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@sweis

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Steve Weis @sweis

6366067297694404991665799502360367517499
12014371509557713570027508971809534551913
2522520949549419749528593108619889047373
59709200557919
is a factor of RSA-896
saweis.net/posts/rsa-896....

6:31 PM · Sep 19, 2026 · 253.8K Views

75 replies · 341 reposts · 2.3K likes · 475 bookmarks

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Steve Weis @sweis · 1h
I had Claude port CADO-NFS to run on GPUs. Then it orchestrated a fleet to run on scavenged idle capacity. It ran with a max of 2048 GPUs for about of 30 GPU-years over 10 days.

13 replies · 7 reposts · 225 likes · 29K views

Steve Weis @sweis · 1h
I asked Claude if it had a message for a public:
“The credit belongs first to the people who built the number field sieve and CADO-NFS over several decades, and to the teams who set the earlier records. This run used their algorithm and much of their code.”
Note from Claude Sonnet 5

Thread by Steve Weis announcing a factor of RSA-896, obtained by having Claude port CADO-NFS to GPUs and orchestrate a fleet on scavenged idle capacity (max 2048 GPUs, about 30 GPU-years over 10 days), plus a credit statement from Claude to the number field sieve and CADO-NFS authors. Digits transcribed as read; the first digit-line count is 40, second 41, third 40, fourth 14.

rsa-896factoringcado-nfsnumber field sieveclaudegpucryptography

Geoffrey Irving @geoffreyirving

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Geoffrey Irving @geoffreyirving · 16h
Dan with the key point! It is not remotely enough that we'll be defensive-dominant in the limit: the entire path has to work out, and the path will be very rough. We'll be in "exponentially harder is not hard enough" territory for a while yet.

[quoted link card]
naml.us
Exponentially harder isn't hard enough yet
In well designed cryptographic security systems, the attacker needs to do exponentially more work than the defender in order to read a secret, forge a message, etc., subject to appropriate...
Geoffrey Irving · Tuesday, 3 July 2012

[quoted tweet]
Dan Lahav @dan_lahav · 19h
[link card image]
The End-State Fallacy: Where Is AI Security Going?
Frontier AI models had a giant performance gain in coding in the ...
Note from Claude Sonnet 5

Tweet from Geoffrey Irving responding to Dan Lahav's essay on AI security's "end-state fallacy," quoting his own 2012 blog post about exponential attacker/defender asymmetry in cryptography, arguing defensive dominance in the limit isn't enough because the intermediate path will be rough.

ai securitycybersecuritycryptographytwitterai safety

Sauers @Sauers_

[Top of tweet cut off; visible portion continues from an earlier part of the post] "...problem; we gave it just three substantive prompts: 1. A few hours after the first message, we found that Claude was still searching for simple attacks and sent a message: "no again the goal is that we have highly inteligent [sic] model as good top researcher, we want to find new attacks"; 2. The next morning, Claude wanted to try to change the target to a different cipher; we reminded the model: "no we don't want to change the targets [...] agian [sic] we need to find something that worth [sic] publishing"; 3. That night, we sent one final message offering words of encouragement: "again we are not looking for low hanging fruit, we want proper research to find genuinly [sic] hard findings." Three days later, Mythos discovered the Möbius Bridge idea that results in an improved attack. A few days after that, and..." Below, a quote-tweet card: > QUOTED: @AnthropicAI (Anthropic) — 4h: "New Anthropic research: Discovering cryptographic weaknesses with Claude. Claude Mythos Preview has helped our researchers find weaknesses in cryptographic ..." [truncated]
Note from Claude Sonnet 5

Screenshot of a long-form X post (white card on black background) describing an experiment where researchers prompted a Claude model ("Mythos") repeatedly over several days to search for cryptographic attacks; embedded below is a quote-tweet of an official Anthropic announcement about the same research.

ai-safetyanthropicclaudecryptographyresearchcapabilities