International Association for Cryptologic Research

International Association
for Cryptologic Research


Implementing Grover oracles for quantum key search on AES and LowMC

Samuel Jaques , University of Oxford
Michael Naehrig , Microsoft Research
Martin Roetteler , Microsoft Quantum
Fernando Virdia , Royal Holloway, University of London
DOI: 10.1007/978-3-030-45724-2_10 (login may be required)
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Presentation: Slides
Conference: EUROCRYPT 2020
Abstract: Grover's search algorithm gives a quantum attack against block ciphers by searching for a key that matches a small number of plaintext-ciphertext pairs. This attack uses O(N) calls to the cipher to search a key space of size N. Previous work in the specific case of AES derived the full gate cost by analyzing quantum circuits for the cipher, but focused on minimizing the number of qubits. In contrast, we study the cost of quantum key search attacks under a depth restriction and introduce techniques that reduce the oracle depth, even if it requires more qubits. As cases in point, we design quantum circuits for the block ciphers AES and LowMC. Our circuits give a lower overall attack cost in both the gate count and depth-times-width cost models. In NIST's post-quantum cryptography standardization process, security categories are defined based on the concrete cost of quantum key search against AES. We present new, lower cost estimates for each category, so our work has immediate implications for the security assessment of post-quantum cryptography. As part of this work, we release Q# implementations of the full Grover oracle for AES-128, -192, -256 and for the three LowMC instantiations used in Picnic, including unit tests and code to reproduce our quantum resource estimates. To the best of our knowledge, these are the first two such full implementations and automatic resource estimations.
Video from EUROCRYPT 2020
  title={Implementing Grover oracles for quantum key search on AES and LowMC},
  booktitle={39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings},
  series={Lecture Notes in Computer Science},
  keywords={Quantum cryptanalysis;Grover's algorithm;AES;LowMC;post-quantum cryptography;Q# implementation},
  author={Samuel Jaques and Michael Naehrig and Martin Roetteler and Fernando Virdia},