CAREER: Efficient Cryptography with Provable Security Guarantees

本研究开发了有效的密码工具，提供可证明的安全保证。这些工具纠正了与现存的可证明安全的密码系统相关的广泛认识到的缺陷：它们过高的计算需求。 事实上，尽管可证明安全的系统提供了高度放大的安全性，但效率方面的考虑阻止了它们的广泛采用;因此，常用的工具通常涉及以速度而不是安全性为首要任务的特设方法。 本研究解决了这一难题，构建密码工具（如加密引擎，数字签名方案和伪随机发生器），可以同时拥有可证明的安全保证和竞争力的效率。该计划与康涅狄格大学开发安全和通用信息技术课程材料的教育计划相一致。 可证明安全构造中的安全性通常通过重复应用某些底层密码原语（例如单向函数）来积累。对于一个固定的底层原语，“生成足够的安全性”所需的计算时间，比如说，加密一条长消息，本质上取决于（i）可以从底层原语的单个应用中快速提取的证券的数量，以及（ii.）加密过程所需的安全性总量。 本研究解决了这两个问题，开发可证明安全的密码学框架，充分利用底层原语的安全能力，并以最有效的方式利用这种提炼的安全性。是解决的单向函数的安全能力和边界上的计算复杂性提取一般单向函数的安全性的定量界限的发展。 问题（二）是解决了一个新的家庭的密码原语的发展，平衡可证明的安全性和竞争力的效率。对于加密，研究的重点，这是通过耦合强（信息理论）伪随机结构与语义安全的加密机制。这种方法可直接应用于加密、密码学上的强散列和伪散列。

This research develops efficient cryptographic tools which offer provable security guarantees. Such tools rectify the widely-recognized deficiency associated with extant provably-secure cryptosystems: their prohibitive computing demands. Indeed, despite the highly amplified security offered by provably-secure systems, efficiency considerations have prevented their widespread adoption; as a result, tools in common use typically involve ad-hoc methods designed with speed, rather than security, as their first priority. This re-search resolves this difficulty, constructing cryptographic tools (like encryption engines, digital signature schemes, and pseudo-random generators) which can simultaneously boast provable security guarantees and competitive efficiency. This program is undertaken in concert with an educational initiative which develops security and general information technology course material at the University of Connecticut. Security in provably-secure constructions is generally accumulated by repeated application of some underlying cryptographic primitive (a one-way function, for example). For a fixed underlying primitive, the computing time required to "generate enough security" to, say, encrypt a long message, depends essentiallyon (i.) the quantity of security which can be quickly extracted from a single application of the underlying primitive, and (ii.) the total quantity of security necessary for the encryption process. This research ad-dresses both of these issues, developing provably-secure frameworks for cryptography which fully exploit the security capacity of underlying primitives and utilize this distilled security in the most effective manner.Issue (i.) is addressed by the development of quantitative bounds for the security capacity of one-way functions and bounds on the computational complexity of extracting security from general one-way functions. Issue (ii.) is addressed by the development of a new family of cryptographic primitives, balancing provable security and competitive efficiency. For encryption, a focal point of the research, this is attained by coupling strong (information-theoretic) pseudo-random constructions with semantically secure encryption machinery. Such methods have direct applicability to encryption, cryptographically strong hashing, and pseudo