{"id": "card_crypto_hardness", "kind": "reference", "title": "Hardness — security is a hard problem", "body": "RSA is secure only because factoring n into its primes is believed hard; break that (or prove P = NP, or run Shor's quantum algorithm) and it falls. Security IS a hardness assumption. Rests on the P vs NP region.", "source": {"label": "Narrow Highway — cryptography", "url": "", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "cryptography", "bands": ["cryptography", "pillar", "hardness", "one map"], "subject": "Hardness — security is a hard problem", "connections": [{"to_card_id": "card_floor_cryptography", "relationship": "part_of", "evidence": "a pillar of cryptography (Hardness)"}, {"to_card_id": "card_floor_p_vs_np", "relationship": "connects_at", "evidence": "RSA's security is the belief that factoring is hard - a P vs NP hardness assumption"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.cryptography", "facets": {"subject": ["hardness", "one map", "pillar"]}, "presentation": {"glyph": "•", "kind_label": "cryptography", "by": "Narrow Highway — cryptography", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_cryptography", "title": "Cryptography — public keys and hard problems", "relationship": "part of", "why": "a pillar of cryptography (Hardness)", "href": "/card/card_floor_cryptography", "resolved": true}, {"id": "card_floor_p_vs_np", "title": "The P versus NP chain - from the machine and the circuit to the three barriers", "relationship": "connects at", "why": "RSA's security is the belief that factoring is hard - a P vs NP hardness assumption", "href": "/card/card_floor_p_vs_np", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_crypto_hardness", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_crypto_hardness"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}