Lightweight ciphers designed with a fully unrolled architecture, capable of encryption/decryption in a single clock cycle, have gained momentum in the last few years. They've shown that very low latency encryption/decryption is possible with modest costs in comparison with traditional round-based designs. This paper explores how to most efficiently perform side-channel analysis against such unrolled cryptographic hardware in a setting where the adversary may freely choose the plaintexts processed by the target cipher. We present a method for choosing plaintexts for a straightforward recovery of the encryption/decryption key by side-channel analysis without any template attack-like profiling phase of the device. Finally, we demonstrate the validity of our method with experiments on fully unrolled implementations of PRINCE and MANTIS. The result shows that our chosen-input attack is significantly more efficient than the corresponding known-input attacks.