中文摘要：

安全两方比较大小是保密计算的一个特例和基本模块，在移动代码和电子商务安全中有重要应用。当前的解决方案存在较高计算和通信开销、比较数的范围有限等缺点。基于修改的ElGamal算法提出并证明了乘法、混合乘法、加法和减法同态加密系统。用同态加密系统双方共同构建一个双方都未知的保密函数，基于此保密函数和同态加密系统设计了半诚实模型下安全两方比较协议。证明、实例和与其他协议比较表明其具有安全性、公平性、低的计算和通信开销、秘密比较整数等特点。

英文摘要：

Secure two-party comparing is a special case and a basic module of secure computations, and is applied in mobile code and e-commerce security etc. But known solutions have some disadvantages ： expensive costs of computing and communicating, limited ranges of compared numbers. Based on a modified ElGamal algorithm, this paper presented and proved muhiplicative, mixed-muhiplicative, additive and subtraetive homomorphic cryptosystem. Constructed an encrypted function unknown by two-party using the homomorphic cryptosystem. Based on the homomorphic cryptosystem and evaluation of encrypted functions, designed secure two-party comparing protocol under semi-honest model, proof, example and comparing with other protocols show the proposed protocol has the merits of security, fairness, lower costs of communication and computational complexity, and comparing integers.