Cryptographic primitives and error control coding

第一部分研究了密码学的基本基元，包括同态加密和哈希函数。同态加密系统在许多重要的密码协议中有着广泛的应用。新的同态加密系统将被开发，以使其更有效地应用于某些安全的多方计算协议。哈希函数是许多常用加密协议（如数字签名）的重要组成部分。目前使用的大多数这类函数速度很快，但缺乏安全证明。目前已知的几种具有某种形式的安全证明的散列函数往往依赖于复杂的数学，并且速度非常慢。提议的研究将研究可能的技术来制定一个具有某种形式的安全证明并提高速度的新函数。

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.