The constant-time property is considered the security standard for cryptographic code. Code following the constant-time discipline is free from secret-dependent branches and memory accesses, and thus avoids leaking secrets through cache and timing side-channels. The constant-time property makes a number of implicit assumptions that are fundamentally at odds with the reality of cryptographic code. Constant-time is not robust. The first issue with constant-time is that it is a whole-program property: It relies on the entirety of the code base being constant-time. But, cryptographic developers do not generally write whole programs; rather, they provide libraries and specific algorithms for other application developers to use. As such, developers of security libraries must maintain their security guarantees even when their code is operating within (potentially untrusted) application contexts. Constant-time requires memory safety. The whole-program nature of constant-time also leads to a second issue: constant-time requires memory safety of all the running code. Any memory safety bugs, whether in the library or the application, will wend their way back to side-channel leaks of secrets if not direct disclosure. And although cryptographic libraries should (and are) written to be memory-safe, it is unfortunately unrealistic to expect the same from every application that uses each library. We formalize robust constant-time and build a RobustIsoCrypt compiler that transforms the library code and protects the secrets even when they are linked with untrusted code. Our evaluation with SUPERCOP benchmarking framework shows that the performance overhead is less than five percent on average.