共密钥下），则加密方案是不可恶意的。 Fischlin引入了一个更强的概念，即完全的不可恶意攻击性，它要求攻击者具有微不足道的优势，即使允许他们转换用来加密相关消息的公钥也是如此。 Ventre和Visconti随后提出了该安全概念的基于比较的定义，这与Bellare等人提出的经过充分研究的定义更加一致。通过提出两种完全不可恶意的方案的构造，作者还提供了其他的可行性结果，一种是在公共参考字符串模型中使用非交互式零知识证明，另一种是使用交互式加密方案。因此，标准模型中唯一已知的完全不可恶意（且非交互式）的方案效率低下，因为它依赖于通用的NIZK方法。他们将有效的方案留在通用参考字符串模型中作为一个开放问题。最近，Libert和Yung以及Barbosa和Farshim提出了两种有效的公钥加密方案，它们都基于基于配对身份的加密。在ACISP 2011上，Sepahi等人。提出了一种使用晶格在公钥设置中实现完全不可恶意加密的方法，但是该方案没有安全性证明。在本文中，我们回顾了上述方案，并在标准模型中提供了其安全性证明。我们的研究表明，即使对于后量子世界，Sepahi的方案也将保持安全性，因为目前尚无解决比最著名的经典（即非量子）算法性能更好的解决晶格问题的量子算法。

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