Verifiable Pairing and Its Applications

Abstract

Pairing-based cryptography is rapidly emerging in recent years. Many cryptographic protocols, such as signcryption, threshold decryption and undeniable signature enabled by pairing require sending the result of the pairing function with private key as one of the input. Since private key is only known to its owner, the correctness of the result may not be easily verifiable (which requires solving the decisional bilinear Diffie-Hellman problem). In this paper, we introduce the notion of Verifiable Pairing, together with a concrete construction, to ensure the robustness of these protocols. Verifiable pairing is a useful primitive in many information security applications. As examples, we show how verifiable pairing can be applied in signcryption, threshold decryption and how it can help in fixing insecure protocol. In adding verifiability to threshold decryption, our solution is more efficient than the previous proposal in [21]. As a bonus result, we find that our scheme for verifiable pairing gives rise to a new identity-based signature that is provably secure in the random oracle model without using the forking lemma, assuming the hardness of the computational bilinear Diffie-Hellman problem.