an1 means 'safe'
an1 means 'safe' 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'.