# Compute euclidian distance on encrypted data

The scenario is described as following: Let $$A$$ an user that is transmitting an encrypted (with its own public key $$PK_A$$) data vector containing its position as $$p = Enc(PK_A, [x,y])$$ towards a group of users $$U = [u_1, u_2, \dots, u_n]$$.

Is it possible that each of these users belonged to the group $$U$$ positioned at different distances from $$A$$ can compute respective the euclidian distance on it (on the encrypted data that they received I mean)?

One sufficient reason: in any scheme matching the standard goals of public-key encryption, including homomorphic, nothing about information encrypted with a public key can be determined from the cryptogram without the matching private key. Thus $$p$$, encrypted under A's public key, can't be used by others (not knowing A's private key) to determine the distance of A to another point.