Source: https://guthlabs.ai/docs/instruments/rsa-toy-cipher-educational/

instrument / verified-clean

# RSA Toy Cipher (Educational)

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/rsa-toy-cipher-educational/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/rsa-toy-cipher-educational/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/rsa-toy-cipher-educational/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/rsa-toy-cipher-educational/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Computing & Information

**Tranche**: tranche-4

**Evidence ID**: t4-100

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The honest-label warning is appropriate and should remain prominent. Verdict is NEEDS_REVIEW because the exact input constraints, invalid-input behavior, and arithmetic type are unspecified; the stated RSA formulas are correct under the listed assumptions.

### Formula and scope findings

- The core RSA formulas are standard, but the specification does not require p and q to be distinct primes; if p=q, φ(n)=(p-1)(q-1) is generally incorrect for n=pq.

- The specification does not state the required domain 0≤m<n for the message representative.

- The specification says to choose e coprime to φ(n) but does not require an explicit validation that gcd(e,φ(n))=1 before computing d.

- The modular inverse d=e⁻¹ mod φ(n) is undefined when gcd(e,φ(n))≠1, and the specification does not define the error behavior.

- The phrase “BigInt-safe primes (<2^20)” is ambiguous: primes below 2^20 are not sufficient for ordinary JavaScript Number arithmetic during modular multiplication, although they are safe as BigInt operands.

### Unit assumptions

- p, q, e, m, n, φ(n), d, and ciphertext are dimensionless integers; RSA has no physical units or unit conversions.

- p and q are assumed positive prime integers, distinct from each other.

- e is assumed to be an integer with 1<e<φ(n) and gcd(e,φ(n))=1.

- The message is assumed to be an integer representative satisfying 0≤m<n.

- All modular arithmetic is assumed to use exact integer arithmetic, preferably JavaScript BigInt rather than Number.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

Invalid exponents can produce an undefined private exponent, so the instrument must reject e values with gcd(e,φ(n))≠1. Inputs at or beyond the canonical message boundary can also silently lose information: message 15 encrypts and decrypts to 0 modulo 15. Negative-message handling is convention-dependent and can expose a mismatch between residue output 14 and signed plaintext −1.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "p": 5,
    "q": 11,
    "e": 3,
    "message": 7
  },
  "expected_outputs": {
    "n": 55,
    "phi": 40,
    "d": 27,
    "ciphertext": 13,
    "decrypted_plaintext": 7
  },
  "working": "n=p·q=5·11=55. φ(n)=(5-1)(11-1)=4·10=40. gcd(3,40)=1. Find d: 3·27=81=2·40+1, so d=27. Encryption: c=7^3 mod 55. 7^2=49, 7^3=49·7=343=6·55+13, so c=13. Decryption: 13^2=169 mod55=4; 13^4=4^2=16; 13^8=16^2=256 mod55=36; 13^16=36^2=1296 mod55=31. Since 27=16+8+2+1, 13^27 mod55=((31·36 mod55)·4 mod55)·13 mod55=(16·4 mod55)·13 mod55=9·13 mod55=117 mod55=7."
}
````

## Related workflows

[Crypto & Number Theory Classroompublic key](<https://guthlabs.ai/docs/instrument-workflows/crypto-classroom/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`