Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for implementing a zero knowledge prover are disclosed. In one aspect, a method includes the actions of executing a software program. The method further includes storing an execution trace that includes, for each address in memory, a value at each clock cycle during execution of the software program. The method further includes generating a sorted execution trace by sorting the execution trace. The method further includes determining a constraint for given values in the memory at adjacent clock cycles. The method further includes determining whether the sorted execution trace complies with the constraint and whether the sorted execution trace is a permutation of the execution trace. The method further includes providing, for output, data indicating whether the software program executed correctly while preventing outputting data included in the execution trace or the sorted execution trace.