What is the difference between implausibility vs impossibility in the context of Crypto? I came to know that differing input indistinguishability Obfuscation (diO) implausibile but not impossible. Can I know the difference between the two terminologies?
This is a fairly clear cut mathematical distinction and not really phraseology nor semantics, especially in the sciences.
Implausible ~= Unlikely
Go back 10 years and consider the SHA-1 hash function. Reversing this function is (was) hard and therefore very unlikely. Today this has been kinda achieved in being able to generate collisions, but at great computational expense. This has started us on a path where perhaps tomorrow Google might improve on the technique and allow SHA-1 reversal on mobile phone level computational power. Or to only need the computational power of the iPhone10 when it starts selling. This fate befell MD5.
Similarly, Ivan Verykleverkov might be working in his Moscow University dorm room today at improving Shor's Algorithm. If the Verykleverkov Algorithm allows easy factorisation of primes on non quantum machines, RSA encryption and Blum Blum Shub random number generators become useless cryptographically overnight.
The theme here is something that is unlikely now does not preclude it (on a logical or mathematical basis) from becoming likely tomorrow.
Impossible = Impossible
Decrypting a properly applied One Time Pad (OTP) encryption is impossible. If the pad was generated using true entropy, there is no mathematical solution to reversal. The only solution is brute force attack leading to many possible alternative solutions. Contextual and semiotic analysis may ween some out (as implausible) but you'll still be left with many plain texts each of equal validity. This perfect secrecy is the OTP's draw and reason for all the related questions on this forum.
So in summary, one means the cryptography is currently secure but might be broken with future scientific advances whilst the other is mathematically proven to be secure for all time.