Factoring with known factor structure ⇒ PRG

Factoring with known factor structure implies PRG.

Statement

Migrated verbatim from factoring § Factoring with known factor structure:

Some protocols assume factoring is hard even given additional structural information about $N$ (e.g., $N=pq$ with $p\equiv q\equiv 3(\mathrm{mod}4)$, so-called Blum integers). Blum integers are used in the Blum-Blum-Shub PRG.

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 (BBS82 missing).
• The link from Blum integers to the Blum-Blum-Shub PRG is asserted as usage, not as a reduction.
• factoring-blum-integers has no page.