Research On Signature Algorithm Based On Cryptographic Hash Function

As a major component of post-quantum cryptography,signature algorithms based on cryptographic hash functions are the most attractive "answer" in the post-quantum era.Compared to other post-quantum signature algorithms,such as lattice-based signature algorithms,code-based signature algorithms,and signature algorithms based on homomorphic cryptosystems,hash-based signatures have the advantages of fast operation,short signature and key length.Through research and analysis of cutting-edge signature schemes based on hash algorithms,this thesis proposes three signature algorithms based on cryptographic hash algorithms to address the problems of traditional signature schemes,such as vulnerability to quantum attacks,excessively long keys for one-time signatures,and the need to improve the robustness of multi-signatures.The specific signature algorithms are as follows:(1)To address the problem of traditional digital signature algorithms’ vulnerability to quantum attacks,this thesis proposes a one-time group signature algorithm based on cryptographic hash functions.The algorithm mainly includes the generation of signature keys,the generation of group public keys,the signature process,and the verification process,and only uses hash algorithms.The security proof and theoretical efficiency analysis of the protocol demonstrate that the algorithm has unforgeability,nonrepudiation,anonymity,and high efficiency.(2)To address the problem of excessively long keys for one-time signatures,a onetime signature algorithm with authentication function is designed based on the data structure of the authenticated tree using a prefix Chameleon cryptographic hash function.This algorithm can achieve multiple {i,j} range queries.The security of the protocol relies on the structural integrity and one-wayness of the prefix Chameleon cryptographic hash function authenticated tree.The security proof of the algorithm demonstrates that it is unforgeable under adaptive chosen-plaintext attacks.Through theoretical efficiency analysis and comparison,the algorithm has high efficiency and can achieve verifiable range queries in data streams.(3)To address the issue of improving the robustness of multi-signatures,a chameleon hash function-based identity-based multi-signature algorithm is proposed.The protocol is divided into nine parts: system setup,probabilistic algorithm,public key generation,private key generation,group public key generation,aggregate public key generation,group signature,aggregate signature,and multi-signature.The security of the protocol can be reduced to the computational Diffie-Hellman(CDH)assumption,and the security proof of the algorithm shows that it is unforgeable and robust under adaptive chosen message attacks.