{"query": "Cryptography — public keys and hard problems", "count": 20, "results": [{"id": "card_floor_cryptography", "title": "Cryptography — public keys and hard problems", "shelf": "codex", "surface": "secular", "snippet": "Secrecy built on number theory and computational hardness. RSA encrypts with a public key and decrypts with a private one (the round-trip sealed), its security the belief that factoring is hard; the o", "authority_tier": "engine_derived", "source": "Narrow Highway — cryptography", "readable": false, "generated": false}, {"id": "card_theory_quantum_information___entanglement__von_neumann_entr", "title": "Quantum information & entanglement (von Neumann entropy)", "shelf": "theories", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) — an engine domain that can touch it: information_theory. Calibration: seals. S = -Tr(ρ log ρ), the entropy of a density matrix, which reduces ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_algebraic_geometry", "title": "Algebraic geometry (solution sets as shapes)", "shelf": "theories", "surface": "secular", "snippet": "Algebraic geometry (solution sets as shapes) — an engine domain that can touch it: mathematics. Calibration: map-only — specific curve computations verify; the theory is abstract. The study of the sha", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_computational_complexity__p__np__reductions", "title": "Computational complexity (P, NP, reductions)", "shelf": "theories", "surface": "secular", "snippet": "Computational complexity (P, NP, reductions) — an engine domain that can touch it: computer_science. Calibration: map-only — P vs NP is open, and this card says so. Not whether a problem can be solved", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_cryptographic_security", "title": "Cryptographic security (hashing, checksums, PKI)", "shelf": "theories", "surface": "secular", "snippet": "Cryptographic security (hashing, checksums, PKI) — an engine domain that can touch it: cybersecurity. Calibration: seals — digests and signatures verify exactly. Three different things people routinel", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_diffie_hellman_key_exchange", "title": "Diffie-Hellman key exchange", "shelf": "theories", "surface": "secular", "snippet": "Diffie-Hellman key exchange — an engine domain that can touch it: cybersecurity. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computation. Two parties agre", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_sys_oneway_function", "title": "The one-way function — the computational rectifier", "shelf": "systems", "surface": "secular", "snippet": "Some computations are cheap one way and infeasible the reverse. A one-way function is easy to evaluate (polynomial time) but computationally infeasible to invert; a TRAPDOOR one-way function adds a se", "authority_tier": "reference", "source": "The recurring form — the system analogies (standard engineering) + the design they witness to", "readable": false, "generated": false}, {"id": "card_tool_sha256", "title": "SHA-256 / BLAKE3 cryptographic hashing", "shelf": "tools", "surface": "secular", "snippet": "SHA-256 / BLAKE3 cryptographic hashing — cryptography. GOOD AT: a fixed-size, collision-resistant fingerprint of any input — same bytes always hash the same, different bytes practically never collide.", "authority_tier": "battle-tested standard", "source": "The Tool Concordance — discern, connect, incorporate", "readable": false, "generated": false}, {"id": "card_works_hash", "title": "Cryptographic strength: a fingerprint and a cipher", "shelf": "the-works", "surface": "secular", "snippet": "SHA-256 of the three letters 'abc' is a fixed 256-bit fingerprint — change one bit and it changes utterly (the property this engine's seals rest on) — and a 256-bit AES key is, by the standard, strong", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_bridge_master_modular_exponentiation", "title": "Master equation: c = a^k mod n", "shelf": "bridges", "surface": "secular", "snippet": "the one-way power at the root of the discrete world: raising to a power modulo n is cheap, but inverting it — recovering the exponent, or factoring n — is hard on a classical machine and easy on a qua", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_alm_located_modular_exponentiation_trapdoor", "title": "Almanac: The modular-exponentiation trapdoor: fast one way, hard the other", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Public-key cryptography needs an operation that is easy to do and ruinous to