How to factor 2048 bit RSA integers with less than a million noisy qubits · HackerPapers discussions

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by plopilop

Tue, 21 Jul 2026 19:51:47 GMT

There has been a lot of new stuff over the last few years. For instance, breaking RSA or ECDSA is requiring much fewer logical qubits than previously thought, and thus fewer physical qubits as well. Progress in error codes, quantum processing etc. made it that in 2019, it was estimated we needed ~20 million noisy qubits to factor RSA 2048. In 2025, we know we need fewer than 1 million. [0]. Some other papers even claim the need of 1000 physical qubits but they rely on a very exotic architecture so I would not consider them feasible. Progress on the hardware is also continuing, see [1].…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by adgjlsfhk1

Fri, 28 Nov 2025 13:02:36 GMT

"How to factor 2048 bit RSA integers with less than a million noisy qubits" (https://arxiv.org/abs/2505.15917) is the most up to date paper here, and uses ~1400 logical and ~900k physical

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by qnleigh

Fri, 21 Nov 2025 06:17:28 GMT

From the comments section, Scott says > To clarify — if, before the 2028 presidential election, a fully fault-tolerant Shor’s algorithm was used even just to factor 15 into 3×5, I would view the “live possibility” here as having come to pass. Now that might sound a bit disappointing, as factoring 15 only requires 7 logical qubits and ~20 entangling gates, but - Usable logical qubits were a pipe dream only a few years ago. - He's partly coming from the perspective that Nature might somehow make quantum computing impossible by destroying quantum information before it gets 'big enough' to do…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by adgjlsfhk1

Wed, 29 Oct 2025 15:05:57 GMT

https://arxiv.org/pdf/1208.0928 is a pretty good into to surface codes. https://www.nature.com/articles/s41586-024-08449-y is a paper that shows surface codes work on real computers. https://arxiv.org/abs/2505.15917v1 is the most recent costing of factoring various size of N using all the recent papers on optimizing the logical qbit counts.

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by qnleigh

Thu, 23 Oct 2025 02:03:57 GMT

The quantum algorithm that would break certain kinds of public key cryptography schemes (not even the core part of Bitcoin blockchains, which are not vulnerable to quantum computers) will take days to weeks to break a single key [0]. This is another reason why we will have plenty of warning before quantum computing causes any major disruptions to daily life. What I would start worrying about is the security of things like messages sent via end-to-end encrypted services like WhatsApp and Signal. Intercepted messages can be saved now and decrypted any time in the future, so it's better to…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by adgjlsfhk1

Mon, 01 Sep 2025 20:22:11 GMT

This is already done. Qbits is the size of the state space and gates is the measure of operations (like flops but quantum operations). https://arxiv.org/pdf/2505.15917 shows a factoring algorithm using 1 million qbits and ~10^10 gates.

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by Strilanc

Sun, 31 Aug 2025 18:37:59 GMT

> So how many gates are we talking to factor some "cryptographically useful" number? Table 5 of [1] estimates 7 billion Toffoli gates to factor 2048 bit RSA integers. > Is there some pathway that makes quantum computers useful this century? The pathway to doing billions of gates is quantum error correction. [1] estimates distance 25 surface codes would be sufficient for those 7 billion gates (given the physical assumptions it lists). This amplifies the qubit count from 1400 logical qubits to a million physical noisy qubits. Samuel Jacques had a pretty good talk at PQCrypto this year, and he…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by gjrq

Sun, 31 Aug 2025 18:27:21 GMT

Latest numbers are about 1e6 qubits with 1e-4 error rate: https://arxiv.org/abs/2505.15917. Gates (in the sense the OP means) is harder to quantify in the error corrected context once you compile to the operations that are native to your code. Total compute time of about a week assuming a 1MHz "clock" (code cycle time, for the experts). In some ways this is the harder metric to meet than the qubit numbers. Note that the magic of quantum error correction (exponential improvement in the error rate goes both ways): if you could get another 9 in qubit fidelity, you get a much larger improvement…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by Strilanc

Mon, 11 Aug 2025 13:36:15 GMT

That paper is hilarious, and is correct that there's plenty of shit to make fun of... but there's also progress. I recommend watching Sam Jacques' talk from PQCrypto 2025 [0]. It would be silly to delay PQC adoption because of focusing on the irrelevant bad papers. In the past ten years, on the theory side, the expected cost of cryptographically relevant quantum factoring has dropped by 1000x [1][2]. On the hardware side, fault tolerance demonstrations have gone from repetition code error rates of 1% error per round [3] to 0.00000001% error per round [fig3a of 4], with full quantum codes…

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by greyface-

Tue, 27 May 2025 04:15:00 GMT

Paper: https://arxiv.org/pdf/2505.15917 The focus on Bitcoin appears to be synthesis on Decrypt's part - it's not mentioned once in the paper.

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — mentioned by rurban

Sun, 25 May 2025 05:26:27 GMT

The linked HTML version of the arxiv paper sucks. Read the pdf, esp for the python code: https://arxiv.org/pdf/2505.15917v1

Paper and discussion history. A mention is not an endorsement.

How to factor 2048 bit RSA integers with less than a million noisy qubits — HN submission

Fri, 23 May 2025 15:23:21 GMT

How to factor 2048 bit RSA integers with less than a million noisy qubits

3 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.