Grover's Algorithm: Quantum Search
Bhupendra Singh, Mohankumar Mylsamy, Thamaraimanalan Thangarajan
“Grover's Algorithm: Quantum Search” explores Grover's Algorithm in the context of quantum search, beginning with an overview of its mechanics. The section includes a literature survey that covers Grover's algorithm, stream ciphers, and the Grover attack, as well as quantum resource estimation. The section then introduces a simplified 4-bit Grain cipher (with a 4-bit key and 4-bit IV), detailing its design, initialization, and key stream generation. Following this, the chapter discusses about key recovery using Grover's algorithm, with an emphasis on quantum circuit development for the simplified Grain 4-bit cipher. It outlines key steps in the circuit, such as executing the Boolean function and XORing the NFSR's fourth bit. Further, the section details the development of a Grover attack quantum circuit, describing both single and double pair methods. Experimental results are provided across multiple cases, with a summary of test cases and classical computation times. Quantum resource estimation, including the costs associated with the simplified Grain 4-bit cipher and the Grover oracle, is analyzed. The section concludes with a discussion on the results, classical and quantum resource estimations, and the potential for future enhancements to the approach.
CRC Press eBooks•Nov 14, 2025•0 citations