Implementation of an encrypted SQL SELECT query, executed in FHE over a clear database.

The client encrypts the query, and the server, which has access to the clear database, executes run_fhe_query on it. The encrypted result is then decrypted by the client and compared against the duckdb SQL backend result.

To run the program you will need to specify a path to the database directory, with each table as a csv file, and the path to a file containing the SQL query.

cargo run --release -- --input-db path/to/db_dir --query-file path/to/query.txt

The supported table types are bools, 8-bit, 16-bit, 32-bit and 64-bit signed and unsigned integers, as well as short strings (up to 32 ASCII characters). The csv files must contain column headers with the following format:

column_1_name:int64,column_2_name:uint64,column_3_name:string,column_4_name:bool

Tests can simply be run with cargo test --release, although this will be very slow.

• = and != for all types. For boolean columns, you can use the column name without an operator to check if it is true (e.g. is_employed is equivalent to is_employed = true).
• >, <, >=, <=, BETWEEN, NOT BETWEEN, IN and NOT IN for all types except bools.
• AND, OR and NOT to combine conditions. Nested NOTs are properly reduced before encryption.
• The DISTINCT flag.

Our encrypted query contains an encrypted bool vector signaling which columns are selected, the encrypted selected table name (FROM), a perfect Abstract Syntax Tree with encrypted node operators and leaves (the WHERE conditions) and the encrypted DISTINCT boolean flag.

The selected columns vector is set to the maximum column length across all tables to prevent the server from inferring information about the selected table.

Additionally, the WHERE AST is filled with (encrypted) NoOp leaves to conceal the exact tree structure. Leaves contain arguments for comparison operators, which require a single encrypted value, and for BETWEEN and IN operators, which can contain two or more values. We pad the leaves to a constant size to prevent the server from inferring the leaf operator. The minimum leaf size is 2, as the BETWEEN operator requires two values (lower and upper bounds).

Finally, all leaf values must be encrypted with the same bit length to prevent the server from deducing the column type. For example, SELECT ... WHERE enc_col enc_op 64_bit_enc_value would reveal information about the column type being compared.

The server needs to perform the WHERE and DISTINCT computations on the selected table. If there's only one table in the database, server doesn't need to perform any table selection in FHE. That table is the selected one as the client cannot select a non-existing table.

However, if there are two or more tables in the database, the server will compute the union of all tables. In this union, only overlapping values between two or more tables are selected using FHE. Values from a table that do not overlap with others at the same position are kept in the clear.

To optimize leaf operations we "recycle" computations in the following way (note that the boolean operators here refer to the FHE boolean methods):

• != is computed as NOT =.
• > is computed as NOT = AND NOT <.
• >= is computed as NOT <.
• <= is computed as NOT >.
• The lower bound comparison of BETWEEN is the >= result.
• The first equality comparison of IN is the = result.

Technically, our leaf evaluation functions are not aware of the !=, >=, and <= operations, as these operators are rewritten before encryption as a negated =, <, and >, respectively.

Another potential optimization would be to use 7 bits (rather than 8) for each ASCII character. Since all the leaf values are stored with the maximum bit length, we could reduce this length by 12.5%. While this optimization is straightforward, it is not particularly interesting, so we are currently using 8 bits.