The only thing required to sign transactions is the private key (the mnemonic seed is not needed), you already have the public key once a transaction is signed in the blockchain.
Elliptic Curve Cryptography guarantee that it is computationally hard to determine the private key given only the public key. Quantom computers can change that assertion but today they are really far from being close.
It is kind of useless to calculate the mnemonic seed, because you already have the private key. But it is hard to determine seed from the private key. To derive the private key you use a key derivation to get a binary seed, and then further transform it to generate a hd wallet.
The security of this steps is based on key derivation function used PBKDF2. From the wikipedia page:
One weakness of PBKDF2 is that while its number of iterations can be adjusted to make it take an arbitrarily large amount of computing time, it can be implemented with a small circuit and very little RAM, which makes brute-force attacks using application-specific integrated circuits or graphics processing units relatively cheap.
So it is hard but it might not ressist a determined attack with ASIC chips.