Depth–measurement trade-off for quantum search on block ciphers

Abstract

Grover’s algorithm has been widely used for quantum key search to attack block ciphers with a quadratic speedup as compared to classical brute-force attacks and also used for evaluating the post-quantum security of block ciphers against quantum computer attack. But, this quantum key search on block ciphers has a high quantum circuit depth and AES-128 is still secure against such attack. In this paper, we introduce a method called the depth–measurement trade-off method that reduces the overall quantum circuit depth of quantum key search to attack block ciphers by increasing the number of measurements of the circuit. This method is to introduce dummy keys in the quantum circuit as part of the correct key. This will reduce both quantum circuit resource and quantum circuit depth. Based on this technique, the quantum circuit depth of AES-128 is less than $2^{64}$, while NIST suggested circuit depth should be greater than MAXDEPTH, which is $2^{40}$, $2^{64}$ and $2^{96}$ in order to resist the respective attacks. In addition, we also simulated the depth–measurement trade-off method on the reduced SIMON block cipher algorithm as a proof of concept. Furthermore, we also apply the depth–measurement technique on various block ciphers, for example AES, PRESENT, SIMON, GIFT, SPECK, RECTANGLE, LowMC, KNOT, PIPO, etc.