This paper studies information-theoretically secure quantum homomorphic encryption (QHE) schemes of classical data. Previous works on information-theoretically secure QHE schemes (like Childs'05, Liang'13, and others) are typically based on the Quantum-One-Time-Pad (QOTP) approach of Ambainis et al. [AMTdW'00]. There, the encryption of a bit is a qubit, randomly selected from a set of four possible qubits. This paper takes a different approach and presents the RBE (Random-Basis Encryption) scheme -- a QHE scheme in which the encryption of a bit is a qubit, randomly selected from a set of an immense number of qubits. Second, this paper studies weak measurements (WM) and presents a WM-based attack on legacy QOTP-based Quantum Key Distribution (QKD) protocols. Then, we use the RBE scheme to construct a QKD protocol and argue that this protocol is resilient to such WM-based attacks. Finally, this paper raises the following question. Entanglement is an essential resource in quantum information and quantum computation research. Hence, once generated, how can its owner secure entangled systems of qubits? We inspect possible QOTP-based solutions, suggest an RBE-based solution, and discuss some of the benefits of the latter.