The correctness of the algorithm relies on a number-theoretic heuristic assumption reminiscent of those used in subexponential classical factorization algorithms. It is currently not clear if the algorithm can lead to improved physical implementations in practice.
Shor's celebrated algorithm allows to factorize n-bit integers using a quantum circuit of
size O(n^2). For factoring to be feasible in practice, however, it is desirable to reduce this number further. Indeed, all else being equal, the fewer quantum gates there are in a circuit, the likelier it is that it can be implemented without noise and decoherence destroying the quantum effects.
The new algorithm can be thought of as a multidimensional analogue of Shor's algorithm. At the core of the algorithm is a quantum procedure.
Without full fault tolerance in quantum computers we will never practically get past 100 qubits but full fault tolerance will eventually open up the possibility of billions of qubits and beyond. In a Wright Brothers Kittyhawk moment for Quantum Computing, a fully fault-tolerant algorithm was executed on real qubits. They were only three qubits but this was never done on real qubits before.
If the new decryptian algorithm is verified and we get fault tolerant qubits at scale, then all current internet and financial encryptian would be broken. There quantum computing resistant math for encoding that would not be vulnerable to quantum computers, but they will likely take a decade or more to implement. It will still take many years for fault tolerant quantum qubits to scale.