Perfect Secrecy under Deep Random assumption

We present a new idea to design perfectly secure information exchange protocol, based on so called Deep Randomness, which means randomness relying on hidden probability distribution. Such idea drives us to introduce a new axiom in probability theory, thanks to which we can design a protocol, beyond Shannon limit, enabling two legitimate partners, sharing originally no common private information, to exchange secret information with accuracy as close as desired from perfection, and knowledge as close as desired from zero by any unlimitedly powered opponent.

💡 Research Summary

The paper introduces a novel concept called “Deep Randomness” and claims that it enables perfectly secure information exchange beyond Shannon’s limit without any pre‑shared secret. Deep Randomness is defined as a situation where the probability distribution that generates the random variables is itself hidden from any observer; the observer can see only the sampled outcomes but cannot infer the underlying distribution, no matter how many samples are collected. To formalize this, the authors propose a new axiom – the Axiom of Hidden Distribution – which states that an adversary has zero prior knowledge of the true distribution and that statistical tests cannot reveal it.

Building on this axiom, the authors design a two‑party protocol (Alice and Bob) that proceeds in three phases. First, each party independently generates deep‑random variables and sends encrypted versions of them to the other side. Second, using only the received messages, both parties compute a set of candidate secret keys that are guaranteed to be identical with high probability, despite the fact that the adversary sees only apparently random data. Third, a public verification step confirms that the same key has been derived, again without leaking any information. The protocol is claimed to achieve information‑theoretic perfect secrecy: the mutual information I(K;E) between the secret key K and the eavesdropper’s view E is asymptotically zero, even if the eavesdropper has unlimited computational power.

The security proof relies heavily on the hidden‑distribution axiom. The authors argue that because the adversary cannot learn any statistical regularities about the distribution, any Bayesian inference about the key is impossible, leading to zero leakage. They also provide an analysis of correctness, showing that the probability of key mismatch can be made arbitrarily small by adjusting protocol parameters, and that the error probability decays exponentially.

However, several critical issues arise. First, the hidden‑distribution axiom lacks a concrete physical or mathematical justification. In practice, any sufficiently large sample set will allow statistical estimation of the underlying distribution, contradicting the claim that it remains forever unknowable. Second, the model assumes that the adversary has no side‑information about the generation process, which is unrealistic; real‑world attackers may exploit implementation details, hardware imperfections, or prior communications to approximate the hidden distribution. Third, the paper does not demonstrate how to generate truly hidden distributions in hardware or software, leaving the core assumption unimplemented. Fourth, the introduction of a new axiom into probability theory raises consistency questions: it appears to conflict with Bayes’ theorem and the law of large numbers, yet the authors provide no rigorous proof of compatibility.

The authors acknowledge these limitations in a brief discussion and suggest future work such as leveraging quantum phenomena to physically conceal distributions or designing dynamic hardware random number generators whose distribution changes unpredictably. They also propose extending the protocol to multi‑party settings and performing empirical tests to quantify security margins.

In summary, the paper offers an intriguing theoretical framework that challenges conventional bounds on secret key agreement. While the idea of “deep randomness” is conceptually appealing, the current work falls short of establishing a feasible implementation or a mathematically sound security proof. Substantial further research is required to validate the hidden‑distribution assumption, reconcile the new axiom with established probability theory, and demonstrate practical constructions that can withstand realistic adversarial models.