Proxy Signature Scheme Based On Braid Group

Digital signature, one of the important issue of cryptology, can be used to protect data integrity and authentiacate the identity of the sender of a message. Proxy signature is one special signature, such a scheme allows one signer, called original siger, to delegate his signing capability to another siger, called proxy signer. After that, the proxy signer can sign messages on behalf of the original signer. Public-key cryptosystem can gain a considering attention bacause it can assure the secuity requirements of many application.Since public-key cryptosystem was presented, most of successful public-key cryptosystems are based on number theory. The difficulty of factorization of integers with large prime factors forms the ground of RSA, and the difficulty of the discrete logarithm problem forms the ground of ELGmal. Different from the cryptosystems as above, cryptosystem presented in this paper is based on braid groups in combinatorial groups.The braid groups, one of infinite non-commutative groups, can be finitely represented. The feature makes the braid groups useful in cryptography in the followings: the word problem is solved via a fast algorithm which computes the canonical form which can be efficiently manipulated by computers, the groups operations can be performed efficiently, the braid groups have many mathematically hard problems that can be utilized to design cryptographic primitives. So braid groups have been used recently as a new soure for pulic-key cryptography.In this paper, we propose the first proxy signature scheme based on the conjugacy problem, multiple simultaneous conjugacy problem, and root problem, which are belived to be hard problems in braid groups, and anlyze the the security of the scheme.