Analysis of Atom against quantum attacks

Abstract

A significant amount of study is being done to review the security promises made for the various ciphers now in use as a result of the development of quantum computing technology. A general attack against symmetric key cryptography primitives that can reduce search costs to the square root is Grover's search algorithm. To implement Grover's algorithm, it is necessary that the target cipher be implemented as a quantum circuit. Despite being relatively new, this area of study has received significant attention from the research community. The authors have estimated the cost of Grover's key search attack against the stream cipher Atom, for the first time, under circuit depth restrictions defined in National Institute of Standards and Technology (NIST) PQC standardisation process. The authors implement the quantum circuit of Atom in QISKIT, (open-source software development kit for working with quantum computers running on IBM Quantum Experience). The results are also compared with other existing literature on LFSR-based stream ciphers, such as Grain-v1, Grain-128-AEAD, and Lizard. The authors also find that, to the best of their knowledge, in the existing literature on estimating the cost of Grover's attack on symmetric ciphers, Atom is the only 128-bit key cipher that meets the threshold of ≈2¹⁷⁰ set by NIST for quantum security of 128-bit key ciphers. The authors also analyse the security of Atom against quantum TMDTO attacks.