System-level Non-interference for Constant-time Cryptography

International audience ; Cache-based attacks are a class of side-channel attacks that are particularly effective in virtualized or cloud-based en-vironments, where they have been used to recover secret keys from cryptographic implementations. One common ap-proach to thwart cache-based attacks is to use constant-time implementations, i.e. which do not branch on secrets and do not perform memory accesses that depend on secrets. How-ever, there is no rigorous proof that constant-time implemen-tations are protected against concurrent cache-attacks in virtualization platforms with shared cache; moreover, many prominent implementations are not constant-time. An alter-native approach is to rely on system-level mechanisms. One recent such mechanism is stealth memory, which provisions a small amount of private cache for programs to carry po-tentially leaking computations securely. Stealth memory in-duces a weak form of constant-time, called S-constant-time, which encompasses some widely used cryptographic imple-mentations. However, there is no rigorous analysis of stealth memory and S-constant-time, and no tool support for check-ing if applications are S-constant-time. We propose a new information-flow analysis that checks if an x86 application executes in constant-time, or in S-constant-time. Moreover, we prove that constant-time (resp. S-constant-time) programs do not leak confidential infor-mation through the cache to other operating systems exe-cuting concurrently on virtualization platforms (resp. plat-forms supporting stealth memory). The soundness proofs are based on new theorems of independent interest, includ-ing isolation theorems for virtualization platforms (resp. plat-forms supporting stealth memory), and proofs that constant-time implementations (resp. S-constant-time implementa-tions) are non-interfering with respect to a strict information flow policy which disallows that control flow and memory ac-cesses depend on secrets. We formalize our results using the Coq proof assistant and we demonstrate the ...