Practical Reliability Constraints on Grover-Based Quantum Attacks Against Symmetric Cryptography

Grover’s algorithm represents a cornerstone quantum attack against symmetric cryptography, offering a quadratic speedup for exhaustive key search. While its theoretical properties are well established, the practical robustness of Grover’s algorithm under non-ideal oracle execution remains insufficiently quantified, particularly in security-relevant contexts. This work presents a comprehensive quantitative analysis of Grover’s robustness against intermittent oracle failures, modeling realistic execution imperfections that may arise in practical quantum attack scenarios. Using a reduced two-dimensional representation of amplitude amplification, we define and measure a practical reliability threshold beyond which Grover’s success probability collapses abruptly. Our results demonstrate that this threshold decreases exponentially with problem size, scaling as ( p^{ast}(n) propto 2^{-n/2} ), implying that cryptographically relevant problem sizes require unrealistically high oracle reliability to preserve quantum advantage. For ( n=40 ), the oracle must fail less than once every ( sim 800{,}000 ) iterations to preserve practical advantage, a requirement that becomes exponentially more stringent for larger key sizes. These findings do not contradict Grover’s theoretical correctness but highlight critical robustness limitations that must be explicitly considered when assessing quantum threats to symmetric cryptography. We provide actionable insights for post-quantum security assessment by translating abstract quantum assumptions into concrete reliability requirements, demonstrating that the practical feasibility of Grover-based attacks may be significantly lower than commonly assumed under realistic hardware constraints.