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量子计算的发展给经典公钥密码系统的安全性构成了严重威胁,因此探索新的公钥密码平台、设计新的可抵抗量子攻击的密码方案成为信息安全理论的前沿课题.辫群密码系统是具有抵抗量子攻击潜力的密码系统之一.本文分析了基于辫群的密码学的研究现状,提出了辫群上的新密码学难题——共轭链接问题.基于此问题,本文构造了一种新的基于辫群的数字签名方案.该方案不仅高效,而且在随机预言模型下具有可证明安全性.本文亦将基于辫群的签名方案与基于RSA的签名方案做了对比.结果表明:基于辫群的签名方案的签名效率要远远高于基于RSA的方案,但是签名的验证过程较慢,因此适合于那些签名需要迅速完成而验证可以相对延迟的应用场景(如离线电子货币系统).此外,基于辫群的密码系统的密钥长度较大——私钥约2K比特位,公钥约12K比特位.相对于模指数等运算而言,辫群运算非常简单,因此可以考虑在那些计算能力相对较低而存储空间不太紧的设备上使用.最后,本文也从隐藏子群问题的角度对辫群密码系统抵抗现有量子攻击的能力进行了讨论.
The development of quantum computing poses a serious threat to the security of classical public-key cryptosystems. Therefore, exploring new public-key cryptosystem and designing new cryptosystems that can resist quantum attacks have become the forefront topic of information security theory. One of the cryptosystems with the potential of resisting quantum attacks.This paper analyzes the research status of cryptography based on braid group and proposes the new cryptography puzzle-conjugate linking problem on braid group.Based on this problem, this paper constructs a The new scheme based on braid group is not only efficient but also provably secure under random prediction model.This paper also compares the signature scheme based on braid group with the RSA-based signature scheme.The results show that: Signature schemes for braid groups are much more efficient than RSA-based schemes, but their signature verification process is slow, making them suitable for scenarios where signatures need to be completed quickly and verification can be relatively delayed (such as offline electronic monetary systems). In addition, the key length of the plait group-based cryptosystem is larger - about 2K bits for the private key and about 12K bits for the public key. In summary, the braid group operation is very simple, so it can be considered on those devices with less computing power and less storage space.Finally, this paper also discusses how the braid group cryptosystem can resist the existing The ability of quantum attacks is discussed.