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提出一种满足强安全要求且安全归约紧致的认证密钥交换协议,协议安全性可归约到标准的大整数分解假设.协议的实现基于带符号二次剩余群,且协议的安全性可归约到SDH假设.由于带符号二次剩余群上存在从SDH假设到大整数分解假设的归约,因此该协议的安全性可最终归约到标准的大整数分解假设.其次,协议的安全性分析基于PACK模型.该模型允许攻击者同时发起Session State Reveal与Ephemeral Key Reveal,刻画了能力更为强大的攻击者.分析、证明显示该协议能够满足PACK模型的安全需求,因此,该协议体现出更好的安全性.此外,该协议的安全性证明满足紧致性,即无需使用分叉引理.与相关协议对比显示,该协议达到了相当的高效性,提供紧致的安全证明,而协议安全分析所基于的假设更弱,安全分析使用的模型更强,因而该协议在效率与安全性上达到了更好的平衡.
This paper proposes a certified key exchange protocol that satisfies the strong security requirements and reduces the security to compactness.The protocol security can be reduced to the standard big integer decomposition assumption.The implementation of the protocol is based on the signed quadratic residue group and the protocol security Can be reduced to the SDH hypothesis.The security of this protocol can be finally reduced to the standard large integer decomposition hypothesis due to the existence of the reduction from the SDH assumption to the big integer decomposition assumption on the signed quadratic residual group.Secondly, Security analysis is based on the PACK model, which allows attackers to launch both the Session State Reveal and the Ephemeral Key Reveal, portraying a more capable attacker, and analyzes and proves that the protocol meets the security requirements of the PACK model. Therefore, the protocol In addition, the security of this protocol proves that the compactness is satisfied, that is, no need to use bifurcated leapfrog.Compared with the related protocols, the protocol achieves considerable efficiency and provides a compact security certificate , While protocol security analysis is based on a weaker assumptions and a more robust security analytics model so that the protocol achieves a better balance of efficiency and security.