How many qubits are needed to effectively break RSA encryption?
RSA encryption relies on the difficulty of factoring large prime numbers, which is currently feasible for classical computers but becomes vulnerable with the advent of quantum computers using Shor's algorithm.
Shor's algorithm can factor integers in polynomial time, specifically O((log N)^2 (log log N) (log log log N)), which is a significant improvement over the best-known classical algorithms that operate in sub-exponential time.
To effectively break a 2048-bit RSA key, estimates suggest that a quantum computer would need around 4096 logical qubits, but due to error rates and the need for error correction, the physical qubit requirement could rise dramatically.
Current estimates from researchers indicate that achieving fault-tolerant quantum computing may require millions of physical qubits when factoring RSA keys due to the complexity of error correction codes.
A paper from Fujitsu proposed that factoring a 2048-bit RSA key would require 10,000 qubits and take about 104 days on a quantum computer, highlighting the large resource requirement even for advanced quantum systems.
The number of qubits needed for RSA decryption is sublinear relative to the size of the integer, meaning that as RSA key lengths increase, the qubit requirement grows at a slower rate than the bit length.
A quantum computer currently estimated to possess 20 million qubits could potentially break RSA encryption in just eight hours, which poses a serious threat to long-term data security.
In 2020, researchers demonstrated that quantum computers could theoretically break smaller RSA keys (like 1024-bit) with significantly fewer qubits; estimates suggest around 512 logical qubits may suffice.
The practical implementation of quantum computers today faces challenges with qubit coherence times, meaning qubits can only hold information for a limited duration before decohering, complicating computations.
Quantum error correction is essential for practical quantum computing, requiring multiple physical qubits to represent a single logical qubit, which can inflate the total qubit count significantly.
It is estimated that as technology advances, achieving a fault-tolerant quantum computer capable of breaking RSA encryption could be feasible within the next couple of decades, depending on continued innovations in quantum hardware.
The development of new encryption methods, known as post-quantum cryptography, is already underway to safeguard against potential quantum attacks, as current classical encryption methods are expected to become obsolete against sufficiently powerful quantum computers.
Some researchers claim that merely achieving a non-fault-tolerant quantum state (NISQ) could allow for limited attacks on RSA encryption, indicating that breakthroughs in quantum technology may come sooner than expected.
The relationship between qubit count and RSA key length is not linear; for example, breaking a 4096-bit RSA key may require an estimated 8192 logical qubits, illustrating the exponential growth in resource requirements.
Quantum computers are not exclusively designed to break encryption; they also hold potential for solving complex problems in various fields such as materials science, pharmaceuticals, and optimization.
The ongoing race between advancements in quantum computing and the development of post-quantum cryptographic methods reflects the urgency of securing data against future quantum threats.
The concept of superposition in quantum mechanics allows qubits to exist in multiple states simultaneously, enabling quantum computers to perform many calculations at once, which is key to their potential power.
Quantum entanglement creates correlations between qubits that can be leveraged for error correction and more efficient algorithms, further increasing the complexity of quantum computations.
Existing quantum computers have demonstrated the ability to perform specific tasks faster than classical computers, a phenomenon known as quantum supremacy, though these tasks do not yet include breaking RSA encryption.
As of April 2025, the field of quantum computing is rapidly evolving, and while substantial progress has been made, practical, large-scale quantum computers capable of breaking RSA encryption remain a goal rather than a reality.