In addition, this sub-team hopes the incoming VIP sub-teams would make use of this report and expand upon our research into homomorphic encryption. In this report, we build on previous Georgia Tech VIP works of and illustrate various lattice-based encryption schemes and brie y describes how Gentry used lattice-based cryptography to construct the first fully homomorphic encryption scheme. Lattice-based cryptography still lies at the heart of many fully homomorphic encryption schemes. In Gentry's original implementation, lattice-based cryptography is used as a basis of the Homomorphic encryption scheme. In 2009, Gentry proposed the first plausible algorithm for fully homomorphic encryption and various improvements have been built upon this result, significantly increasing the efficiency of homomorphic encryption. While the algorithm is still not efficient enough for practical applications, homomorphic encryption has potential in many areas such as voting, storage of sensitive personal information, and analyzing demo-graphical data. Homomorphic encryption is a type of encryption that allows performing operation on the ciphertext without having access to the plaintext. Additionally, we discuss future research areas that are essential for the continued development of lattice-based cryptography. In this paper we focus on recent developments and the current state-of-the-art in lattice-based digital signatures and provide a comprehensive survey discussing signature schemes with respect to practicality. Due to significant research advancements in recent years, lattice-based schemes have now become practical and appear to be a very viable alternative to number-theoretic cryptography. A potential alternative approach is the construction of signature schemes based on the hardness of certain lattices problems which are assumed to be intractable by quantum computers. In the case of classical cryptanalytic advances or progress on the development of quantum computers the hardness of these closely related problems might be seriously weakened. He received a PhD from the University of Pisa in 1961. However, almost all popular signature schemes are either based on the factoring assumption (RSA) or the hardness of the discrete logarithm problem (DSA/ECDSA). Can you list the top facts and stats about Carlo Ginzburg Summarize this article for a 10 years. Digital signatures are an important primitive for building secure systems and are used in most real world security protocols.
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