弱随机源下的密码方案研究

Random numbers play vital roles in cryptosystems, as randomness is an important guarantee for the security of cryptosystems. However, randomness may be of bad quality in practice due to various reasons. As a result, cryptosystems that are based on the assumption of perfect and unbiased randomness can be completely insecure under bad or weak randomness..This project aims to investigate the constructions of cryptosystems which are secure under weak randomness. It includes the following contents: .1. to develop in the standard model public key and identity-based encryption algorithms that are secure under a weak randomness source by utilizing some primitives such as lossy trapdoor function, identity-based hash proof system, dual encryption system and Déjà Q reduction technique;.2. to develop cryptographic schemes resilient to the simultaneous leakage of secret-key and randomness based on updatable hash proof system and lossy encryption;.3. to investigate secure cryptographic protocols under weak randomness using some primitives such as UC-framework, deterministic public-key encryption and hedged public-key encryption;.4. to propose identity-based lossy trapdoor functions by employing a number of primitives such as lossy trapdoor function, lossy encryption, nonce-based cryptography, hedged extractor, dual encryption systems and Deja Q reduction techniques..The fruits of the proposed research will promote and enrich the traditional cryptosystems. This project is of great significance in both theory and practice.

随机数在密码方案中扮演着至关重要的角色，其随机性是密码方案安全性的重要保证。而在实际应用中使用的随机数的质量会受到很多因素的影响，造成随机数质量的下降，出现弱随机环境，从而导致以完美随机数为前提的密码方案可能被完全攻破。.本项目研究弱随机环境下的密码方案，具体内容包括：（1）利用损耗陷门函数、基于身份的哈希证明系统、对偶系统加密、Deja Q归约技术，研究在弱随机源下标准模型的加密方案与基于身份的加密方案；（2）利用可更新的哈希证明系统和损耗加密方案，研究抵抗随机数和密钥同时泄露的密码方案；（3）利用UC定理、确定性公钥加密和对冲公钥加密，研究基于弱随机源的密码协议；（4）利用损耗陷门函数、损耗加密、时标技术与对冲提取器、对偶系统加密、Deja Q归约技术等，研究基于身份的损耗陷门函数。.项目的研究成果将推广和丰富传统上的密码方案，选题具有重要的理论意义和实用价值。

随机数在密码方案中扮演着至关重要的角色，其随机性是密码方案安全性的重要保证。而在实际应用中使用的随机数的质量会受到很多因素的影响，造成随机数质量的下降，出现弱随机环境，从而导致以完美随机数为前提的密码方案可能被完全攻破。针对上述问题，本项目研究了弱随机环境下的密码方案，主要贡献包括：.（1）在弱随机源下，设计了标准模型的加密方案与基于身份的加密方案；.（2）设计了抵抗随机数和密钥同时泄露的密码方案；.（3）设计了确定性密码机制的具体构造；.（4）设计了基于身份的损耗陷门函数的具体构造。.研究成果具有重要的理论意义和实用价值。