Research On Some New Threshold Encryption And Threshold Signature Schemes

Threshold encryption and threshold signature schemes are two basic types of thresholdcryptography. With the rapid development of computer network and information technol-ogy, many domestic and foreign experts and scholars carried out deep research on the theory,technology and applications of threshold cryptography. Especially, in recent years, manynew public key encryption and digital signature schemes have been developed. Certificate-less encryption, certificateless signature, proxy re-signature, ID-based broadcast encryption,attribute based encryption are among these newly proposed public key encryption and digitalsignature schemes. Lots of work remains to be done in order to make threshold version ofthese schemes. For example, improve the security model of certificateless threshold scheme,prove certificateless threshold scheme in the standard model, improve the efficiency of ID-based threshold broadcast encryption scheme, define the security model of threshold proxyre-signature scheme, design attribute based encryption and signature schemes using thresh-old techniques.In this thesis, we do research on solving these open questions. We make four achieve-ments as follows:1. We do research on certificateless threshold cryptography. First, we do research oncertificateless threshold signature scheme. We improve the security model of certificate-less threshold signature. In our security model, we consider normal third party attacker andmalicious key generation center separately. At the same time, we define the simulatabilityof certificateless threshold signature and present the relation between certificateless thresh-old signature scheme and the underlying certificateless signature scheme. Furthermore, weput forward a certificatless threshold signature scheme against two kinds of attackers in thestandard model. Our scheme is proved existentially unforgeable against adaptively cho-sen message attack based on computational Diffie-Hellman assumption. Our certificatelessthreshold signature scheme has three features: a) raising the whole efficiency a lot; b) using the improved security model making our scheme resist two kinds of attackers; c) proving ourscheme secure in the standard model. Second, we do research on certificateless threshold en-cryption. We improve the security model of certificateless threshold encryption scheme. Inour security model, we present the new model for the malicious key generation center. Fur-thermore, we put forward a secure and efficient certificateless threshold encryption scheme,and prove its security against chosen ciphertext attacks in the standard model based on deci-sional bilinear Diffie-Hellman assumption. Our certificateless threshold encryption schemehas three features: a) raising the efficiency of our scheme; b) utilizing the improved securitymodel making our scheme resist the attack of malicious key generation center; c) provingour scheme secure in the standard model.2. We do research on threshold proxy re-signature. Firstly, we give the formal def-inition of threshold proxy re-signature, its security model, and the definition of simulata-bility. Secondly, we put forward and prove the relationship between threshold proxy re-signature scheme and proxy re-signature scheme. Thirdly, we put forward a threshold proxyre-signature scheme which is proved secure in the standard model and an unidirectionalthreshold proxy re-signature scheme which is proved secure under random oracles. Ourschemes have the following advantages: a) the power of the proxy is distributed; b) reducethe risk of system's malfunction due to some proxies'failure; c) have the ability to withstandthe attacks of the malicious proxies.3. We do research on ID-based threshold broadcast encryption. We put forward a secureand efficient ID-based threshold broadcast encryption scheme, and prove that our scheme isrobust and chosen ciphertext secure in the random oracle model based on decisional bilin-ear Diffie-Hellman assumption and the unforgeability of one-time signature scheme. Ourscheme has three strong points: a) avoiding the bilinear pairing computation and raising theencryption speed; b) short ciphertext length (O(n?t)); c) discovery of malicious decryptionserver attacks.4. We do research on attribute based cryptography. Firstly, we do research on fuzzyID-based signature. We present a practical fuzzy ID-based signature scheme using thresholdtechniques. At the same time, we prove that our scheme is existentially unforgeable againstadaptively chosen message attack in the standard model based on the computational Diffie-Hellman assumption. Furthermore, we demonstrate the application of our construction in se-cure biometric authentication. Secondly, we do research on attribute based signature (ABS).We contribute the definition, formalization, and security model of attribute based signature. Furthermore, we provide an attribute based signature scheme using threshold techniques,and prove our scheme existentially unforgeable against adaptively chosen message attack inthe standard model based on the computational Diffie-Hellman assumption.