Can Intelligence Outgrow Cryptography?

Two uses of encryption suggest a larger question

Imagine two teams protecting the same set of research notes. One is planning for an attacker who stores encrypted network traffic today and tries to decrypt it with a future quantum computer. The other wants a cloud AI service to analyze the notes while they remain encrypted.

The first problem motivates post-quantum cryptography. The second motivates Fully Homomorphic Encryption. Many important constructions in both areas use lattice mathematics.

Our original intuition was that this overlap might be a clue about the limits of intelligence. Could mathematics let a person with modest computing resources keep a secret from a vastly more capable system? If so, stronger intelligence would not automatically bring access to every private thought.

That is a useful question to investigate. It also leads to a separate question: what physical processes make intelligence possible? We want to examine the connection without treating a shared mathematical tool as an answer to every question it raises.

What the lattice connection actually gives us

A lattice can be pictured as a regular arrangement of points. In cryptography, the important problems involve structures with many dimensions and carefully chosen parameters; a simple picture on paper does not show their difficulty.

One family of problems asks an attacker to recover hidden relationships from equations that include controlled noise. The noise makes recovery difficult, while the algebra still permits useful operations. Learning with Errors is an example of this approach.

NIST’s ML-KEM uses a related module-lattice problem to establish shared keys. Brakerski and Vaikuntanathan showed how Learning with Errors can support Fully Homomorphic Encryption.^[1][2] Related mathematics supplies different capabilities: agreeing on a secret in one case, and computing on protected inputs in the other.

These schemes run on classical computers. Their connection is a mathematical construction, not evidence that the computer performing the encryption needs consciousness or quantum cognition. Post-quantum cryptography also includes other approaches, such as hash-based signatures.^[3]

For our research program, the practical opportunity is to study these protections together: how their assumptions hold up, how keys are controlled, and how an organization can update its systems as knowledge changes.

Ask what the stronger attacker can actually do

Suppose an exceptionally capable AI receives an encrypted copy of the notes. Saying “it is much smarter than the researcher” does not tell us how it recovers the contents. An attack needs a method and resources.

There are several concrete possibilities to examine. It could find a faster method for breaking the encryption. It could discover a weak parameter choice. It could exploit a software defect. Or it could infer something from surrounding information, such as the author’s identity and the size of the document. These are different mechanisms and should be tested separately.

We would compare attacks on declared schemes and parameters, with stated time, memory, hardware, and success rates. AI-assisted attacks belong in that evaluation, just as AI-assisted optimization belongs in efforts to make Fully Homomorphic Encryption more practical. Security guidelines and attack-estimation tools provide a starting point for these comparisons.^[4]

The claim we want to investigate is that privacy can rest on computational difficulty, even when the observer is more intelligent than the user. Such protection is a claim about feasible attacks under specified assumptions. It earns confidence through analysis and testing, and its assessment should change when a better attack appears.

This gives the lattice observation a concrete AI safety purpose: look for protections that do not require a weaker person to match a stronger system’s intelligence or trust its promises.

A weather model can lose the storm in its own retelling

Now consider the question about machine-generated data. Imagine a weather archive with many ordinary days and a few rare hailstorms. A model learns from it and generates a new set of weather reports. By chance, or because its fit is imperfect, the generated set underrepresents hail.

If the next model trains only on those generated reports, it learns less about hail. Repeating that replacement can make the rare event progressively less visible. The reports may remain fluent while the model’s picture of the weather becomes less faithful.

This hypothetical example illustrates a mechanism studied in model-collapse research. Shumailov and colleagues found that recursive training on generated data can lose parts of the original distribution, including rare cases.^[5] Gerstgrasser and colleagues found that retaining original data while accumulating synthetic data avoided collapse in their studied settings.^[6] How the data are retained and used matters.

Human authors are not exempt from the underlying problem. If ten writers rewrite the same inaccurate weather bulletin without checking the sky, their authorship does not restore the missing hailstorms. Human-produced data are valuable partly because people observe, experiment, disagree, and encounter events that correct their expectations.

Machines can also obtain new constraints. A sensor can measure weather; a program can check a proposed proof step; a game supplies rules and outcomes. AlphaZero’s learning from self-play is a concrete example of useful machine-generated experience tied to a defined environment.^[7]

Our distinction is therefore between learning that keeps contact with independent evidence and learning that repeatedly treats its own output as fresh observation. To test it, we would compare a replacement-only weather dataset, one that retains the original observations, and one that adds fresh measurements. Hold the training budget comparable and evaluate all three against held-out real events, including rare ones.

What would a quantum explanation of intelligence need to show?

The weather example explains one way learning can deteriorate without invoking a special property of human consciousness. The question about quantum processes in the brain remains a different, interesting investigation.

All brain chemistry follows quantum physics. The more specific proposal is that a particular quantum process plays an essential information-processing role in cognition or consciousness. To examine that proposal, we need to identify the process and the work it is supposed to do.

Fisher’s nuclear-spin proposal is an example: it suggests a mechanism by which certain physical states might retain and process information in the brain.^[8] Research on tryptophan networks has also reported a collective quantum optical effect in biological structures.^[9] These are specific ideas and observations to investigate. Establishing their role in cognition requires a further causal link to brain function.

For example, a theory might predict that disrupting a particular physical process changes a particular cognitive ability. A useful test would have to distinguish that prediction from ordinary chemical damage or other explanations. The proposed process must occur under relevant biological conditions, last long enough, and affect the computation the theory assigns to it.

A quantum source of randomness also needs a learning process that evaluates the variations it produces. Randomly generating a hailstorm report is different from establishing that a hailstorm occurred. Fresh variation and reliable evidence play different roles.

We remain interested in whether a quantum mechanism could expand the capabilities of future intelligence. The lattice connection motivates questions about what such an intelligence could overcome; experiments on the mechanism must establish what it actually contributes.

Protect both private questions and access to fresh evidence

Return to the researcher with encrypted notes. Fully Homomorphic Encryption could help her ask a cloud model a private question. But what if every answer draws on a weather archive controlled by one institution, which removed all reports of a disputed storm?

She needs two things: privacy for her inquiry and access to observations that can challenge the accepted account. A perfectly private conversation about an incomplete archive would still be a conversation about an incomplete archive.

This extends our concern about concentrated power. An institution may gain influence by reading everyone’s questions. It may also gain influence by deciding which observations future models learn from. Privacy, independent auditing, and the ability to collect new evidence address these different forms of control.

Our proposed research asks three concrete questions: can an attacker recover the protected information; can a learning process preserve rare facts and incorporate new observations; and does a proposed quantum mechanism make a prediction that survives a fair test?

Those questions preserve the original possibility we find important: more capable intelligence may still face meaningful mathematical and physical limits. Understanding those limits could help people use powerful AI while retaining privacy and the ability to question what it tells them.