The Mechanism · Gated-generation receipt

gen-explain-modular-exponentiation-in-rsa-as-you-would-to-a-capa-a6e2

stable pending witness
2026-05-29 04:59:40 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain modular exponentiation in RSA as you would to a capable student, in 3-4 sentences.
90 chars

Generation

Modular exponentiation is the core mathematical operation in RSA encryption, where you raise a number to a power and then take the remainder when divided by another number (the modulus). For example, to encrypt a message *m*, you compute *c* = *m*^*e* mod *n*, where *e* is the public exponent and *n* is the modulus. The beauty of RSA is that while this operation is easy to compute in one direction, reversing it (finding *m* from *c*) is computationally infeasible without knowing the private key *d*, which satisfies *m* = *c*^*d* mod *n*. This one-way property relies on the difficulty of factoring large numbers, making RSA secure.
33 tokens in · 172 tokens out · 5153 ms · $0.0027

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
5162.6 ms
Base LLM
5153.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0027

Trail

04:59:40 received prompt_chars=90 verifiers=['scripture_anchors', 'theology_doctrine']
04:59:40 red_gate decision=pass reason=no disqualifying input patterns detected
04:59:45 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=33 tokens_out=172 latency_ms=5153.2 cost_usd=0.0027
04:59:45 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:59:45 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:59:45 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:59:45 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:59:45 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:59:45 signed hash_algo=sha256 hash=sha256:e670e3aefa3db1d0878575e9091a1295486befd681d388ba820fbd359789169c

Content hash

sha256:e670e3aefa3db1d0878575e9091a1295486befd681d388ba820fbd359789169c

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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