Is it possible that a backdoor key exists?
If a backdoor exists then you could simply compute the private key given the public key and the backdoor key.
If a backdoor exists then you could simply compute the private key given the public key and the backdoor key.
I think it's possible, but how likely I don't know. Seems unlikely because cryptography experts would have probably tuned the larger bitcoin community into the risk of that, and there would be more chatter of developing alternate hashing algorithms.
If there is a backdoor it's a closely guarded secret that no one has seen any evidence of.