Design And Analysis Of Three Signature Schemes

With the arrival of the Internet Information Age,electronic information has become the main carrier of communication and interaction in today's society.Under such environment and actual need,the digital signature for electronic information has gradually become more and more important.Because of its advantages of identity authentication,data integrity,non-repudiation,etc.,digital signature technology plays an important role in the field of information security.The digital signature also generates various special signatures in order to meet the special needs of users.For instance,proxy signature scheme is a kind of digital signature scheme that the original signer delegates his signing right to the proxy signer for some reason.Ring signature scheme is another kind of digital signature scheme that the signer wants to achieve the purpose of anonymous signing.Symmetric cryptosystem has its advantages of low computational cost,simple algorithm,and fast encryption speed.However,since both the encryption key and the decryption key in the symmetric cryptosystem are identical,resulting in poor openness,the two parties need to pass this key through a very reliable channel before communication and the key must also be kept properly.Digital signature schemes require public keys for ident.ity authentication.Naturally,symmetric cryptosystems can not be used for digital signatures.Diffie and Hellman broke the limitation of symmetric cryptosystem for the first time in an article about the new direction of cryptography in 1976,and put forward the concept of public key cryptosystem([1]).The user's key in the public key cryptosystem appears in pairs and is divided into a public key(public)and a private key(stored by the user).Then public key cryptosystem has become the basis for cryptographers to design digital signature schemes.In 2003,Al-Riyami and Paterson proposed a certificateless public key cryptosystem([3]).The certificateless public key cryptosystem has no certificate,so it can solve the problem of certificate management cost in the traditional public key cryptosystem.Moreover,the key generation center of the certificateless public key cryptosystem can only generate part of the private key for the user,thus avoiding the problem that the private key generation center of the identity-based public key cryptosystem generates all the private keys of the user and thus leads to excessive rights.This paper first designs a new ring signature scheme under the certificateless public key cryptosystem.In terms of safety,with the random oracle model,we show that our certificateless ring signature is unforgeable against adaptive chosen message attacks under the assumption that the computational Diffie-Hellman(CDH)problem and computational co-Diffie-Hellman(co-CDH)are intractable.In terms of efficiency,our certificateless ring signature scheme uses only three bilinear operations during the signature verification phase,and its design is more efficient.Secondly,this paper also makes a new structure for the proxy ring signature scheme.In terms of safety,with the random oracle model,we prove that our proxy ring signature is unforgeable against adaptive chosen message attacks under the assumption that the discrete logarithm problem(DLP)of an elliptic curve group is intractable.In terms of efficiency,the biggest feature of our proxy ring signature scheme is that it does not use bilinear pairings.In the stage of signature verification,we use hash function which has little operation time to complete.In this way,the efficiency of our scheme will be greatly improved.We know that the security of digital signature technology is based on the difficult degree of hard problems about mathematics,such as the factorization problems of large numbers,discrete logarithm problems and so on.However,the theory of quantum computing can seriously threaten the security of these difficult problems.Therefore,the security of traditional digital signatures has been severely challenged.In order to resist the crisis that quantum computers bring to digital signatures,the theory of quantum cryptography came into being([86]).Quantum signature scheme makes use of the basic principle of quantum mechanics and is combined with the knowledge of cryptography.The current quantum signature schemes have been proved to be unconditionally safe in theory.Finally,this paper designs a new arbitration quantum signature scheme(AQS).The thinking process is as follows.Liu et al.improved the quantum one-time pad algorithm(QOIP)into a new quantum one-time pad algorithm(T-QOTP)in the text[113],and designed an arbitration quantum signature scheme using the new quantum one-time pad algorithm(T-QOTP).Xu and Zou pointed out in the literature[115]that Liu et al.'s AQS scheme had a denial of the signer and receiver's existence forgery attack.The analysis of Xu and Zou showed that the main reason for the security attacks of Liu et al.'s scheme was that the arbitrator Trent could not judge the reliability of the message.Our paper combining QOTP algorithm with T-QOTP algorithm to encrypt the quantum message can deal with this key problem.Thus it can make up for the security attacks that exist in Liu et al.'s AQS scheme.Our AQS scheme also remains all the features of the original Liu et al.'s scheme.