Research On Multi-Signature Scheme Based On Obfuscation

Multi-signature is a kind of digital signature,which is signed by multiple signers on the same message then composed a Multi-signature.In real life,Multi-signature is widely used in many fields,such as electronic contract signing,educational management system,performance management system and expert consultation.Since the Multi-signature has been proposed,many scholars proposed a variety of Multi-signature schemes.There are two main kinds of Multi-signature schemes.One is based on the traditional difficult problem.The other is based on quantum cryptography.The former scheme have a high efficiency but not able to resist the quantum attack.And the latter Multi-signature scheme could resist the quantum attack but with poor stability.With the high-speed development of quantum computers,it is urgent to propose a Multi-signature scheme with stability property and anti quantum attack.Obfuscation is an advanced cryptographic primitive.Since Barak proposed the formal definition of obfuscation in 2001,the study of obfuscation has become a hot topic in the field of cryptography.The obfuscation of specific function classes is a major direction of obfucation research.For instance,Hohenberger proposed obfuscator with the re-encryption function,Hada proposed secure obfuscation for encrypted signatures.This kind of obfuscation has the high practicability and the high security.This paper focuses on Multi-signature and obfuscation.In the field of Multi-signature and obfuscation,the following results have obtained :(1)Based on the indistinguishability obfuscation,which is based on the LWE problem on the lattice Lin proposed in 2016.This paper proposes a new broadcast Multi-signature scheme and provides a strict security proof.This scheme uses the obfuscated program as a verification key that can ensure the scheme safety.By comparing with other schemes,the advantages and disadvantages of this scheme are analyzed.This scheme has been proven to possess the property of unforgeability and anti quantum attack.(2)Based on the RSA digital signature and Boneh linear encryption technology.This paper proposes a Encrypted Multi-Signatures scheme.A special encryption Multi-signature function is extracted from this scheme.The unforgeability of function is proved under the oracle model.(3)Through the study of the obfuscators with special function,this paper proposes an obfuscator which have a special encrypted Multi-Signatures function.The scheme encrypts the signed private key and then uses the encrypted signature private key for signature.The security proof of scheme have been given in this paper.The scheme satisfies the averagecase of the virtual black box property and the unforgeability property under the chosen plaintext attack.