Real-time, online-editing web apps provide free and convenient services for collaboratively editing, sharing and storing files. The benefits of these web applications do not come for free: not only do service providers have full access to the users' files, but they also control access, transmission, and storage mechanisms for them. As a result, user data may be at risk of data mining, third-party interception, or even manipulation. To combat this, we propose a new system for helping to preserve the privacy of user data within collaborative environments. There are several distinct challenges in producing such a system, including developing an encryption mechanism that does not interfere with the back-end (and often proprietary) control mechanisms utilized by the service, and identifying transparent code hooks through which to obfuscate user data. Toward the first challenge, we develop a character-level encryption scheme that is more resilient to the types of attacks that plague classical substitution ciphers. For the second challenge, we design a browser extension that robustly demonstrates the feasibility of our approach, and show a concrete implementation for Google Chrome and the widely-used Google Docs platform. Our example tangibly demonstrates how several users with a shared key can collaboratively and transparently edit a Google Docs document without revealing the plaintext directly to Google.
@cite_5: We describe two improvements to Gentry’s fully homomorphic scheme based on ideal lattices and its analysis: we provide a more aggressive analysis of one of the hardness assumptions (the one related to the Sparse Subset Sum Problem) and we introduce a probabilistic decryption algorithm that can be implemented with an algebraic circuit of low multiplicative degree. Combined together, these improvements lead to a faster fully homomorphic scheme, with a O(λ 3.5) bit complexity per elementary binary add mult gate, where λ is the security parameter. These improvements also apply to the fully homomorphic schemes of Smart and Vercauteren [PKC’2010] and van [Eurocrypt’2010].
@cite_14: We construct a simple fully homomorphic encryption scheme, using only elementary modular arithmetic. We use Gentry’s technique to construct a fully homomorphic scheme from a “bootstrappable” somewhat homomorphic scheme. However, instead of using ideal lattices over a polynomial ring, our bootstrappable encryption scheme merely uses addition and multiplication over the integers. The main appeal of our scheme is the conceptual simplicity. We reduce the security of our scheme to finding an approximate integer gcd – i.e., given a list of integers that are near-multiples of a hidden integer, output that hidden integer. We investigate the hardness of this task, building on earlier work of Howgrave-Graham.
@cite_10: 
@cite_23: We propose the first fully homomorphic encryption scheme, solving an old open problem. Such a scheme allows one to compute arbitrary functions over encrypted data without the decryption key—i.e., given encryptions E(m1), ..., E( mt) of m1, ..., m t, one can efficiently compute a compact ciphertext that encrypts f(m1, ..., m t) for any efficiently computable function f. Fully homomorphic encryption has numerous applications. For example, it enables encrypted search engine queries—i.e., a search engine can give you a succinct encrypted answer to your (boolean) query without even knowing what your query was. It also enables searching on encrypted data; you can store your encrypted data on a remote server, and later have the server retrieve only files that (when decrypted) satisfy some boolean constraint, even though the server cannot decrypt the files on its own. More broadly, it improves the efficiency of secure multiparty computation. In our solution, we begin by designing a somewhat homomorphic "boostrappable" encryption scheme that works when the function f is the scheme's own decryption function. We then show how, through recursive self-embedding, bootstrappable encryption gives fully homomorphic encryption.
There are also a number of methods of ensuring data confidentiality with the help of the cloud provider, most notably based on the use of fully-homomorphic encryption (see, for example, @cite_23 @cite_14 @cite_5 @cite_10 , although there is a wealth of additional literature within their citations and reverse-citations). These methods aim to have the server agnostically compute functions of a user's data, and they are aimed toward an honest-but-curious provider. Our approach does not require any server-side modifications while maintaining transparency to the user or multiple collaborating users. We also avoid the heavy computational machinery required for these schemes.