Systems and methods for hiding response volume with encrypted multi-maps
A volume hiding structured encryption system and method is provided. According to some embodiments, the system leverages the principle that a STE scheme can leak cumulative information about the query volumes of the data stored in multi-map format, while still hiding the volumes of client queries at query time. According to various examples, the system implements encryption schemes that have smaller storage and better query complexity than the current state-of-the-art, for some input distributions. According to one example, the STE schemes are adapted to the input data structure in order to improve efficiency over known approaches. Further examples includes schemes that are configured to partition a multi-map into smaller multi-maps, and use different allocation functions for different efficiency trade-offs: (i) random allocation, (ii) cuckoo-hashing allocation, and (iii) Garbled Bloom Filter allocation. In one example, the GBF construct enables a stash-less encryption scheme that hides query volumes.
1. A volume hiding encryption system comprising:
at least one processor operatively connected to a memory, the at least one processor when executing, is configured to:
execute setup operations on an input multi-map data structure;
transform the input multi-map data structure into at least two multi-map data structures as part of the setup operations, wherein the operation to transform includes an operation to generate a minimum number of encrypted values based on at least one characteristic of one or more tuples in the input multi-map;
encrypt the at least two multi-map data structures;
store the encrypted form of the at least two multi-map data structures for executing queries; and
execute queries on the encrypted form of the at least two multi-map data structures, wherein execution of each query reads a system defined number of encrypted values irrespective of a length of a tuple stored in the input multi-map.
2. The system of claim 1 , wherein the system defined number is a fixed number.
3. The system of claim 1 , wherein the operation to generate the minimum number of encrypted values based on at least one characteristic of one or more tuples in the input multi-map includes an operation to generate the minimum number of encrypted values based on at least a minimum length of a tuple in the input multi-map.
4. The system of claim 1 , wherein the operation to transform the input multi-map data structure into at least two multi-map data structures as part of the setup operations includes an operation to build a first multi-map storing a first set of values from every tuple in the input multi-map for tuple values up to a minimum response length.
5. The system of claim 4 , wherein the at least one processor is configured to construct a second multi-map storing tuple values for tuples exceeding a minimum response length.
6. The system of claim 5 , wherein the at least one processor is configured to assign storage locations in the second multi-map based on logarithmic choice for the storage location.
7. The system of claim 5 , wherein the at least one processor if configured to assign storage locations in the multi-map data structure based on cuckoo-hashing allocation or garbled bloom filter allocation.
8. The system of claim 5 , wherein the at least one processor is configured to assign dummy values to any empty storage locations in the second multi-map.
9. The system of claim 4 , wherein the at least one processor is configured to store any excess values in a stash repository responsive to identifying allocated locations.
10. The system of claim 4 , wherein the at least one processor is configured to generate an encrypted dictionary storing the storage location labels and contents.
11. The system of claim 1 , wherein a first one of the at least two multi-map data structures is constructed based on a consistent size tuple, and the second one of the at least two multi-map data structures is constructed to include at least some values that store data exceeding the consistent size of the first multi-map data structure.
12. The system of claim 1 , wherein the at least one processor is configured to execute queries to include at least operations to:
retrieve encrypted values from the first one of the at least two multi-map data structures; and
obscure a volume associated with a client query based on retrieving encrypted values from an encrypted dictionary needed to reconstruct a plaintext query response at the client.
13. The system of claim 1 , wherein the at least one processor is configured to store the encrypted form of the at least two multi-map data structures for executing queries without requiring a stash for excess values.
14. A computer implemented method for volume hiding encryption, the method comprising:
executing, by the at least one processor, setup operations on an input multi-map data structure;
transforming, by the at least one processor, the input multi-map data structure into at least two multi-map data structures as part of the setup operations, wherein transforming includes generating a minimum number of encrypted values based on at least one characteristic of one or more tuples in the input multi-map;
encrypting, by the at least one processor, the at least two multi-map data structures;
storing, by the at least one processor, the encrypted form of the at least two multi-map data structures for executing queries; and
executing, by the at least one processor, queries on the encrypted form of the at least two multi-map data structures, wherein the act of executing for each query reads a system defined number of encrypted values irrespective of a length of a tuple stored in the input multi-map.
15. The method of claim 14 , wherein the system defined number of encrypted values is a fixed number for a given input multi-map.
16. The method of claim 14 , wherein generating the minimum number of encrypted values based on at least one characteristic of one or more tuples in the input multi-map includes generating a minimum number of encrypted values based on at least a minimum length of a tuple in the input multi-map.
17. The method of claim 16 , wherein transforming includes generating a second multi-map storing tuple values for tuples exceeding a minimum response length.
18. The method of claim 14 , wherein transforming the input multi-map data structure into at least two multi-map data structures as part of the setup operations includes generating a first multi-map storing a first set of values from every tuple in the input multi-map for tuple values up to a minimum response length.
19. The method of claim 18 , wherein generating the second multi-map includes assigning storage locations in the second multi-map based on logarithmic choice for the storage location.
20. The method of claim 14 , wherein the method further comprises assigning storage locations in the multi-map data structure based on cuckoo-hashing allocation or garbled bloom filter allocation.