- The use of constraint solvers, such as SAT- or Pseudo-Boolean-solvers, allows the extraction of the secret key from one or two side-channel traces. However, to use such a solver the cipher must be represented at bit-level. For byte-oriented ciphers this produces very large and unwieldy instances, leading to unpredictable, and often very long, run times. In this paper we describe a specialized byte-oriented constraint solver for side channel cryptanalysis. The user only needs to supply code snippets for the native operations of the cipher, arranged in a flow graph that models the dependence between the side channel leaks. Our framework uses a soft decision mechanism which overcomes realistic measurement noise and decoder classification errors, through a novel method for reconciling multiple probability distributions. On the DPA v4 contest dataset our framework is able to extract the correct key from one or two power traces in under 9 seconds with a success rate of over 79%.