Study Of Provably Secure Public Key Cryptosystems From Bilinear Pairings

Bilinear pairing is a significant tool for designing cryptographic schemes at present.The pairing-based schemes are able to attain complex functions required by diferentapplications. Provable security theory is a hot topic of research on cryptographic schemesin recent years. It alters the traditional way (design-attack-improve) of constructingcryptographic schemes and provides an efective approach of measuring the security ofcryptographic schemes. In this dissertation, taking provable security theory as clue, westudy the construction of public key cryptographic schemes and their security proofs. Themain results are specified as follows.1. New hierarchical identity-based signature schemes are introduced. The first schemeis constructed in selective-identity model. It has short public parameter and itssecurity is reduced to the computational Dife-Hellman(CDH) assumption. Thesecond scheme is constructed in full-identity model and proved secure in standardmodel. It achieves constant-size ciphertexts and private keys in this scheme shrinkas the identity depth increases. Only three bilinear operations are required in theverification phase.2. We construct three efcient identity-based encryption schemes with wildcards instandard model. The first scheme is constructed under the BDHI assumption andhas short public parameters. However, the size of private keys and ciphertexts in-creases as the depth of identity increases. So two modified schemes are proposed.Both schemes achieve constant-size ciphertexts and consist of only two group ele-ments. Furthermore, their private keys shrinks as the identity depth increases. Thelast two schemes base on L-wDBDHE assumption and DBDH assumption, respec-tively.3. We construct two biometric identity based encryption schemes and one signaturescheme. First, the method to extract public key from user’s biometric characteristicswith fuzzy extractor is introduced. The schemes are error tolerant and flexible dueto the combining of Shamir’s threshold secret sharing and error correction code.Both scheme I and II are encryption schemes and base on standard model. Theirsecurities are reduced to DBDH assumption. Scheme II has higher efciency thanscheme I and requires only two bilinear operations in the decryption phase. SchemeIII is a biometric identity based signature scheme. It has good efciency and baseson random oracle model.4. A novel identity based broadcast encryption scheme is presented. The scheme is constructed in standard model and proved secure against chosen ciphertext attack.This scheme achieves constant-size of public parameter, private key and ciphertext.No bilinear operation is required in the encryption phase and the decryption phasemerely needs two bilinear operations. This is one of the most efcient constructionsat present. This scheme has short transmissions and low cost of user storage. Thesecharacters are desirable for mobile ad hoc networks. When user joins or leaves thenetwork, the broadcaster only needs to add or delete user’s ID to securely distributethe group key. The complex information interchange process in traditional ad hocprotocols is avoided.