# An Identity-Based Anti-Quantum Privacy-Preserving Blind Authentication in Wireless Sensor Networks
## 1 Introduction  
With the development of wireless sensor networks, Internet of Things (IoT) devices play an important role in smart cities. IoT devices in e-payment and e-voting services are crucial for modernisation [1; 2; 3]. Meanwhile, a large amount data generated by these IoT devices face the threats of security and privacy leakage since the state-of-art authentication protocols in e-payment and e-voting systems can be attacked by quantum computers successfully [4], i.e., in e-payment and e-voting systems, blind signature (BS) is crucial to protect user privacy and guarantee trustworthy of big data in the cloud [5; 6; 7; 8]. However, these schemes based on traditional number theory can be attacked successfully by quantum computer. BS was firstly introduced by [PERSON]. Then many BS schemes based on number theory were proposed [9], which can be presented as follows:  
The first factoring BS scheme based on RSA was proposed by [PERSON], this scheme can guarantee the security of payer. However, they did not prove its security. Later, [PERSON] et al. defined the hard problem of RSA formally. Based on it, they proved the security of [PERSON]'s scheme. Then a novel proven-secure RSA scheme was proposed by [PERSON] and [PERSON] etc., it was secure in the standard model. However, these schemes have to use long keys to guarantee security. In order to overcome the shortages of factoring BS schemes, BS schemes based on discrete logarithm problem (DLP) were proposed for their short keys and high security. [PERSON] et al. proposedan e-wallet. Later, [PERSON] proposed a BS scheme based on DLP. However, these schemes were not proven secure and only satisfy blindness. Then [PERSON] et al. initially considered the property of unforgeability. After that, researchers were interested in constructing provably-secure BS schemes based on bilinear pairing. [PERSON] proposed a BS scheme based on GDH assumption, this scheme outperformed the other existing schemes in attribution and efficiency. Later, [PERSON] proposed a BS scheme based on 2 SDH assumption, which is stronger than SDH assumption. However, their efficiency is low. Meanwhile, all the schemes outlined above need to depend on Public Key Infrastructure (PKI). In order to simplify key management of PKI, an identity-based signature scheme (IDS) was firstly presented by [PERSON]. In an IDS scheme, given a user's identity, his public key can be easily obtained. Also, his private key can be obtained easily. Until 2001, [PERSON] et al. initially proposed an IDS scheme, it has high efficiency, its security is dependent on the bilinear pairing problem. Then some new IDS schemes based on pairing were proposed by researchers. After that, combining BS with identity-based signature, [PERSON] et al. initially presented an identity-based BS (IDBS) scheme, its security is based on hard problem of bilinear pairing, this scheme was secure and efficient. Unfortunately, its computation cost was too high. Later, a new IDBS based on DLP was presented, the running time and signature size of their scheme [10] were significantly improved. However, these schemes still face the threat of quantum computer attack [4]. Thus, the replaceable IDBS schemes are based on lattice for their high-efficiency and sufficiently secure to quantum computer attack [11; 12]. In the paper, a lattice-based IDBS scheme is proposed by using the advantages of number theory research unit lattice (NTRU) such as high efficiency, extremely tight keys, and sufficient safety once properly parameterized. 1. Inspired by [13; 14; 15], we propose a new IDBS scheme on NTRU Lattice (named IDBS-NTRU), which can be secure to resist quantum computer attack. 2. We evaluate our IDBS-NTRU's security. We demonstrate that the proposed scheme is secure. Then we prove that the proposed scheme satisfies confidentiality, integrity, and non-repudiation. 3. We compare our IDBS-NTRU's performance with the other IDBS schemes.