A method is provided for use in secure electronic communication. The method may include obtaining a password shared with an intended key exchange entity and sending a key exchange request including a first value to the intended key exchange entity. The method may also include receiving a key exchange reply including a permutation of a first quadratic residue of the first value, and calculating a second quadratic residue of the first value based on the key exchange reply. Further, the method may also include determining a second value shared with the key exchange entity based on the first quadratic residue and the second quadratic residue.