TC: Small: Collaborative Research: Implications of Fully Homomorphic Encryption

最近，Gentry等人证明了构造完全同态加密方案的可行性。简而言之，完全同态加密(FHE)方案是允许具有多个消息的密文的第三方在不知道解密密钥的情况下构造对应于应用于原始消息的任意高效可计算函数的新密文的方案。完全同态加密有可能允许不同的组织在其汇集的数据集上计算基本函数，而不会向彼此透露此类数据。因此，这是实现“需要知道”隐私的最终解决方案。在詹特的发现之前，很少有研究人员相信FHE是可以构建的。因此，尽管这一概念显然具有以保护隐私的方式解决重要任务的潜力，但它还没有得到很好的研究。特别是，FHE和传统公钥密码术之间的基本关系仍然不清楚。本研究项目的目标是形式化这种关系，建立满足更强的安全保证的FHE概念，例如即使当对手可以访问受限的解密神谕时也满足安全，并潜在地使用这些更强的安全保证来应用于安全和隐私保护计算。为了确保研究产生更广泛的影响，该项目包括指导从本科生到博士后的各级学生，并向传统上代表性不足的学生和K-12学生开展外联活动。该项目的研究成果将通过在会议、期刊和互联网上发表的演讲和出版物进行传播。

Recently, Gentry and others have established the feasibility of constructing fully homomorphic encryption schemes. Briefly, a fully homomorphic encryption (FHE) scheme is one that allows a third-party who has ciphertexts of several messages to construct---without knowing the decryption key---a new ciphertext that corresponds to an arbitrary efficiently computable function applied to the original messages. Fully homomorphic encryption has the potential to allow disparate organizations to compute basic functions on their pooled data-sets without revealing such data to each other. It is thus an ultimate solution for implementing ``need-to-know'' privacy. Until Gentry's discovery, few researchers believed that FHE could be constructed. As a result, the concept has not been well-studied despite its clear potential to solve important tasks in a privacy-preserving manner. In particular, the basic relationship between FHE and traditional public-key cryptography remains unclear. The goals of this research project are to formalize this relationship, to build notions of FHE that satisfy stronger security guarantees such as security even when the adversary has access to a restricted decryption oracle, and to potentially use these stronger security guarantees to apply FHE in secure and privacy preserving computation. To ensure the broader impact of the research, this project includes mentoring of students at all levels from undergraduate to post-doctoral and outreach activities to traditionally under-represented students and K-12 students. Research from this project will be disseminated through presentations and publications in conferences, journals and on the Internet.