DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Information leakage and equivocation for finite observations

Definition

For finite random variables $M, Z$ , information leakage is the finite mutual information $I (M; Z)$ in nats, as defined in Finite mutual information, and equivocation is the finite conditional entropy $H (M ∣ Z)$ , as defined in Finite conditional entropy. For an $n$ -use code with Eve's observation $Z^{n}$ , its normalized leakage is $n^{- 1} I (M; Z^{n})$ . When $M$ is uniform on a finite message set $M$ , its entropy is $H (M) = \ln ∣ M ∣$ . Zero-probability symbols are handled by the finite entropy and KL conventions cited above.

Depends on

Used by

Operational weak and strong secrecy capacities Definition
Weak and strong secrecy for wiretap code sequences Definition
Weak secrecy does not imply strong secrecy Example
Strong-secrecy capacity of a finite DMC wiretap channel Theorem

Dependency tree · two levels

7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Abbas El Gamal and Young-Han Kim, Network Information Theory, arXiv:1001.3404v3 (standard reference, not scraped)
Matthieu R. Bloch and J. Nicholas Laneman, Strong Secrecy from Channel Resolvability, arXiv:1105.5419 (standard reference, not scraped)