This would massively break basically all traditional public key crypto i think (depends a bit on if it extends to eliptic-curve or just integer based RSA [edit: meant to say whether the algorithm can be adapted to solving discrete logrithms over eliptic curves]). It would be the biggest crypto thing to happen in the last 30 years at least.

The mitigation would be to move to experimental post-quantum crypto systems immediately (quantum computers have all the fuss because they can break rsa).

This is basically an unbelievable result. Without actually providing some factored numbers i am very doubtful.

[I have not read paper]

Edit: as pointed out below, i may have gotten overexcited. Still an incredible result if true.