Asymptotic Structure of Key-Collision Fibers

Characterize the asymptotic structure of the collision fibers formed by admissible keys that map a fixed payload rank vector to the same stegotext rank vector in CARTS.

Background

For a fixed payload rank vector and output rank vector, the paper defines the candidate-key fiber consisting of all keys that induce the same input-output mapping. It analyzes finite cardinality effects and reports no collisions in a randomized finite-key experiment, while also exhibiting a deliberately constructed local collision. The asymptotic behavior and structure of these fibers remain unresolved.

References

On the theoretical side, the hardness of the context search problem, the asymptotic structure of collision fibers, the conditions under which commuting key pairs exist, and the design of more general CARTS transforms are all concrete open problems that follow naturally from the framework.

— CARTS: Contextual Autoregressive Rank Transcoding Steganography for Full-Capacity Keyed Text Encoding  (2609.10744 - Ghantous et al., 9 Sep 2026) in Section 7, Conclusion