Multi-Party Cryptosystem Based On Braid Group

Cryptography is a science that studies the deformation,concealment and legal reproduction of information to prevent the third party from stealing information.In recent years,the combination of cryptography and non-commutative algebra has made the development of cryptography rapidly.There are many difficult assumptions on braid groups that can be used to construct the cryptographic process.Because of its unique algebraic structure,braid groups have become an effective bridge between algebra and cryptography.For example,there have been many related researches on the cryptosystem based on the conjugate problem on braid groups.In this thesis,according to the various applications of the braid group's difficult assumptions in the existing cryptosystem,we consider to combine the different difficult assumptions on the braid group to construct a more secure and effective cryptosystem and extend it to the multi-party construction of the cryptographic process.The conjugate problems and the cycling problems on the braid group are closely intertwined,the cycling problems can be shown as a special kind of more complex conjugate problems.In this thesis,the key exchange process among three parties is constructed by using the conjugate problem and the cycling problem on the braid group,and then the cryptographic process is extended to design the cryptographic process among many parties.Finally,the process of provably security cryptosystem is constructed by combining the two kinds of difficult problems and then applied to the signature scheme.