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International Conference on Artificial Intelligence, Big Data and Algorithms (CAIBDA)

Applying Grover’s Algorithm to Synergy: Quantum Resource Estimates

Honghan Yan

Published Jun 1, 2026• 0 citations
Publisher
DOI
10.1109/caibda70336.2026.11621700

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“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.
Existing classical cryptanalytic techniques against ChaCha primarily rely on differential cryptanalysis, leveraging probabilistic neutral bits (PNBs) introduced by Aumassonet al. Separately, Batheet al. proposed a quantum brute force search attack using Grover’s algorithm with complexity 2128. However, since the setups for brute force attacks and differential attacks with probabilistic neutral bits differ significantly, the feasibility of applying Grover’s algorithm to the existing differential attacks on ChaCha remained unclear. In this paper, we demonstrate for the first time that a quantum setup for a PNB-based differential attack is indeed possible on ChaCha, where we can utilize the power of Grover’s algorithm to improve further. By combining Grover’s algorithm with PNB-based differential attack, we propose a quantum algorithm for PNB based differential attack and present a quantum attack on 6-round ChaCha that provides more than a quadratic speedup. Specifically, our attack achieves a complexity of 270, surpassing the quadratic speedup of the brute-force attack applying Grover’s algorithm, proposed by Batheet al. We achieve a circuit depth of 283with our algorithm, marking a substantial advancement in efficiency.
In this paper, we propose a quantum circuit for the SPEEDY block cipher for the first time and estimate its security strength based on the post-quantum security strength presented by NIST. The strength of post-quantum security for symmetric key cryptography is estimated at the cost of the Grover key retrieval algorithm. Grover’s algorithm in quantum computers reduces the n-bit security of block ciphers to n2 bits. The implementation of a quantum circuit is required to estimate the Grover’s algorithm cost for the target cipher. We estimate the quantum resource required for Grover’s algorithm by implementing a quantum circuit for SPEEDY in an optimized way and show that SPEEDY provides either 128-bit security (i.e., NIST security level 1) or 192-bit security (i.e., NIST security level 3) depending on the number of rounds. Based on our estimated cost, increasing the number of rounds is insufficient to satisfy the security against quantum attacks on quantum computers.