Ideal PRC ⇒ PRC

Ideal PRC implies PRC.

Statement

Migrated verbatim from pseudorandom-error-correcting-code § Ideal PRC:

An ideal PRC additionally requires that codewords are indistinguishable from uniformly random strings even to an adversary who holds the decoding key $k$. That is, the joint distribution $(k,{\mathsf{Enc}}_k(m))$ is computationally indistinguishable from $(k,U_n)$ where $U_n$ is a uniformly random $n$-bit string. This is strictly stronger than pseudorandomness (which only requires indistinguishability without the key). Ideal PRCs support watermarking schemes where even a user who knows the watermarking key cannot detect whether a given string is a codeword.

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• ‘This is strictly stronger than pseudorandomness’ asserts BOTH an implication (ideal PRC ⇒ PRC) and a separation (PRC does not imply ideal PRC); the separation half is uncited and should be migrated as a distinct claim.
• No citation.
• ‘ideal-prc’ has no page.