Quantum differential cryptanalysis based on Bernstein-Vazirani algorithm

Abstract Recent research has demonstrated the potential of quantum algorithms to exploit vulnerabilities in various popular constructions, such as certain block ciphers like Feistel, Even-Mansour, and multiple MACs, within the superposition query model. In this study, we delve into the security of block ciphers against quantum threats, particularly investigating their susceptibility to cryptanalysis techniques, notably exploring quantum adaptations of differential cryptanalysis. Initially, we introduce a BV-based quantum algorithm for identifying linear structures with a complexity of $O(n)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>)</mml:mo> </mml:math> , where n denotes the number of bits in the function. Subsequently, we illustrate the application of this algorithm in devising quantum differential cryptanalysis techniques, including quantum differential cryptanalysis, quantum small probability differential cryptanalysis, and quantum impossible differential cryptanalysis, demonstrating polynomial acceleration compared to prior approaches. By treating the encryption function as a unified entity, our algorithm circumvents the traditional challenge of extending differential paths in differential cryptanalysis.