Physical unclonable function (PUF), a cryptographic primitive, has recently been used in protocol design because it can ensure a tamper-evident feature. In many PUF-based protocol schemes, helper data algorithms (HDA) or fuzzy extractors (FE) are used to generate strong keys from unreliable PUF responses. However, these methods inevitably introduce complex error correction techniques, which not only increase the overhead of embedded devices but also pose some security risks. We propose a novel HDA technology, which does not use any high-overhead error correction mechanism, greatly reducing the implementation complexity and execution overhead. The novel HDA exploits the strategy of bit-self-test (BST) and the PUF can extract the robust responses by using the real-time generated reliable flags, and then an entropy extractor is used to generate the reliable and random key with high entropy. Based on this novel HDA, we design a lightweight anonymous authentication protocol. The protocol uses pseudo-random function (PRF) and XOR operation instead of the traditional hash function and symmetric encryption algorithm, which ensures security while reducing the overhead. Moreover, the proposed protocol does not require the server to store a large number of challenge–response pairs (CRPs), which reduces the storage overhead on the server while avoiding the risk of leakage of CRPs. Moreover, the device identity ID is updated during each round of the authentication process, which prevents the device from being tracked and protects the privacy of the device. The implementation and performance analysis of the protocol prototype on a Zynq-7000 SoC XC7Z010 FPGA shows that the proposed scheme solves the problems encountered with existing schemes and has additional security properties.