Combining Classical and Probabilistic Independence Reasoning to Verify the Security of Oblivious Algorithms (Extended Version)
<|reference_start|>Combining Classical and Probabilistic Independence Reasoning to Verify the Security of Oblivious Algorithms (Extended Version): We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and invariant needed to verify the security of many practical probabilistic oblivious algorithms. We propose an approach based on reasoning over perfectly oblivious approximations, using a program logic that combines both classical Hoare logic reasoning and probabilistic independence reasoning to support all the needed features. We formalise and prove our new logic sound in Isabelle/HOL and apply our approach to formally verify the security of several challenging case studies beyond the reach of prior methods for proving obliviousness.<|reference_end|>
@article{yan2024combining,
    title={Combining Classical and Probabilistic Independence Reasoning to Verify
  the Security of Oblivious Algorithms (Extended Version)},
    author={Pengbo Yan, Toby Murray, Olga Ohrimenko, Van-Thuan Pham and Robert
  Sison},
    journal={arXiv preprint arXiv:2407.00514},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.00514},
    primaryClass={cs.PL}
}