Fog computing extends the cloud computing to the network edge and allows deploying a new type of semioffline services, which can provide real-time transactions between two entities, while the central cloud server is offline and network edge devices are online.For an e-payment system and e-voting with such feature, proxy blind signature is a cornerstone to protect users' privacy. However, the signature based on number theorem, such as hard mathematical problems on factoring problem, discrete logarithm problem, and bilinear pairings, cannot defeat quantum computers attack. Meanwhile, these schemes need to depend on complex public key infrastructure. Thus, we construct an identity-based proxy blind signature scheme based on number theorem research unit lattice, which can defeat quantum computers attack and does not need to depend on public key infrastructure. The security of the proposed scheme is dependent on Ring-Small Integer Solution problem over number theorem research unit lattice. The proposed scheme meets the properties of blind signature and proxy signature. Then we compare the proposed scheme with other existing proxy blind signature schemes; the result shows that the proposed scheme outperforms ZM scheme except in proxy signer's signature size and can be more secure than TA scheme and MMHP scheme.