Secure multi-party reach and frequency estimation

A method of generating an encrypted data structure representative of a set of identifiers having attributes that satisfy target criteria for secure and computationally efficient transmission, comprising:

• maintaining, by a data processing system comprising one or more processors and a memory, in a database, a set of device identifiers, each of the set of device identifiers comprising a device attribute;
• generating, by the data processing system, a vector data structure comprising a plurality of coordinates each corresponding to a respective one of a plurality of counter registers;
• hashing, by the data processing system, a device identifier of the set of device identifiers using each of a plurality of hash functions to generate a plurality of hashed data record values;
• extracting, by the data processing system, a plurality of register identifiers from the plurality of hashed data record values, each of the plurality of register identifiers corresponding to a respective counter register of the plurality of counter registers;
• accessing, by the data processing system, each of the plurality of counter registers that correspond to the plurality of register identifiers to identify a set of counter registers that satisfy a minimum value threshold, wherein identifying the set of counter registers that satisfy the minimum value threshold comprises:
• determining a value for each respective counter register of the plurality of counter registers to determine a minimum value;
• comparing the value for each respective counter register of the plurality of counter registers;
• and
• identifying one or more counter registers of the plurality of counter registers as satisfying the minimum value threshold if the value of the respective counter register is equal to the minimum value;
• incrementing, by the data processing system, each of the set of counter registers that satisfy the minimum value threshold;
• encrypting, by the data processing system, the vector data structure to create an encrypted data structure, such that the encrypted data structure can be combined with a second encrypted data structure;
• and
• transmitting, by the data processing system, the encrypted vector data structure to a worker computing device.