Prabhanjan Ananth London & Kavli Institute. Definitive limits on predicting shared data without communication have now been established; Barbara’s team has achieved a quantifiable upper bound on success in these scenarios for the first time.

The work shows that if two parties can both recover a hidden string with probability p using only local measurements, then their ability to predict its parity, a key property used in cryptography, is limited by min{1, ½ + 5p/22}. A new upper limit quantifies how well two parties can predict shared data when unable to communicate directly, building upon earlier work which considered outcomes based solely on chance.

This bound defines that successful recovery of hidden information with probability p limits predicting its parity, a fundamental concept in secure communications, to a specific value dependent on p. These findings clarify constraints relevant to technologies like unclonable encryption and quantum copy-protection systems. The team has established a fundamental limit on the effectiveness of prediction for two parties sharing data without direct communication; this builds upon previous research assessing only outcomes based purely on chance.

If both individuals successfully recover hidden information, akin to each holding half of a puzzle and attempting collective solution without speaking, with probability p, then their ability to predict its parity, determining whether an unknown number is even or odd, is constrained by a specific value linked to p. This ‘parity’ represents a basic building block in secure communications protocols such as unclonable encryption where messages are split into parts distributed between parties, similar to tearing a photograph in half for Alice and Bob.

Quantified limits now exist for successful prediction of shared data without communication

A major improvement has quantified how well two parties can predict shared data, achieving a bound of min1,frac12+5p^1/22 on parity prediction success compared to previous methods lacking quantifiable limits. It represents a leap forward as it allows provable guarantees where previously only chance outcomes were possible. Before this point, assessing how well two parties could predict shared information without communicating was fundamentally limited by an inability to define precise boundaries on potential successes.

These findings have relevance to developing more secure unclonable encryption and quantum copy-protection systems because they highlight limitations in retrieving information when direct communication is prohibited. When two parties attempt to predict a shared random parity with an optimal probability of success denoted by p, their probability of both correctly answering the challenge is at most min{1, ½ + 5p 1/22 }. This result builds upon earlier work which lacked precise boundaries for successful prediction; instead it establishes a quantifiable limit rather than relying on chance outcomes.

The bound applies even using unrestricted local quantum measurements, meaning predictions aren’t constrained by specific technologies or measurement types. Applying this theorem to unclonable encryption, a method designed to prevent perfect copying of data, reveals any scheme claiming information-theoretic search security will have its identical-challenge distinguishing success capped at one half plus a negligible function related to key length.

Prediction success diminishes as the ability to reconstruct original hidden data through independent measurements decreases in scenarios where each party possesses only part of an encoded string and attempts to determine overall parity without revealing individual shares.

Predicting shared randomness defines boundaries for secure key generation

Understanding fundamental limits to information retrieval without direct communication between parties is crucial for unbreakable encryption and strong data protection. This work clarifies how much knowledge can be gleaned from limited individual observations when attempting to predict shared secrets, which is a key consideration for technologies like unclonable encryption designed to prevent perfect copying. Establishing that determining absolute limits on information retrieval is inherently complex and relies on theoretical bounds rather than practical demonstrations provides a vital benchmark for evaluating data security protocols. The researchers quantified potential knowledge gained through limited observation by defining a limit to how accurately two parties can predict shared random information without directly revealing it; this concept applies in designing unclonable encryption aiming to create uniquely identifiable physical keys.

The research demonstrated a quantifiable boundary for predicting shared randomness between two parties with partial information about an encoded string. This finding means any system relying on such predictions, like certain forms of unclonable encryption, has inherent limitations regarding its ability to prevent successful challenges based on key length and reconstruction possibilities.

Specifically, the probability of both parties correctly answering a parity challenge is capped at one half plus five times the twenty-second root of their success rate in reconstructing the original data. The authors developed these results using assistance from large language models during proof construction and exposition.

👉 More information
🗞 Non-Local Search-to-Decision Reduction over F2
✍️ Prabhanjan Ananth
🧠 ArXiv: https://arxiv.org/abs/2608.19091

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