SymCerts: Practical Symbolic Execution for Exposing Noncompliance in X.509 Certificate Validation Implementations

Analyzing Semantic Correctness with Symbolic Execution: A Case Study on PKCS#1 v1.5 Signature Verification

“…As explained in previous work [15], inputs like X.509 certificates that are DER-encoded ASN.1 objects, can be viewed as a tree of {Tag, Length, Value} triplets, where the length of Value bytes is explicitly given. Hence, if all the Tag and Length are fixed to concrete values, the positions of where Value begins and ends in a test input buffer would also be fixed.…”

“…Hence, one can generate a few concrete inputs, and manually mark Value bytes of interests as symbolic to obtain meaningful concolic test cases. In fact, just a handful of such manually produced test cases managed to uncover a variety of verification problems [15].…”

“…This means there could be many combinations of lengths of components that constitute the input buffer, all meaningful for testing. Consequently, the concretization strategy used in previous work [15] in this case requires a huge amount of manual effort to enumerate and prepare concolic inputs, and would easily miss out on meaningful corner cases.…”

“…While the logical formulas extracted by symbolic execution capture the implemented decision-making logic of the test target with respect to its inputs, which enable analysis of semantic correctness and provide a common-ground for differential testing as demonstrated by previous work [15], we argue that after discrepancies have been identified, a root-cause analysis from formula level back to code level is non-trivial to perform, as multiple different code locations of an implementation could have contributed to the various constraints being imposed on a specific symbolic variable. This is further exacerbated by the fact that, modern symbolic engines, like KLEE for example, would actively simplify and rewrite path constraints in order to reduce the time spent on constraint solving [14].…”

“…In order to make root-cause analysis easier when it comes to finding bugs with symbolic execution, on top of merely harvesting the final optimized path constraints like previous work did [15], we propose a new feature to be added to the execution engine, dubbed Constraint Provenance Tracking (CPT). The main idea is that, during symbolic execution, when a new clause is to be introduced, the engine can associate some source level origin (e.g., file name and line number) with the newly added clause, and export them upon completion of the execution.…”