Strong RSA ⇒ DS

Strong RSA implies DS.

Statement

Migrated verbatim from rsa-assumption § Strong RSA:

The strong RSA assumption strengthens the standard assumption by allowing the adversary to choose the exponent $e$ itself (subject to $e>1$). Formally, the adversary outputs a pair $(\hat{x},\hat{e})$ with $\hat{e}>1$ and ${\hat{x}}^{\hat{e}}\equiv y(\mathrm{mod}n)$. This is used in constructions of signature schemes and commitments with stronger security guarantees.

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:

• No citation (Cramer-Shoup; Gennaro-Halevi-Rabin).
• content/Primitives/digital-signature.md exists but “signature schemes” is left as plain text with no wikilink.
• “with stronger security guarantees” is vague — presumably standard-model EUF-CMA without random oracles, but the page does not say so.