Abstract: Aggregate statistics are securely determined on private data by first sampling independent first and second data at one or more clients to obtain sampled data, wherein a sampling parameter substantially smaller than a length of the data. The sampled data are encrypted to obtain encrypted data, which are then combined. The combined encrypted data are randomized to obtain randomized data. At an authorized third-party processor, a joint distribution of the first and second data is estimated from the randomized encrypted data, such that a differential privacy requirement of the first and second is satisfied.

Abstract: Aggregate statistics are determined by first randomizing independently data X and Y to obtain randomized data {circumflex over (X)} and ?. The first randomizing preserves the privacy of the data X and Y. Then, the randomized data {circumflex over (X)} and ? is randomized secondly to obtain randomized data {tilde over (X)} and {tilde over (Y)} for a server, and helper information T{tilde over (X)}|{circumflex over (X)} and T?|? for a client, wherein T represents an empirical distribution, and wherein the randomizing secondly preserves the privacy of the aggregate statistics of the data X and Y. The server then determines T{tilde over (X)},{tilde over (Y)}. Last, the client applies the side information T{tilde over (X)}|{circumflex over (X)} and T?|? to T{tilde over (X)},{tilde over (Y)} to obtain an estimated {dot over (T)}X,Y, where “|” and “,” between X and Y represent a conditional and joint distribution, respectively.

Abstract: Aggregate statistics are securely determined on private data by first sampling independent first and second data at one or more clients to obtain sampled data, wherein a sampling parameter substantially smaller than a length of the data. The sampled data are encrypted to obtain encrypted data, which are then combined. The combined encrypted data are randomized to obtain randomized data. At an authorized third-party processor, a joint distribution of the first and second data is estimated from the randomized encrypted data, such that a differential privacy requirement of the first and second is satisfied.

Abstract: Aggregate statistics are determined by first randomizing independently data X and Y to obtain randomized data {circumflex over (X)} and ?. The first randomizing preserves the privacy of the data X and Y. Then, the randomized data {circumflex over (X)} and ? is randomized secondly to obtain randomized data {tilde over (X)} and {tilde over (Y)} for a server, and helper information T{tilde over (X)}|{circumflex over (X)} and T?|? for a client, wherein T represents an empirical distribution, and wherein the randomizing secondly preserves the privacy of the aggregate statistics of the data X and Y. The server then determines T{tilde over (X)},{tilde over (Y)}. Last, the client applies the side information T{tilde over (X)}|{circumflex over (X)} and T?|? to T{tilde over (X)},{tilde over (Y)} to obtain an estimated {dot over (T)}X,Y, where “|” and “,” between X and Y represent a conditional and joint distribution, respectively.

Abstract: A method for dynamic channel allocation for access points in wireless networks. Communication information of wireless devices is gathered. A network topology formed by the wireless devices is derived according to the communication information. Switch channel indexes for each wireless device are calculated according to the communication information and network topology. Desired wireless devices for switching channels are determined according to the switch channel indexes.

Abstract: A method for dynamic channel allocation for access points in wireless networks. Communication information of wireless devices is gathered. A network topology formed by the wireless devices is derived according to the communication information. Switch channel indexes for each wireless device are calculated according to the communication information and network topology. Desired wireless devices for switching channels are determined according to the switch channel indexes.