an1 is made up of . The first component is a non-character that is a graphical representation of a shelter or roof while the second component is nü3 which means 'woman' (a hierogylph depicting a woman with a belly sitting with her legs crossed). When a woman has shelter she is 'safe'. Other meanings of an are 'peaceful' and 'to let rest'.
an1quan2 means 'safe and secure' and literally translates as 'safe'-'complete'.
quan2 is the modern written form and the original character had the following components instead . The first component is the character ru4 meaning 'enter' while the second component is the character yu4 meaning 'jade'. It is believed that possession of jade brings good omen and therefore jade that is entered into our safe custody makes us complete.
gong1an1 means 'police' and literally translates as 'public'-'safe'.
gong1 can be broken down into . Etymologists believe that the first component originally meant 'to divide' with the connotation of 'break up'. The second component is the character si which means 'selfish'. By 'breaking up selfishness' things are 'fair' and therefore 'public'.