1. A computer-based method for securely sharing sensitive documents, wherein a non-sensitive vector space is embodied in a computer readable medium, and the non-sensitive vector space includes non-sensitive term vectors and non-sensitive document vectors corresponding to a collection of non-sensitive documents, the computer-based method comprising: (a) transmitting a subset of the non-sensitive term vectors to a plurality of entities that each manage a sensitive document database, each non-sensitive term vector corresponding to a non-sensitive term; (b) receiving offset vectors from the plurality of entities responsive to sensitive documents in the sensitive document databases that contain the non-sensitive terms; (c) updating the term vectors in the non-sensitive vector space responsive to the offset vectors from the sensitive documents, wherein step (c) comprises: updating the term vectors in the non-sensitive vector space responsive to the offset vectors, such that a first term vector is updated based on a combination of offset vectors respectively received from each entity, and updating the term vectors in the non-sensitive vector space responsive to the offset vectors, such that a new term vector is generated for each offset vector; (d) generating a vector representation of a query in the non-sensitive vector space based on the updated term vectors; and (e) identifying at least one non-sensitive document based on a comparison between the vector representation of the query and the non-sensitive document vectors.