Font Size: a A A

The Design And Analysis Of Public Key Cryptosystems From Lattices

Posted on:2016-05-23Degree:DoctorType:Dissertation
Country:ChinaCandidate:C L YangFull Text:PDF
GTID:1108330482960399Subject:Cryptography
Abstract/Summary:PDF Full Text Request
With the development of quantum communication and quantum computation, the problems that based on the classical cryptosystems (such as the large integer factoring problem and the discrete logarithm problem) can be solvedby quantum algorithm in polynomial time, which leads to the corresponding cryptosystems are threatened. Therefore, seeking cryptography that can resist known quantum algorithms is a very pressing problem. Lattice cryptography as one of typical post-quantum cryptography, it has attracted great attention in recent years. Lattice cryptography not only has the advantages of worst-case reduction, linearity and resistance quantum attacks, it has wide applications in fully homomorphic encryption and multi-linear pairing.Encryption and digital signature are mainly means to ensure the confidentiality and authentication of messages, respectively. Based on hard lattice problems, constructing encryption schemes and digital signature schemes that can resist known quantum attacks is a main research direction of the lattice cryptography. In this paper, using lattice trapdoor generation algorithm, lattice delegation algorithms and preimage sampling algorithm, we designed one encryption scheme and three digital signature schemes with special properties. We briefly gave the innovation achievements of this paper as follows:(1) Broadcast encryption is a kind of one to many communication system, it is widely used in pay TV, satellite broadcast communication, digital copyright products distribution etc. We constructed a hierarchical identity-based broadcast encryption scheme based on LWE problem in this chapter and proved that our scheme is indistinguishable under an adaptive chosen-plaintext and adaptive chosen-identity attacks in the random oracle model. In addition, we gave the efficiency analysis and comparison of our scheme and the existing schemes. It is shown that the size of public parameters and the master secret key are very similar of our scheme and the existing schemes, but the size of user’s private key of our scheme is smaller than the existing schemes, and the length of the ciphertext is shorter than the existing schemes.(2) A fuzzy identity-based signature scheme is an extension of the identity-based signature scheme. It uses biological characteristics as user’s identity. If two identities string are very similar, an identity’s public key can be used to verify the other identity’s signature. In order to get a fuzzy identity-based signature scheme that can resist known quantum attacks. We proposed a fuzzy identity-based signature from SIS problem, and proved that it achieves strong unforgeability under selective chosen-identity and adaptive chosen-message attacks in the standard model. To the best of my knowledge, there is only one fuzzy identity-based signature scheme from lattices. We analyzed and compared the security and efficiency of these two schemes. It is shown that the size of the public parameters of our scheme is larger than the other one, while the size of the master secret key and identity’s private key are all smaller than the other one. In addition, the length of the signature of our scheme is shorter than the existing scheme. Our scheme can achieve strong unforgeability, while the existing scheme can only achieve existentially unforgeability.(3) The identity-based signature is an extension of the traditional digital signature based on certificate authentication. It uses the user’s identity information as public key, which can simplify the procedure of key management and key maintenance. We firstly analyzed the problem that existing in the security proof of Liu’s identity-based signature scheme from lattices. Aiming at this problem, we improved Liu’s scheme by using BoyenlO signature algorithm, and proposed a new identity-based signature from lattices. We proved our scheme can achieve the strong unforgeability under selective identity and adaptive chosen-message attacks in the standard model. In addition, throng the efficiency comparison of our scheme and the existing schemes, the results shows that the size of public parameters, signature key and signature length of our scheme are all similar with the existing schemes and even larger. But our scheme is proved in the standard model, while the other schemes are proved in the random oracle model.(4)Proxy signature is a special type of digital signature, and it has wide application in practice. In order to obtain a high efficiency proxy signature scheme that can resist the known quantum attacks, we using the idea of Lyu12 signature gave a proxy signature scheme from lattices without trapdoor, and proved that it has existentialy unforgeability, verifiability, strong identifiability, strong undeniability, key denpendent and not abuse security in the random oracle model. In addition, we compared the efficiency of our scheme and the existing schemes. The size of original signer’s signature key, the original signer’s verification key, the proxy signer’s signature key, the proxy signer’s verification key, the proxy signature key and the proxy signature are all smaller of our scheme than the existing schemes.
Keywords/Search Tags:lattices cryptography, public key encryption, digital signature, security, efficiency
PDF Full Text Request
Related items