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

instrument implementation / implementation-contract

# RSA Toy Cipher (Educational) implementation

A source-bound implementation contract for RSA Toy Cipher (Educational); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-100

**Effect**: Computation or source lookup only

## Input and validation requirements

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.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "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."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/rsa-toy-cipher-educational/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/rsa-toy-cipher-educational/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/rsa-toy-cipher-educational/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

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