Cryptographic primitives and error control coding

该方案的第一部分是关于同态加密和散列函数密码学的基本原语的研究。同态加密系统在众多重要的密码协议中有着广泛的应用。将开发新的同态加密系统，以期使其在某些安全多方计算协议中的应用更加有效。散列函数是许多常用密码协议(例如数字签名)的重要组成部分。目前使用的大多数此类功能速度都很快，但缺乏安全证明。目前为数不多的具有某种形式安全性证明的散列函数往往依赖于复杂的数学，并且速度非常慢。建议的研究将调查可能的技术来制定一个新的函数，具有某种形式的安全证明，并提高速度。

The first part of the proposal is concerned with the investigation of the fundamental primitives of cryptography of homomorphic encryption and hash functions. Homomorphic encryption systems find wide application in numerous important cryptographic protocols. New homomorphic encryption systems will be developed with a view to making their application to certain secure multiparty computation protocols more efficient. Hash functions are an essential part of many commonly used cryptographic protocols such as digital signatures. Most currently used such functions are fast but lack a security proof. The few currently known hash functions that have some form of security proof tend to rely on sophisticated mathematics and are very slow. The proposed research will investigate possible techniques to formulate a new function that has some form of security proof and improves on the speed.