Secure equi-join apparatus, secure equi-join method, and program
A secret equi-join device uses as inputs a first concealed table that is concealed information of a first table having a plurality of keys and a second concealed table that is concealed information of a second table having a plurality of keys, obtains a first concealed additional table that is concealed information of a first additional table which is obtained by adding a subkey column to the first table, obtains by secure computation a second concealed additional table that is concealed information of a second additional table which is obtained by adding a subkey column further to a third table obtained by copying each record in the second table a plurality of times and adding the copied records, and obtains a concealed joined table that is concealed information of a joined table which is obtained by equi-joining the first additional table and the second additional table.
1 . A secret equi-join device comprising:
(a) a storage;
(b) a first subkey column addition processing circuitry;
(c) a second subkey column addition processing circuitry; and
(d) a secret equi-join processing circuitry, wherein
(a) the storage stores
a first concealed table that is concealed information of a first table including a first key column having a plurality of first keys and a first arbitrary element column having a plurality of first arbitrary elements, and
a second concealed table that is concealed information of a second table including a second key column having a plurality of second keys and a second arbitrary element column having a plurality of second arbitrary elements,
(b) the first subkey column addition processing circuitry obtains, by secure computation using the first concealed table, a first concealed additional table that is concealed information of a first additional table which is obtained by adding a first subkey column to the first table,
the first subkey column has a plurality of first subkeys,
each of the first keys is associated with any of the first subkeys,
a maximum value of a number of the first keys of same value contained in the first key column is KL,
KL is an integer of 2 or more,
the first keys of the same value are associated with the first subkeys of different values,
(c) the second subkey column addition processing circuitry obtains, by secure computation using the second concealed table, a second concealed additional table that is concealed information of a second additional table which is obtained by adding a second subkey column to a third table,
respective records in the second table include the respective second keys and the respective second arbitrary elements,
the third table is a table which is obtained by adding a plurality of copied records, obtained by copying each of the records in the second table K times, to the second table, and K≥KL,
the third table includes a third key column having a plurality of third keys that include the second key and a copy of the second key, and a third arbitrary element column having a plurality of third arbitrary elements that include the second arbitrary element and a copy of the second arbitrary element,
the second subkey column contains a plurality of second subkeys,
each of the third keys is associated with any of the second subkeys,
when the third key column contains the third keys representing a same common value as any of the first keys, at least some of the third keys representing the common value are associated with the second subkeys of same value as the first subkeys associated with the first keys representing the common value, and
(d) the secret equi-join processing circuitry obtains, by secure computation using the first concealed additional table and the second concealed additional table, a concealed joined table that is concealed information of a joined table which is obtained by equi-joining the first additional table and the second additional table, using a pair of the first key and the first subkey as a key attribute of the first additional table and a pair of the third key and the second subkey as a key attribute of the second additional table.
2 . The secret equi-join device according to claim 1 , wherein when the third key column contains the third keys representing the common value, a value of any of the first subkeys associated with the first keys representing the common value is same value as any of the second subkeys associated with the third keys representing the common value.
3 . The secret equi-join device according to claim 1 , wherein
K=KL.
4 . The secret equi-join device according to claim 1 , wherein
a maximum value of a number of the second keys of same value contained in the second key column is equal to or less than the maximum value of the number of the first keys of the same value contained in the first key column.
5 . The secret equi-join device according to claim 1 , further comprising:
(e) a table resetting processing circuitry that, when a maximum value of a number of the second keys of same value contained in the second key column is larger than a maximum value of the number of the first keys of same value contained in the first key column,
swaps the first concealed table with the second concealed table, and
resets the first table including the first key column having the first key and the first arbitrary element column having the first arbitrary element and the second table including the second key column having the second key and the second arbitrary element column having the second arbitrary element as the second table including the second key column having the second key and the second arbitrary element column having the second arbitrary element and the first table including the first key column having the first key and the first arbitrary element column having the first arbitrary element, respectively.
6 . The secret equi-join device according to claim 1 , wherein
a number of records in the first table is LRN,
a number of records in the second table is RRN,
LRN and RRN are integers of 2 or more,
(b) j=0, . . . , LRN−1,
a j-th first key in the first key column is TL.Key j ,
the j-th first subkey in the first subkey column is TL s .S j ,
when j=0, TL s .S j =0,
when j>0 and TL.Key j ≠TL.Key j−1 , TL s .S j =0,
when j>0 and TL.Key j =TL.Key j−1 , TL s .S j =TL s .S j−1 +1,
(c) i=0, . . . , RRN*K−1,
a quotient of i divided by K is idk,
imk=i−idk*K
an idk-th record in the second table is TR idk ,
an i-th record in the third table is TR ci ,
TR ci =TR idk ,
the i-th second subkey in the second subkey column is TRs.S i , and
TRs.S i =imk.
7 . A secret equi-join method of a secret equi-join device, the secret equi-join method comprising:
(a) a storage step;
(b) a first subkey column addition step;
(c) a second subkey column addition step; and
(d) a secret equi-join step, wherein
(a) the storage step is a step of storing, into a storage,
a first concealed table that is concealed information of a first table including a first key column having a plurality of first keys and a first arbitrary element column having a plurality of first arbitrary elements, and
a second concealed table that is concealed information of a second table including a second key column having a plurality of second keys and a second arbitrary element column having a plurality of second arbitrary elements,
(b) the first subkey column addition step is a step of obtaining, by secure computation using the first concealed table, a first concealed additional table that is concealed information of a first additional table which is obtained by adding a first subkey column to the first table,
the first subkey column has a plurality of first subkeys,
each of the first keys is associated with any of the first subkeys,
a maximum value of a number of the first keys of same value contained in the first key column is KL,
KL is an integer of 2 or more,
the first keys of the same value are associated with the first subkeys of different values,
(c) the second subkey column addition step is a step of obtaining, by secure computation using the second concealed table, a second concealed additional table that is concealed information of a second additional table which is obtained by adding a second subkey column to a third table,
respective records in the second table include the respective second keys and the respective second arbitrary elements,
the third table is a table which is obtained by adding a plurality of copied records, obtained by copying each of the records in the second table K times, to the second table, and K≥KL,
the third table includes a third key column having a plurality of third keys that include the second key and a copy of the second key, and a third arbitrary element column having a plurality of third arbitrary elements that include the second arbitrary element and a copy of the second arbitrary element,
the second subkey column contains a plurality of second subkeys,
each of the third keys is associated with any of the second subkeys,
when the third key column contains the third keys representing a same common value as any of the first keys, at least some of the third keys representing the common value are associated with the second subkeys of same value as the first subkeys associated with the first keys representing the common value, and
(d) the secret equi-join step is a step of a obtaining, by secure computation using the first concealed additional table and the second concealed additional table, a concealed joined table that is concealed information of a joined table which is obtained by equi-joining the first additional table and the second additional table, using a pair of the first key and the first subkey as a key attribute of the first additional table and a pair of the third key and the second subkey as a key attribute of the second additional table.
8 . A non-transitory computer-readable recording medium storing a program for causing a computer to function as the secret equi-join device according to claim 1 .