Mutual entity authentication plays an important role in securing wireless sensor networks. In this paper, we propose a computationally efficient authentication framework, based on a well-studied problem-learning parity with noise (LPN). This kind of LPN-based authentication approaches only involve simplest bit-operations, which makes them suitable for resource-restrained sensor nodes. The proposed HB-hybrid framework introduces a new noise mode to prevent a general man-in-the-middle attack against previous LPN-based protocols, presents a gentle approach to securely combine several HB-like one-way authentication protocols and extends to mutual authentication which effectively thwarts the reflection attack. It spawns three specific protocols with different trade-offs between communication overload and memory cost. We extensively analyze their performance and security properties. Moreover, some optimization mechanisms on communication costs are given and the application scenarios for different wireless sensor networks are discussed at length.