Paper 2026/1412

Quantum Implementation and Analysis of Rijndael

Abstract

We present a quantum resource estimation of the Rijndael variants \[ N_b = N_k \in \{4,5,6,7,8\}, \qquad N_r = N_b + 6, \] under the NIST MAXDEPTH quantum cost model. Extending the AES quantum encryption oracle~\cite{ref5} parametrically to arbitrary $N_b = N_k$, we generalize the in-place key schedule, including the single- and double-\texttt{SubWord} cases, the \texttt{ShiftRows} offsets, and the round constants. We implement and verify the resulting oracles using ProjectQ. The verified variants range from 1,624 qubits at a full depth of 1,090 for Rijndael-128/128 to 3,240 qubits at a full depth of 1,839 for Rijndael-256/256. Under the NIST PQC MAXDEPTH bounds $\{2^{40}, 2^{64}, 2^{96}\}$, the Grover key-recovery qubit cost in $\log_2$ units ranges from $\{80.15, 32.15, 10.67\}$ for Rijndael-128/128 to $\{210.65, 162.65, 98.65\}$ for Rijndael-256/256. The standardized analogues at Categories 1, 3, and 5, namely Rijndael-128/128, Rijndael-192/192, and Rijndael-256/256, meet the corresponding AES-based bounds. The intermediate Rijndael-160/160 and Rijndael-224/224 variants provide reference points between the standardized AES key lengths.