Quantum Implementation of the SAND Algorithm and Its Quantum Resource Estimation for Brute-Force Attack

Abstract

The SAND algorithm is a family of lightweight AND-RX block ciphers released by DCC in 2022. Our research focuses on assessing the security of SAND with a quantum computation model. This paper presents the first quantum implementation of SAND (including two versions of SAND, SAND-64 and SAND-128). Considering the depth-times-width metric, the quantum circuit implementation of the SAND algorithm demonstrates a relatively lower consumption of quantum resources than that of the quantum implementations of existing lightweight algorithms. A generalized Grover-based brute-force attack framework was implemented and employed to perform attacks on two versions of the SAND algorithm. This framework utilized the g-database algorithm, which considered different plaintext–ciphertext pairs in a unified manner, reducing quantum resource consumption. Our findings indicate that the SAND-128 algorithm achieved the NIST security level I, while the SAND-64 algorithm fell short of meeting the requirements of security level I.

Keywords

• grover algorithm
• brute-force attack
• SAND algorithm
• lightweight block cipher