DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated

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.

Weak and strong secrecy for wiretap code sequences

Definition

Consider a sequence of finite wiretap codes from Finite discrete memoryless wiretap channel and code model, with uniform message $M_{n}$ and Eve's observation $Z^{n}$ . Call it reliable when its average error tends to zero; maximal reliability is the stronger condition that its maximal error tends to zero. Among reliable sequences, weak secrecy means

$\frac{1}{n} I (M_{n}; Z^{n}) ⟶ 0,$

and strong secrecy means

$I (M_{n}; Z^{n}) ⟶ 0,$

where leakage is the unnormalized finite mutual information of Information leakage and equivocation for finite observations and all quantities are in nats. Exact independence at every blocklength, total-variation secrecy, and per-message secrecy are separate conditions and are not identified with either limit here.

Depends on

Used by

Operational weak and strong secrecy capacities 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)
Paul Cuff, Princeton ELE 538: Information Theoretic Security, Lecture 15 (standard reference, not scraped)
Matthieu R. Bloch and J. Nicholas Laneman, Strong Secrecy from Channel Resolvability, arXiv:1105.5419 (standard reference, not scraped)