The Mechanism · Gated-generation receipt

gen-state-modular-exponentiation-in-rsa-precisely-and-explain-wh-f70a

stable pending witness
2026-05-29 07:58:30 UTC · anthropic/claude-sonnet-4-5

Prompt

State modular exponentiation in RSA precisely and explain why it matters in 2-3 sentences.
90 chars

Generation

# Modular Exponentiation in RSA **Precise statement:** Given message *m*, public exponent *e*, private exponent *d*, and modulus *n*, RSA performs: - **Encryption:** *c* ≡ *m*^*e* (mod *n*) - **Decryption:** *m* ≡ *c*^*d* (mod *n*) **Why it matters:** Modular exponentiation is the trapdoor function that makes RSA secure—computing *m*^*e* mod *n* is efficient, but reversing it (finding *m* from *c* without knowing *d*) requires factoring *n*, which is computationally infeasible for large numbers. This asymmetry enables public-key cryptography where encryption keys can be public while decryption remains private.
30 tokens in · 198 tokens out · 5551 ms · $0.0031

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
5563.5 ms
Base LLM
5551.3 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0031

Trail

07:58:30 received prompt_chars=90 verifiers=['scripture_anchors', 'theology_doctrine']
07:58:30 red_gate decision=pass reason=no disqualifying input patterns detected
07:58:36 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=198 latency_ms=5551.3 cost_usd=0.0031
07:58:36 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:58:36 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:58:36 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:58:36 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:58:36 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:58:36 signed hash_algo=sha256 hash=sha256:deb8f554bec65e74f1eccea456995f26782aca5f7175f5b26d78fe01c0cef939

Content hash

sha256:deb8f554bec65e74f1eccea456995f26782aca5f7175f5b26d78fe01c0cef939

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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