Cryptographic primitives and error control coding

该提案的第一部分涉及同态加密和哈希函数的密码学的基本原语的调查。同态加密系统在许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，以便使它们在某些安全多方计算协议中的应用更有效。哈希函数是许多常用的加密协议（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很快，但缺乏安全性证明。目前已知的几个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，并且非常慢。拟议的研究将调查可能的技术，以制定一个新的功能，具有某种形式的安全证明，并提高了速度。 对于建议的第二部分，将考虑擦除信道的随机编码技术的进一步性质。这样的系统已经证明对于多播互联网下载非常有用，其中符号擦除对应于分组丢失。对于二进制情况，具有线性复杂度（在信息符号的数量上）编码和解码技术的系统是可用的，尽管在实现方面具有限制。非二进制系统将被调查，有可能提高性能和效率方面的收敛速度和简单的实施。

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. For the second part of the proposal, further properties of random coding techniques for the erasure channel will be considered. Such systems have proved very useful for multicast internet downloads where a symbol erasure corresponds to a packet loss. Systems that have linear complexity (in the number of information symbols) encoding and decoding techniques, for the binary case, are available although have limitations in terms of implementation. Nonbinary systems will be investigated that have the potential to improve performance and efficiency in terms of speeds of convergence and simplicity of implementation.