Quantum security analysis of Module-LWE PQC based on practical cost estimates

The security of lattice-based cryptography relies on the computational complexity of solving the Shortest Vector Problem (SVP) on a high-dimensional lattice. Due to its efficacy in addressing SVP, lattice-based cryptographic systems have so far used the sieve algorithm to analyze their security. Previous works have analyzed the theoretical complexity improvement of the sieve algorithm in quantum computing environments, noting that Grover’s algorithm provides a quadratic speed-up for search problems. However, these works have solely focused on the theoretical analysis of query complexity, neglecting to present quantum circuit designs for sieves. Quantum circuit design and quantum resource estimation are necessary for practical analysis of the complexity of quantum sieves. Additionally, the cost of quantum error correction must also be considered, as quantum computation has a large number of errors. In this paper, we present quantum circuit designs for the sieve algorithm and provide estimates of the quantum resources required, including the number of gates and their depth. Furthermore, we evaluate the quantum sieve’s impact on the security level of ML-KEM and ML-DSA, comparing it to the classical sieve algorithm. We do this by evaluating the classical processing cost for quantum error correction using these estimates. Our results show that the quantum sieve algorithm does not break ML-KEM and ML-DSA, but it reduces their security level by 15 to 27 bits compared to the classical sieve.