We introduce eRHL , a program logic for reasoning about relational expectation properties of pairs of probabilistic programs. eRHL is quantitative, i.e., its pre- and post-conditions take values in the extended non-negative reals. Thanks to its quantitative assertions, eRHL overcomes randomness alignment restrictions from prior logics, including pRHL , a popular relational program logic used to reason about security of cryptographic constructions, and apRHL , a variant of pRHL for differential privacy. As a result, eRHL is the first relational probabilistic program logic to be supported by non-trivial soundness and completeness results for all almost surely terminating programs. We show that eRHL is sound and complete with respect to program equivalence, statistical distance, and differential privacy. We also show that every pRHL judgment is valid iff it is provable in eRHL . We showcase the practical benefits of eRHL with examples that are beyond reach of pRHL and apRHL .

The efficacy of address space layout randomization has been formally demonstrated in a shared-memory model by Abadi et al., contingent on specific assumptions about victim programs. However, modern operating systems, implementing layout randomization in the kernel, diverge from these assumptions and operate on a separate memory model with communication through system calls. In this work, we relax Abadi et al.’s language assumptions while demonstrating that layout randomization offers a comparable safety guarantee in a system with memory separation. However, in practice, speculative execution and side-channels are recognized threats to layout randomization. We show that kernel safety cannot be restored for attackers capable of using side-channels and speculative execution, and introduce enforcement mechanisms that can guarantee speculative kernel safety for safe system calls in the Spectre era. We implement three suitable mechanisms and we evaluate their performance overhead on the Linux kernel.

The efficacy of address space layout randomization has been formally demonstrated in a shared-memory model by Abadi et al., contingent on specific assumptions about victim programs. However, modern operating systems, implementing layout randomization in the kernel, diverge from these assumptions and operate on a separate memory model with communication through system calls. In this work, we relax Abadi et al.'s language assumptions while demonstrating that layout randomization offers a comparable safety guarantee in a system with memory separation. However, in practice, speculative execution and side-channels are recognized threats to layout randomization. We show that kernel safety cannot be restored for attackers capable of using side-channels and speculative execution and introduce a new condition, that allows us to formally prove kernel safety in the Spectre era. Our research demonstrates that under this condition, the system remains safe without relying on layout randomization. We also demonstrate that our condition can be sensibly weakened, leading to enforcement mechanisms that can guarantee kernel safety for safe system calls in the Spectre era.

Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving semantics to separation logic formulas in which separating conjunction is interpreted in terms of probabilistic independence. The latter is taken in its exact form, i.e., two events are independent if and only if the joint probability is the product of the probabilities of the two events. There is indeed a literature on weaker notions of independence which are computational in nature, i.e. independence holds only against efficient adversaries and modulo a negligible probability of success. The aim of this work is to explore the nature of computational independence in a cryptographic scenario, in view of the aforementioned advances in separation logic. We show on the one hand that the semantics of separation logic can be adapted so as to account for complexity bounded adversaries, and on the other hand that the obtained logical system is useful for writing simple and compact proofs of standard cryptographic results in which the adversary remains hidden. Remarkably, this allows for a fruitful interplay between independence and pseudorandomness, itself a crucial notion in cryptography.

ArKiv Extended Version https://arxiv.org/abs/2311.15003