Claude AI Solves a 25-Year Cryptography Mystery in Just 30 Minutes

Anthropic's AI research model traces the origins of five NSA-supplied elliptic curve seeds, bringing new clarity to a long-standing question about cryptographic security.

For nearly 25 years, a mystery surrounding some of the most widely used cryptographic standards remained unresolved. Where did the numbers used to generate several NIST elliptic curves originally come from?

In October 2026, researchers reported a surprising breakthrough: an internal Claude research model from Anthropic traced the origins of five elliptic curve seeds supplied by the U.S. National Security Agency (NSA) in less than 30 minutes.

The discovery offers a clearer explanation of how important cryptographic parameters were generated. However, it does not mean that Claude broke encryption, recovered private keys, or discovered a new vulnerability in the affected curves.

Instead, the finding addresses a historical question that has influenced discussions about trust in cryptographic standards for decades.

Why Did These Cryptographic Seeds Matter?

The story dates back to 2000, when the National Institute of Standards and Technology (NIST) adopted the Elliptic Curve Digital Signature Algorithm (ECDSA) in its FIPS 186–2 standard.

ECDSA is a cryptographic algorithm used to create and verify digital signatures. These signatures help establish the authenticity and integrity of digital information.

The standard included parameters for elliptic curves such as:

• P-192
• P-224
• P-256
• P-384
• P-521

These curves play an important role in public-key cryptography. Their parameters determine the mathematical structures used in cryptographic operations.

The controversy centered on the seeds used to generate the curves. Although the seeds were publicly documented, their original sources and selection process were not fully explained.

This lack of transparency encouraged speculation about whether the NSA might have deliberately chosen parameters containing hidden weaknesses.

No demonstrated attack against these curves had established that suspicion. Nevertheless, the missing historical explanation left an important question unanswered.

One theory suggested that the seeds might have been generated by hashing humorous phrases. Former NSA mathematician Jerry Solinas recalled phrases such as "Give Bob and Jerry a raise," which encouraged researchers to investigate possible connections between memorable text and the published values.

Claude approached the problem from a different direction.

How Claude Approached the Mystery

Rather than concentrating on possible phrases, Claude investigated random-number generators commonly used in software during the 1990s.

According to the reported research, the model developed a scanner that examined 34 combinations of random-number generators and output segments to identify patterns matching the published seeds.

One important clue appeared in the binary-curve seeds.

Their 32-bit words consistently had a zero in the highest bit. This pattern was consistent with the behavior of lrand48, a legacy C library pseudo-random number generator that produces 31-bit values from an internal 48-bit state.

That observation gave researchers a way to narrow the search.

Recovering the Hidden Generator States

The lrand48 generator maintains an internal state that determines its output sequence. If enough information about its outputs is available, researchers can sometimes reconstruct that state.

Claude reportedly tested the 17 hidden bits and checked whether the resulting candidate states produced subsequent outputs matching the published data.

The prime-curve seeds presented a more difficult challenge because only eight bits from each generator output had been retained.

To address this problem, the researchers used the Lenstra–Lenstra–Lovász (LLL) lattice reduction algorithm.

LLL is a mathematical technique that finds relatively short, structured vectors in a lattice. In cryptography, it can help solve certain problems involving incomplete numerical information.

By combining these techniques, the researchers found matches for five NIST curve seeds and five example seeds from the ANSI X9.62 standard.

The results pointed toward a shared generation process rather than five unrelated constructions.

The Discovery: A Legacy Random-Number Generator

The researchers traced the seeds to lrand48, initialized using Unix timestamps.

By running the generator backward, they recovered initialization values corresponding to dates between May 1997 and April 1998.

One particularly specific result involved P-256.

According to the report, its published seed corresponded to the 1,842nd candidate in a generator run initialized on August 16, 1997, at 01:52:34 UTC. Each candidate consisted of 20 bytes.

Four binary-curve seeds also matched the generator.

Their values suggested a possible relationship with a clock value divided by two, although the researchers did not establish that interpretation conclusively.

The important point is that the published seeds appear consistent with a reproducible generation process using an ordinary software random-number generator.

That provides a concrete explanation for values whose origins had remained uncertain for years.

Does This Mean the NSA Curves Were Compromised?

No. Reconstructing the origin of a public curve-generation seed is not the same as breaking the cryptography built on that curve.

The distinction matters.

The seeds discussed in the research are public values used during curve generation. They are not the private signing keys used to authenticate messages or digital documents.

Knowing how a public parameter was generated does not automatically reveal anyone's private key or allow an attacker to forge a digital signature.

The discovery also does not establish a new mathematical weakness in ECDSA or demonstrate that the affected curves can be practically attacked.

Instead, the findings provide a plausible, reproducible account of how the seeds were produced.

That historical explanation may reduce concerns about deliberate manipulation, but it does not prove that every decision made during the original curve-selection process was harmless.

Transparency is valuable, but it should not be confused with a formal security proof.

Why This Matters for Modern Cybersecurity

Elliptic curve cryptography remains an important part of modern digital security.

Its applications include digital signatures, secure communications, identity verification, and authentication systems.

P-256, for example, is used in a variety of security protocols and implementations. Understanding the history of its parameters helps researchers evaluate the assumptions behind the cryptographic systems they rely on.

The discovery also highlights a growing role for artificial intelligence in security research.

AI systems can help researchers explore large search spaces, identify unexpected mathematical patterns, develop candidate solutions, and automate repetitive investigations.

In this case, the reported achievement was not the invention of a new cryptographic attack. It was the identification of a historical pattern that researchers had not previously established.

That distinction illustrates an important application of AI: helping people answer difficult technical questions that require connecting evidence across mathematics, software history, and cryptographic standards.

The Mystery Is Not Completely Solved

Despite the progress, several questions remain open.

Researchers have not explained the origin of the B-163 seed or several base points associated with the curves.

They also identified candidates that appeared suitable but were skipped during the original generation process. One example was P-256 candidate 876, whose rejection remains unexplained.

The researchers additionally traced base-point generation for P-192 and five ANSI example curves to FreeLIP, a long-integer arithmetic package. These base points are fixed mathematical starting points used in elliptic curve operations, and their origins are separate from the origins of the curve seeds.

These unresolved details mean the research should be viewed as a significant advance rather than a complete account of every historical decision.

Anthropic reportedly published reproduction code so other researchers could independently check the results. The Internet Security Research Group is set to receive the reported $36,864 bounty.

The report recommends no changes to deployed systems based solely on this discovery.

Final Thoughts

Claude's reported breakthrough offers a compelling example of how AI can contribute to cryptography research without breaking a cryptographic system.

By tracing five NSA-supplied elliptic curve seeds to a legacy random-number generator, the model helped address a question that had remained open for approximately a quarter of a century.

The discovery does not prove that every aspect of the original process was flawless. It does, however, provide researchers with a concrete explanation they can test and reproduce.

The broader lesson is that cryptographic security depends not only on mathematical strength but also on transparency, independent verification, and confidence in how security-critical parameters are created.

Sometimes, the most important AI discovery is not finding a way to break a system. It is helping us understand why we can trust it.