A lot of custom optimization solvers (e.g. Ising Machines) these days benchmark on XOR problems. It's a bit useless in practice because solving a bunch of XOR clauses can be done in polynomial time with Gaussian elimination, yet the solvers all show exponential scaling, but it works as a good way to gauge performance.
A second interesting implementation concerns the McEliece system. It's a public key cryptocipher from the 70s that is enjoying a renaissance these days due to being quantum-resistant. The decoding attack involves finding a solution to a set of XOR equations (again, polynomial), but where the Hamming distance is equal to some number (given, part of the public key).
A second interesting implementation concerns the McEliece system. It's a public key cryptocipher from the 70s that is enjoying a renaissance these days due to being quantum-resistant. The decoding attack involves finding a solution to a set of XOR equations (again, polynomial), but where the Hamming distance is equal to some number (given, part of the public key).