Quantum Factoring: Are We One Step Closer to Unified Encryption?

Friday - October 13 2023, 01:17 UTC - 1 year ago

A new quantum algorithm has been developed to factor n-bit integers. It requires orders of magnitude fewer qubits than the Classical Shor Algorithm. If it were to be verified, all current internet and financial encryption would be rendered vulnerable, requiring new quantum-proof encryption, likely taking a decade to implement.

Researchershow that n-bit integers can be factorized by independently running a quantum circuit with orders of magnitude fewer qubits many times. It then use polynomial-time classical post-processing. 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.

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.