The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-modular-exponentiation-in-rsa-state-3fcb

stable pending witness
2026-05-29 08:10:11 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain modular exponentiation in RSA. State any key formula.
79 chars

Generation

Modular exponentiation in RSA involves raising a number to a power and then taking the remainder when divided by a modulus. The key formulas are **c ≡ m^e (mod n)** for encryption, where m is the plaintext message, e is the public exponent, and n is the modulus, and **m ≡ c^d (mod n)** for decryption, where d is the private exponent. This operation is efficiently computed using algorithms like square-and-multiply to avoid calculating enormous intermediate values. The security of RSA relies on the difficulty of determining d from e and n without knowing the prime factorization of n.
30 tokens in · 149 tokens out · 4065 ms · $0.0023

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
4070.9 ms
Base LLM
4064.8 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0023

Trail

08:10:11 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
08:10:11 red_gate decision=pass reason=no disqualifying input patterns detected
08:10:15 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=149 latency_ms=4064.8 cost_usd=0.0023
08:10:15 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:10:15 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:10:15 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:10:15 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:10:15 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:10:15 signed hash_algo=sha256 hash=sha256:540cd43ad59e66e460d4df057757b8537f7b67055a5cea0db845168dd6c182ec

Content hash

sha256:540cd43ad59e66e460d4df057757b8537f7b67055a5cea0db845168dd6c182ec

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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