QR ⇒ COM

QR implies COM.

Statement

Migrated verbatim from quadratic-residuosity § Known Results:

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:

  • Folklore-labelled with ”— standard”, which CLAUDE.md permits in place of a citation.
  • SUSPECTED ERROR (report only): the textbook QR commitment (commit to b as r^2 y^b for y in J_N minus QR_N) is PERFECTLY BINDING and COMPUTATIONALLY HIDING, not statistically hiding. A statistically hiding commitment from QR needs a different construction, so the folklore label may be covering an incorrect claim.