Verifying and Synthesizing Constant-Resource Implementations with Types

Side channel attacks have been used to extract critical data such as encryption keys and confidential user data in a variety of adversarial settings. In practice, this threat is addressed by adhering to a constant-time programming discipline, which imposes strict constraints on the way in which programs are written. This introduces an additional hurdle for programmers faced with the already difficult task of writing secure code, highlighting the need for solutions that give the same source-level guarantees while supporting more natural programming models. We propose a novel type system for verifying that programs correctly implement constant-resource behavior. Our type system extends recent work on automatic amortized resource analysis (AARA), a set of techniques that automatically derive provable upper bounds on the resource consumption of programs. We devise new techniques that build on the potential method to achieve compositionality, precision, and automation. A strict global requirement that a program always maintains constant resource usage is too restrictive for most practical applications. It is sufficient to require that the program's resource behavior remain constant with respect to an attacker who is only allowed to observe part of the program's state and behavior. To account for this, our type system incorporates information flow tracking into its resource analysis. This allows our system to certify programs that need to violate the constanttime requirement in certain cases, as long as doing so does not leak confidential information to attackers. We formalize this guarantee by defining a new notion of resource-aware noninterference, and prove that our system enforces it. Finally, we show how our type inference algorithm can be used to synthesize a constant-time implementation from one that cannot be verified as secure, effectively repairing insecure programs automatically. We also show how a second novel AARA system that computes lower bounds on resource usage can be used to derive quantitative bounds on the amount of information that a program leaks through its resource use. We implemented each of these systems in Resource Aware ML, and show that it can be applied to verify constant-time behavior in a number of applications including encryption and decryption routines, database queries, and other resourceaware functionality. Keywords-Language-based security; timing channels; information flow; resource analysis; static analysis q q ′ e ⇓ v where q, q ′ ∈ Q + 0 . The intuitive meaning is that under the environment E and q available resources, e evaluates to the value v without running out of resources and q ′ resources are available after the evaluation. The evaluation consumes δ = qq ′ resource units. Fig. 12 presents some selected evaluation rules. In the rule E:FUN for function applications, e g is an expression defining the function's body