The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-modular-exponentiation-in-rsa-an-ea15

stable pending witness
2026-05-29 03:21:22 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of modular exponentiation in RSA? Answer concisely in 2-3 sentences.
93 chars

Generation

Modular exponentiation is the core mathematical operation in RSA encryption and decryption, allowing messages to be raised to public or private exponent powers modulo a large composite number. This operation is computationally efficient to perform but extremely difficult to reverse without knowing the private key, which is what makes RSA secure. The modular arithmetic ensures that encrypted values stay within a manageable range while preserving the mathematical properties needed for the encryption scheme to work.
33 tokens in · 98 tokens out · 4014 ms · $0.0016

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
4021.3 ms
Base LLM
4014.1 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0016

Trail

03:21:22 received prompt_chars=93 verifiers=['scripture_anchors', 'theology_doctrine']
03:21:22 red_gate decision=pass reason=no disqualifying input patterns detected
03:21:26 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=33 tokens_out=98 latency_ms=4014.1 cost_usd=0.0016
03:21:26 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:21:26 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:21:26 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:21:26 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:21:26 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:21:26 signed hash_algo=sha256 hash=sha256:ea7ada4e56134ecc67d964ce8acaef0f91beb31b08dc6fd384656e84c8c4a60d

Content hash

sha256:ea7ada4e56134ecc67d964ce8acaef0f91beb31b08dc6fd384656e84c8c4a60d

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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