Implementing Grover oracles for quantum key search on AES and LowMC

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.

Post-Quantum Logic Locking

“…Post-quantum symmetric cryptography considers (mainly) the logical attack by Grover's algorithm [10], which is a probabilistic quantum algorithm providing a square-root speed-up in the number of evaluations for a black box function. Applying Grover's algorithm to Problem 3 to retrieve the secret key k ∈ F 2 for a symmetric encryption is well investigated (for details see [11], [27], [28]). We recall it in the following theorem and then state our result for logic locking as defined in Def.…”

Lowering the T-depth of Quantum Circuits By Reducing the Multiplicative Depth Of Logic Networks

“…For each cryptographic function and floating-point operation, we report the two quantum circuits with the fewest number of qubits (first row) and the lowest T -depth (second row). The corresponding 10 4 Grassl, Langenberg, Roetteler, Steinwandt [18] Langenberg, Pham, Steindwandt [25] Jaques, Naehrig, Roetteler, Virdia [22] Amy, Matteo, Gheorghiu, Mosca, Parent, Schanck [3] Haener, Soeken, Roetteler, Svore [19] This work…”