##  [Information-Theoretic Security](/information-theoretic-security-0) 

 Definition

Security guarantees about confidentiality or secrecy derived from information measures and coding constructions rather than computational hardness assumptions: statements that an adversary’s information about a message (e.g., mutual information or equivocation) can be made arbitrarily small under specified channel, key, or coding resource constraints.

 

 

 

 

 

 





## Principle

Principle

Secrecy is quantified by information-theoretic measures (entropy, mutual information, equivocation); under the assumed model, a scheme is secure if the adversary’s information measure on the message vanishes (or meets a prescribed bound) as coding parameters grow, independent of the adversary’s computational power.

 

 

 

 

 





## Demonstration

Demonstration

Illustrative scenario → A sender and receiver use a stochastic encoder over a noisy channel with an eavesdropper receiving a degraded version. Recognition: the model specifies channel statistics and available randomness. Action: apply a secrecy code that reduces mutual information between message and eavesdropper output. Consequence: for code blocklengths large enough, the eavesdropper’s information about the message becomes arbitrarily small, achieving information-theoretic secrecy under the channel model and key-rate constraints.

 

 

 

 

## Misapplication

Misapplication

Assuming information-theoretic security against an adversary who has access to side channels or capabilities outside the specified model (e.g., device leaks, stored copies, or physical access). The error is conflating model‑relative, provable secrecy with unconditional real‑world invulnerability.

 

 

 

 

 





## Consequence

Consequence

Permits provable, model-relative secrecy guarantees that do not depend on unproven hardness assumptions; these guarantees guide key-rate requirements, coding design, and system architectures where unconditional secrecy is required or desirable under stated constraints.

 

 

 

 

## Reversal

Reversal

If the assumed model fails (adversary has additional side-channel access, unlimited observation of correlated physical states, different channel statistics, or practical limits like finite blocklength), the theoretical guarantee can break down and must be re-evaluated with the extended model or finite‑block analyses.

 

 

 

 

 





## Boundary

Boundary

Clearly within: secrecy proofs based on channel models, key entropy, and coding constructions that bound adversary information. Boundary case: schemes relying on assumed noise or limited-storage that may fail if assumptions change. Clearly outside: security claims based solely on computational hardness (e.g., RSA) without information-theoretic bounds.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Absolute secrecy (strong, assumption‑free within a model) versus practicality (key length, rate loss, complexity, and physical implementation constraints); stronger information-theoretic guarantees typically require greater resource expenditure.

 

 

 

 

 





## Synthesis

Synthesis

Information‑theoretic security reframes secrecy as a modeling choice: provable guarantees are only as meaningful as the model of adversary capabilities and system channels; achieving practical unconditional secrecy requires explicit accounting for side channels, resource costs, and finite‑block effects.