What is confusing about this "proof" is there is an implicit trusted third party. Let's call him Charlie.
After solving the Sudoku puzzle, Paula needs to give Charlie her solution, ... and a permutation.
Victor gets to ask one of 28 possible questions, and Charlie gives him the (permuted) response.
When Victor wishes to ask another question, Charlie first gets another (random) permutation from Paula, and then discloses the next (differently permuted) response.
The confusion comes from some readers thinking Paula is the one telling Victor a row, column, block, etc., ... and thus perhaps she might lie or cheat.
Victor needs to be able to rely on the trusted referee who knows the solution, and all Paula is allowed to do is give (valid) permutations, ... and then Victor will be convinced. If Victor needs to rely on Paula, then Victor could save everyone a lot of work and simply ask Paula, "Have you solved this Sudoku puzzle?"
In fact, since Victor needs to be able to rely on a trustworthy third party, Victor need only ask Charlie: "Did Paula give you a valid solution?", ... again, saving everyone lots of work.
While article does talk about Victor being convinced of something (Paula solved the puzzle) with Zero-Knowledge of the specific details of the solution, ... it doesn't seem to be a useful example of how Zero-Knowledge proofs can be put to practical use in Computer Science applications.
I don't think you're correct, although I upvoted you before I thought that because you seemed to be explaining the problem I had with the article. However, reading the article's comments it becomes clear that there's 81 locked boxes, one for every cell in the Sudoku grid. The key Victor chooses from the 28 Paula proffers will open nine of the 81 boxes. Those nine have to be consistent amongst themselves, i.e. a permutation of 1-9, despite Paula not know which of the 28 keys would be chosen.
After solving the Sudoku puzzle, Paula needs to give Charlie her solution, ... and a permutation.
Victor gets to ask one of 28 possible questions, and Charlie gives him the (permuted) response.
When Victor wishes to ask another question, Charlie first gets another (random) permutation from Paula, and then discloses the next (differently permuted) response.
The confusion comes from some readers thinking Paula is the one telling Victor a row, column, block, etc., ... and thus perhaps she might lie or cheat.
Victor needs to be able to rely on the trusted referee who knows the solution, and all Paula is allowed to do is give (valid) permutations, ... and then Victor will be convinced. If Victor needs to rely on Paula, then Victor could save everyone a lot of work and simply ask Paula, "Have you solved this Sudoku puzzle?"
In fact, since Victor needs to be able to rely on a trustworthy third party, Victor need only ask Charlie: "Did Paula give you a valid solution?", ... again, saving everyone lots of work.
While article does talk about Victor being convinced of something (Paula solved the puzzle) with Zero-Knowledge of the specific details of the solution, ... it doesn't seem to be a useful example of how Zero-Knowledge proofs can be put to practical use in Computer Science applications.