Cryptographic Protocols Based On Bilinear Pairing Function

The bilinear pairings, namely Weil pairing and Tate pairing, were first used in cryptography as a cryptanalytic tool. With the help of the pairings, the discrete logarithm problem on some elliptic curves is reduced to the discrecte log problem in a finite field.Recently, the use of the bilinear parings has been found to have advantages in building cryptographic schemes. If the Weil or Tate pairing is amended properly and is applied on some appropriate elliptic curves, the cryptographic protocols such as encryption scheme, signature scheme and key agreement scheme etc, which are low-width, provable secure, based on the bilinear pairings can be constructed. These breakthroughs have broken a new path in building cryptographic primitives. Depending on properties of the bilinear pairings, it is possible to design some cryptographic protocols with some special characteristics which were previously unknown, impratical, or pratical but less efficient. For exapmple, short signature scheme, the protocol for three-party one round Diffie-Hellman key aggrement, and identity-based encryption scheme etc, which are all hard to resolved by other techniques.This paper mainly does some research in applications of constructing new cryptographic protocols with bilinear pairings. Our main reseach content includes: (1) We summarize the concepts, characteristics, Diffie-Hellman problems, and some applications of bilinear pairings in cryptography. (2) We proposed a forward-secure signature scheme from a paring-based short signature scheme using bilinear pairings. In the paper, we analyzed the security of this scheme and compared it with the existed forward secure digital signature schemes. The result of the comparison indicated that this scheme has some advantages in the efficiency and size of signatures. (3) This paper proposed an efficient scheme for resolving the following scenario: some users encrypt messages with Alice's public key, and send these encrypted data to the untrusted data storage server such as mail server, file server and others. Alice wants to let the server to retrieve only the documents containing certain words and answer the query; on the other hand, she does not wish to give the server the ability to decrypt all her messages. In this paper, a searchable encryption system is constructed based on public key and stream ciper with bilinear pairings. It can let the server perform the search without loss of data confidentiality. In this scheme, the server cannot learn anything more about the plaintextthan the search result; and the untrusted server can't learn anything about the plaintext when only given the ciphertext. (3) A blind aggregate signature is proposed. It combines blind signature with aggregate signature, and poses the merits of the both. The scheme can save plenty of time and storage and reduce the request of the bandwidth.