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Alice & Bob researchers estimate that factoring RSA-2048 with Shor’s algorithm would take 22,593 physical cat qubits and 3.14 days on a fault-tolerant superconducting quantum computer. The figures are theoretical resource projections, not a demonstration that current quantum computers can break RSA; the company says organizations should begin moving to post-quantum cryptography.
Alice & Bob researchers estimate that a fault-tolerant superconducting quantum computer using 22,593 physical cat qubits could run Shor’s algorithm to factor RSA-2048 in 3.14 days. The estimate, reported in a new paper, is a theoretical resource projection—not a completed attack—and matters because RSA is widely used to protect internet communications and digital signatures.
The paper, titled “Shor’s algorithm compiled on cat qubits: 22 593 qubits for RSA-2048 in 3.14 days,” reports estimates for two cryptographic problems. For RSA-2048, the researchers calculate 22,593 physical qubits and a runtime of 3.14 days. For the 256-bit elliptic-curve discrete logarithm problem, they estimate 29,588 physical qubits and 61.8 minutes. Both results assume fault-tolerant superconducting hardware built around the company’s cat-qubit approach.
Alice & Bob says the work models the circuits and their physical implementation in greater detail than estimates that start with a count of logical qubits and apply an average physical-qubit overhead. For the most resource-intensive parts of the algorithms, the team calculated the work assigned to physical qubits and produced chip layouts and schedules. The company attributes the lower estimate to cat qubits, LDPC-cat error-correction codes and a redesigned adder, alongside algorithm improvements drawing on work from other research groups.
The company says the LDPC-cat codes cut its earlier RSA-2048 estimate from 49,649 physical qubits to 22,593. It also claims its estimate uses 40 times fewer physical qubits than a 2025 estimate by Google Quantum AI researcher Craig Gidney. That comparison is Alice & Bob’s assessment of the estimates; it does not mean a machine with the projected capabilities has been built or has factored RSA-2048.
Implications for Public-Key Security
The estimates matter because RSA and elliptic-curve cryptography underpin widely used security systems, including encrypted connections and digital signatures. A sufficiently capable fault-tolerant quantum computer running Shor’s algorithm could undermine these systems. The paper does not establish that such a computer exists today, but it offers a new estimate of the resources researchers believe a future machine might need.
Alice & Bob recommends that organizations start migrating to post-quantum cryptography, noting that replacing cryptographic systems across large organizations can take years. The company points to US and UK guidance calling for the transition to be completed by 2035. That timing is policy and planning context, not a prediction that RSA will be broken by a particular date. New post-quantum schemes also require continued testing and scrutiny before organizations can rely on them.
The elliptic-curve estimate has a separate practical caveat in the company’s discussion of Bitcoin. Its projected runtime of 61.8 minutes is longer than the network’s stated 10-minute block time, and Alice & Bob says transactions in progress would remain out of reach under that comparison. This is not a general finding that all blockchain systems are safe from future quantum attacks; it is a qualification tied to the estimate and the timing of a transaction.
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How the Resource Estimate Was Built
Shor’s algorithm is a quantum algorithm for factoring large integers and solving discrete-logarithm problems. RSA security depends on the difficulty of factoring large numbers for classical computers, while elliptic-curve systems rely on the difficulty of the discrete logarithm problem. The estimates in the paper describe what it could take to run the relevant algorithms on a fault-tolerant quantum computer, which must manage errors during computation.
Alice & Bob says its cat qubits suppress bit-flip errors in hardware, leaving its error-correction approach to address phase-flip errors. It also uses LDPC-cat codes, which the company says require fewer qubits than the repetition-code approach in its earlier estimate, and an adder redesigned to run at a steady pace without pausing for error correction. These are design and modeling choices underlying the projected counts, not evidence that a working computer has reached the stated scale or performance.
The paper builds on algorithm research from Inria and Google, according to the company’s account. Alice & Bob frames its result as a reduction in estimated resources, while also acknowledging substantial engineering challenges before hardware can carry out the projected computations. The figures should be read as estimates conditional on the paper’s architecture and assumptions, rather than as a timetable for a cryptographic break.
“Fewer than 23,000 physical cat qubits could be enough to factor RSA-2048 in just three days.”
— Théau Peronnin, CEO of Alice & Bob
Limits of the Projected Attack
The reported counts and runtimes are theoretical projections. The source material does not report a quantum computer that has factored RSA-2048, nor does it establish when a fault-tolerant machine capable of the modeled computation will be available. Alice & Bob says substantial engineering challenges remain; the provided material does not quantify those challenges or show that each modeled component has been validated in a full-scale system.
The estimates depend on the assumed cat-qubit hardware, error-correction codes, circuit design and runtime conditions. The available report does not provide enough detail to independently compare every assumption behind Alice & Bob’s estimate with Gidney’s 2025 work. The company’s 40-times comparison should therefore be attributed to the company rather than treated as an independently established measure of practical readiness.
It is also unclear from the supplied material how the projections would change under different hardware performance, error rates or implementation choices. No near-term date for a successful RSA-2048 attack is established by the paper’s estimated qubit count and runtime.
Migration and Further Validation
Alice & Bob says it expects improvements in hardware and reductions in resource requirements to converge in the early 2030s. That is the company’s expectation, not a confirmed development schedule. The next evidence to watch for includes progress in building and testing fault-tolerant hardware and independent scrutiny of the assumptions used in resource estimates.
For organizations, the practical next step is to plan and carry out migration to post-quantum cryptographic standards, while following continuing evaluation of those schemes. Alice & Bob argues that the new algorithms should face ongoing cryptanalysis too. The paper sharpens one estimate of the resources a quantum attack could require, but the arrival of a machine capable of carrying it out remains uncertain.
Key Questions
Has Alice & Bob demonstrated an attack on RSA-2048?
No. The paper presents a theoretical estimate of the resources and runtime for running Shor’s algorithm. The supplied report does not describe a completed attack or a machine that has factored RSA-2048.
How many qubits and how much time does the RSA estimate require?
Alice & Bob estimates 22,593 physical cat qubits and a runtime of 3.14 days on the fault-tolerant superconducting hardware modeled in the study.
What does the paper estimate for elliptic-curve cryptography?
For the 256-bit elliptic-curve discrete logarithm problem, the researchers estimate 29,588 physical qubits and 61.8 minutes. The figure is also a projection, not a reported attack on a deployed system.
Does this mean RSA will be broken by the early 2030s?
No date for an RSA-2048 break is established. Alice & Bob says hardware improvements and lower resource estimates may converge in the early 2030s, but that is the company’s expectation and the report says substantial engineering challenges remain.
What should organizations take from the estimate?
Alice & Bob recommends beginning migration to post-quantum cryptography, since replacing cryptographic infrastructure can take years. The projection does not prove an imminent attack, and post-quantum systems still require testing and scrutiny.
Source: thequantuminsider.com
