Study On A One-time Signature Scheme Based On The Discrete Logarithm Problem

Information security is the precondition and basis of everything that can work regularly based on the computer network communication. But the information security technology is in low level in our country , so we should do much research in this field.The pubic key infrastructure (PKI) is basis of certification authority (CA), and provide a platform to CA to administrate secret keys .The PKI is one kind of new network security technology and security criterion . it pellucidly provides administration of the secret key and certificate which is used as encryption and digital signature to all network applications . At present, the PKI system , which perfect moreover correctly being put into effect, is the best of way to settle the security of business and communicating over network.A signature scheme is a method of singing a message stored in electronic form ,and the signed message can be transmitted over a computer network. The signature scheme can verify the authenticity, integrity and undeniableness of a document, and signature scheme is the important content that information security studies. The signature scheme uses the powerful cryptography technology and PKI , with much force to guarantee the authenticity, integrity and undeniableness of one document.The elliptic curve discrete logarithm problem (ECDLP) is recognized one of three mathematics difficult problems which can be used to design cryptosystem at present. Since 1997,the public key cryptosystem based on ECDLP has been well studied in international cryptography field. At present, the public key cryptosystem based on ECDLP already started from the fundamental study stage to move towards the application realization stage, however it still is in starting phase in our country.Based on the public key cryptosystem and PKI technology criterion ,in the thesis, put forward a one-time signature scheme based on ECDLP.The so-called one-time signature scheme is a signature scheme which signs only one message and the signature can be verified an arbitrary number of times. The security of the one-time signature scheme relies on the intractability of the mathematics difficult problem which used to design the one-way bijective function, and relies on the randomly selected signature key-pairs every time one message is signed too.Mainly study including:Firstly, design a one-way bijective function based on ECDLP;Secondly, put forward a one-time signature scheme based on a one-way bijective function , constitute some theorem to prove the signature scheme is secure ,and verify the security of the scheme by simulating experiment ;Thirdly, give some algorithm of theory model of the signature scheme.