论文标题
基于晶格的密码学和同态加密的教程简介
A Tutorial Introduction to Lattice-based Cryptography and Homomorphic Encryption
论文作者
论文摘要
为什么研究基于晶格的密码学？有几种方法可以回答这个问题。 1。拥有基于各种硬计算问题的密码系统很有用，因此不同的密码系统并非都以相同的方式易受伤害。 2。基于晶格的密码系统的计算方面通常简单地理解，并且在实践中易于实现。 3。基于晶格的密码系统与基于整数分解或离散对数问题的流行密码系统相比，具有较低的加密/解密计算复杂性。 4。基于晶格的密码系统，基于已知的NP-HARD晶格问题的大致版本，享有强烈的最差硬度安全性证明。 5。基于格子的密码系统被认为是量词后加密术的好候选者，因为目前尚无已知的量子算法来解决晶格问题，这些问题比integer cressation and（elliptic curve curve curve and eyliptic curve corverme niverge gorage cormession comploce comploce comploce complation and Integer ance and iNtecriate ance comploce comploys comploce comploce complocy complocy complocy。 6。最后但并非最不重要的一点是，晶格问题中有趣的结构导致了同态加密的重大进步，这是一个具有广泛应用的新研究领域。
Why study Lattice-based Cryptography? There are a few ways to answer this question. 1. It is useful to have cryptosystems that are based on a variety of hard computational problems so the different cryptosystems are not all vulnerable in the same way. 2. The computational aspects of lattice-based cryptosystem are usually simple to understand and fairly easy to implement in practice. 3. Lattice-based cryptosystems have lower encryption/decryption computational complexities compared to popular cryptosystems that are based on the integer factorisation or the discrete logarithm problems. 4. Lattice-based cryptosystems enjoy strong worst-case hardness security proofs based on approximate versions of known NP-hard lattice problems. 5. Lattice-based cryptosystems are believed to be good candidates for post-quantum cryptography, since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best-known classical (non-quantum) algorithms, unlike for integer factorisation and (elliptic curve) discrete logarithm problems. 6. Last but not least, interesting structures in lattice problems have led to significant advances in Homomorphic Encryption, a new research area with wide-ranging applications.
