Forward secrecy of key-establishment (KE) protocol means, that compromising of long-term keys of parties doesn't affect secrecy of established keys in the past.
Example to clarify what PFS means.
Say parties A and B have private keys $s_B$ and $s_B$.
Today they run KE and establish a key $k_1$.
They use this key during a session, and then destroy this key.
During this session, attacker eavesdropped all the messages and remembers the transcript $T$ of the session. Obviously, $T$ includes messages of KE,
and subsequent "data" messages, encrypted with key $k_1$.
Tomorrow, attacker somehow gets keys $s_A$ and $s_B$, but not $k_1$ (because $k_1$ was destroyed and forgotten by $A$ and $B$).
And here comes PFS property of KE: even having $T$, $s_A$ and $s_B$, attacker is unable to find $k_1$ and decrypt messages hidden in $T$.
Then answering your question, why in PFS word "perfect" is ambiguous.
It's an opinion of M.Green obviously, but I will try to guess what he means.
Actually I feel pretty the same regarding this term. "Perfect" is ambiguous here.
E.g., we don't use "perfectly secure signature scheme", we just use "secure".
Moreover, in cryptography word "perfect" appears sometimes in order to describe
that some property (usually some sort of secrecy) is based not on computational assumptions, but it's perfect - i.e., unconditional and doesn't require any assumptions/hypotheses.
Examples:
So, in cryptography "perfect" is usually a synonym to
https://en.wikipedia.org/wiki/Information-theoretic_security.
But for some stupid reason - not in this case (in case of KE).
So, more clear would be to have a term "Forward Secrecy", and then, additional "Perfect" would mean that it doesn't require any assumptions and it's unconditional.
But for some historic reason, in literature PFS is used for regular forward secrecy.
PFS is also known as forward secrecy
. This may indicate FPS was earlier. I've no free access to this document... $\endgroup$ – kelalaka Jul 5 '20 at 19:49