In the algorithm implemented the search key is matched against all rows in the database. There is no short circuit evaluation and there cannot be... you cannot

In the algorithm implemented the search key is matched against all rows in the database. There is no short circuit evaluation and there cannot be... you cannot compare an encrypted value to a plaintext value and know they are equivalent without decrypting it first (which the server-side cannot do). This is true even for writing the code to do the search since you cannot do and if style comparison on encrypted values to break out of a loop. In the example, each value stored in the database is compared to the encrypted search term producing a partial result that is itself encrypted and meaningless to the server side. Once ALL value rows have been searched, the partial results (all those encrypted meaningless things) of all those comparisons are combined to yield a single encrypted result which is returned to the user that initiated the search. That result is then decrypted. There is no leakage because ALL code paths and all data must be evaluated for the program every time. However, from what I gather, the database can be shattered across multiple backend servers and each subset could be searched in parallel for a speedup for a practical deployment.