undo -- and modular exponentiation is it. mathematics confirmed the FAST direction by square-and-multiply: beca", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_tool_aes_gcm", "title": "Authenticated symmetric encryption (AES-GCM / XChaCha20-Poly1305)", "shelf": "tools", "surface": "secular", "snippet": "Authenticated symmetric encryption (AES-GCM / XChaCha20-Poly1305) — cryptography. GOOD AT: fast confidentiality AND integrity together — encrypt-then-authenticate in one AEAD step. REACH WHEN: encrypt", "authority_tier": "battle-tested standard", "source": "The Tool Concordance — discern, connect, incorporate", "readable": false, "generated": false}, {"id": "card_v_9560b3d2e0c0", "title": "SHA-256('abc') = ba7816bf…20015ad · AES-256 → strong", "shelf": "cryptography", "surface": "secular", "snippet": "Verdict: HOLDS.\n• cryptography.hash_match: sha256('abc') = ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad (matches claim)\n• cryptography.key_strength: AES-256 is strong (matches clai", "authority_tier": "engine", "source": "Verified by the engine — cryptography", "readable": false, "generated": false}, {"id": "card_v_4adee145bcb5", "title": "SHA-256('abc') = ba7816bf…20015ad", "shelf": "cryptography", "surface": "secular", "snippet": "Verdict: HOLDS.\n• cryptography.hash_match: sha256('abc') = ba7816bf8f01cfea414140de5dae2223b00361a396177a9cb410ff61f20015ad (matches claim)\nSealed and independently re-checkable: https://narrowhighway", "authority_tier": "engine", "source": "Verified by the engine — cryptography", "readable": false, "generated": false}, {"id": "card_tool_ecc_ed25519", "title": "Elliptic-curve cryptography (ECC / Ed25519)", "shelf": "tools", "surface": "secular", "snippet": "Elliptic-curve cryptography (ECC / Ed25519) — cryptography. GOOD AT: fast digital signatures and key agreement with tiny keys — a 32-byte Ed25519 key carries security comparable to RSA-3072. REACH WHE", "authority_tier": "battle-tested standard", "source": "The Tool Concordance — discern, connect, incorporate", "readable": false, "generated": false}, {"id": "card_src_rfc_3447", "title": "RFC3447 — Public-Key Cryptography Standards (PKCS) #1: RSA Cryptography Specifications Version 2.1", "shelf": "rfcs", "surface": "secular", "snippet": "RFC3447: Public-Key Cryptography Standards (PKCS) #1: RSA Cryptography Specifications Version 2.1 (February 2003). Status: INFORMATIONAL. Obsoleted by RFC8017. Obsoletes RFC2437.", "authority_tier": "reference", "source": "The RFC Index (RFC Editor / IETF) — public domain", "readable": false, "generated": false}, {"id": "card_src_rfc_5349", "title": "RFC5349 — Elliptic Curve Cryptography (ECC) Support for Public Key Cryptography for Initial Authentication in Kerberos (PKINIT)", "shelf": "rfcs", "surface": "secular", "snippet": "RFC5349: Elliptic Curve Cryptography (ECC) Support for Public Key Cryptography for Initial Authentication in Kerberos (PKINIT) (September 2008). Status: INFORMATIONAL.", "authority_tier": "reference", "source": "The RFC Index (RFC Editor / IETF) — public domain", "readable": false, "generated": false}, {"id": "card_domchk_cryptography_claimed_hash_strength", "title": "Cryptography: hash strength", "shelf": "cryptography", "surface": "secular", "snippet": "A worked check in cryptography: hash strength.\n\nGIVEN\n  hash_strength_algorithm = md5\n\nCLAIMED\n  claimed_hash_strength = broken\n\nTHE ENGINE'S VERDICT\n  cryptography.hash_strength: CONFIRMED — md5 is b", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_crypto_public_key", "title": "Public-key cryptography — RSA", "shelf": "codex", "surface": "secular", "snippet": "Encrypt with a public key, decrypt with a private one; the two are inverse modulo phi(n). The RSA round-trip (m -> c -> m by modular exponentiation) is sealed. Rests on the instruments (number theory ", "authority_tier": "engine_derived", "source": "Narrow Highway — cryptography", "readable": false, "generated": false}, {"id": "card_src_rfc_5208", "title": "RFC5208 — Public-Key Cryptography Standards (PKCS) #8: Private-Key Information Syntax Specification Version 1.2", "shelf": "rfcs", "surface": "secular", "snippet": "RFC5208: Public-Key Cryptography Standards (PKCS) #8: Private-Key Information Syntax Specification Version 1.2 (May 2008). Status: INFORMATIONAL. Obsoleted by RFC5958.", "authority_tier": "reference", "source": "The RFC Index (RFC Editor / IETF) — public domain", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_floor_cryptography"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}