Anonymous allocation and majority voting in a compromised environment

1. A system for anonymous job allocation and majority voting in a cloud computing environment, the system comprising:

one or more processors and a non-transitory memory having instructions encoded thereon such that when the instructions are executed, the one or more processors perform operations of:

broadcasting an executable job to a plurality of physical nodes, each of the physical nodes having a single control operations plane (COP) node and one or more service nodes associated with the COP node;

creating, jointly amongst a plurality of COP nodes, a private job assignment schedule;

distributing a set of redundant job assignments with value m to individual COP nodes pursuant to the private job assignment schedule, such that each individual COP node is only aware of its own assignment and corresponding job, wherein at least m COP nodes are assigned to the job with a probability greater than a predetermined threshold;

executing, by the service nodes, the job assigned to the at least m COP nodes such that the service nodes each complete a task associated with the job a forward an individual result y i to their associated COP node;

performing, jointly amongst the at least m COP nodes, a privacy-preserving result checking protocol such that the at least m COP nodes obtain secret shares of a majority result,

where in performing the result checking protocol, a voting algorithm for determining the majority value is implemented, wherein the voting algorithm comprises a voting phase,

wherein during the voting phase,

each node assigned to the job secretly shares [hash(y i )];

each node not assigned the job shares nothing;

each node computes [v i j ]=[b i j ]·[hash(y i )], where [ ] is a notation for shares of a secret, v is an intermediate value, and b is an input;

each node computes [c j ]=Σ i=1 n [v i j ]; and

each P i broadcasts [c j ] for all j,

wherein the majority result is the individual result y i obtained by a determined majority of the service nodes; and

providing the majority result to a client.

2. The system as set forth in claim 1 , wherein a value representing the determined majority of the service nodes is hidden from any corrupted nodes unless a corrupted node is assigned to the job.

3. The system as set forth in claim 2 , wherein the voting algorithm further comprises a majority decision phase.

4. The system as set forth in claim 3 , wherein during the majority decision phase,

each node recovers c j for all j;

each node computes c which appears most frequently among c j values;

each node sends c to the client;

each node assigned to the job sends y i to the client; and

each node not assigned to the job sends nothing to the client.

5. The system as set forth in claim 4 , wherein any y i that satisfies hash(y i )=c is provided as the majority result to the client.

6. A computer implemented method for anonymous job allocation and majority voting in a cloud computing environment, the method comprising an act of:

causing one or more processers to execute instructions encoded on a non-transitory computer-readable medium, such that upon execution, the one or more processors perform operations of:

broadcasting an executable job to a plurality of physical nodes, each of the physical nodes having a single control operations plane (COP) node and one or more service nodes associated with the COP node;

creating, jointly amongst a plurality of COP nodes, a private job assignment schedule;

distributing a set of redundant job assignments with value m to individual COP nodes pursuant to the private job assignment schedule, such that each individual COP node is only aware of its own assignment and corresponding job, wherein at least m COP nodes are assigned to the job with a probability greater than a predetermined threshold;

executing, by the service nodes, the job assigned to the at least m COP nodes such that the service nodes each complete a task associated with the job and forward an individual result y i to their associated COP node;

performing, jointly amongst the at least m COP nodes, a privacy-preserving result checking protocol such that the at least m COP nodes obtain secret shares of a majority result,

where in performing the result checking protocol, a voting algorithm for determining the majority value is implemented, wherein the voting algorithm comprises a voting phase,

wherein during the voting phase,

each node assigned to the job secretly shares [hash(y i )];

each node not assigned the job shares nothing;

each node computes [v i j ]=[b i j ]·[hash(y i )], where [ ] is a notation for shares of a secret, v is an intermediate value, and b is an input;

each node computes [c j ]=Σ i=1 n [v i j ]; and

each P i broadcasts [c j ] for all j,

wherein the majority result is the individual result y i obtained by a determined majority of the service nodes; and

providing the majority result to a client.

7. The method as set forth in claim 6 , wherein a value representing the determined majority of the service nodes is hidden from any corrupted nodes unless a corrupted node is assigned to the job.

8. The method as set forth in claim 7 , wherein the voting algorithm further comprises a majority decision phase.

9. The method as set forth in claim 8 , wherein during the majority decision phase,

each node recovers c j for all j;

each node computes c which appears most frequently among c j values;

each node sends c to the client;

each node assigned to the job sends y i to the client; and

each node not assigned to the job sends nothing to the client.

10. The method as set forth in claim 9 , wherein any y i that satisfies hash(y i )=c is provided as the majority result to the client.

11. A computer program product for anonymous job allocation and majority voting in a cloud computing environment, the computer program product comprising:

computer-readable instructions stored on a non-transitory computer-readable medium that are executable by a computer having one or more processors for causing the processor to perform operations of:

broadcasting an executable job to a plurality of physical nodes, each of the physical nodes having a single control operations plane (COP) node and one or more service nodes associated with the COP node;

creating, jointly amongst a plurality of COP nodes, a private job assignment schedule;

distributing a set of redundant job assignments with value m to individual COP nodes pursuant to the private job assignment schedule, such that each individual COP node is only aware of its own assignment and corresponding job, wherein at least m COP nodes are assigned to the job with a probability greater than a predetermined threshold;

executing, by the service nodes, the job assigned to the at least m COP nodes such that the service nodes each complete a task associated with the job a forward an individual result y i to their associated COP node;

performing, jointly amongst the at least m COP nodes, a privacy-preserving result checking protocol such that the at least m COP nodes obtain secret shares of a majority result,

where in performing the result checking protocol, a voting algorithm for determining the majority value is implemented, wherein the voting algorithm comprises a voting phase,

wherein during the voting phase,

each node assigned to the job secretly shares [hash(y i )];

each node not assigned the job shares nothing;

each node computes [v i j ]=[b i j ]·[hash(y i )], where [ ] is a notation for shares of a secret, v is an intermediate value, and b is an input;

each node computes [c j ]=Σ i=1 n [v i j ]; and

each P i broadcasts [c j ] for all j,

wherein the majority result is the individual result y i obtained by a determined majority of the service nodes; and

providing the majority result to a client.

12. The computer program product as set forth in claim 11 , wherein a value representing the determined majority of the service nodes is hidden from any corrupted nodes unless a corrupted node is assigned to the job.

13. The computer program product as set forth in claim 12 , wherein the voting algorithm further comprises a majority decision phase.

14. The computer program product as set forth in claim 13 , wherein during the majority decision phase,

each node recovers c j for all j;

each node computes c which appears most frequently among c j values;

each node sends c to the client;

each node assigned to the job sends y i to the client; and

each node not assigned to the job sends nothing to the client.

15. The computer program product as set forth in claim 14 , wherein any y i that satisfies hash(y i )=c is provided as the majority result to the client.

16. The system as set forth in claim 1 , wherein the client is a vehicle, and wherein the majority result is an optimal route to a destination for the vehicle.

17. The system as set forth in claim 16 , wherein the one or more processors further perform an operation of causing the vehicle to maneuver along the optimal route.