This paper presents a wireless neural recording system featuring energy-efficient data compression and encryption. An ultra-high efficiency is achieved by leveraging compressed sensing (CS) for simultaneous data compression and encryption. CS enables sub-Nyquist sampling of neural signals by taking advantage of its intrinsic sparsity. It simultaneously encrypts the data with the sampling matrix being the cryptographic key. To share the key over an insecure wireless channel, we implement an elliptic-curve cryptography (ECC) based key exchanging protocol. The CS operation is executed in a custom-designed IC fabricated in 180nm CMOS technology. Mixed-signal circuits are designed to optimize the power efficiency of the matrix-vector multiplication (MVM) of the CS operation. The ECC algorithm is implemented in a low-power Cortex-M0 microcontroller (MCU). To be protected from timing and power analysis attacks, the implementation avoids possible data-dependent branches and also employs a randomized ECC initialization. At a compression ratio of 8x, the average correlated coefficient between the reconstructed signals and the uncompressed signals is 0.973, while the ciphertext-only attacks (CoA) achieve no better than 0.054 over 200,000 attacks. The prototype achieves a 35x power saving compared with conventional implementation in low-power MCUs. This work demonstrates a promising solution for future chronic neural recording systems with requirements in high energy efficiency and security.