# Security Math

Password entropy, crack-time ranges, NIST key sizes, collision odds, Bloom filter sizing, checksums and Shamir threshold maths.

## How to pay

Machine-payable over x402. USDC on: Base (eip155:8453), Solana (solana:5eykt4UsFv8P8NJdTREpY1vzqKqZKvdp), Polygon (eip155:137), Arbitrum One (eip155:42161).
No accounts. No API keys. No signup. The paying wallet is the account.

## Machine-readable

- OpenAPI: https://security-math.x402tookit.com/openapi.json
- x402 manifest: https://security-math.x402tookit.com/.well-known/x402
- Catalog (free): https://security-math.x402tookit.com/catalog
- Health (free): https://security-math.x402tookit.com/health
- Uptime (free): https://security-math.x402tookit.com/uptime

## Endpoints (8)

### GET /birthday-collision — $0.02
Birthday-problem collision odds for random IDs or hash outputs, or the count of items that reaches a target probability.
Params: bits?: number, alphabetSize?: integer, idLength?: integer, space?: number, items?: number, probability?: number
Example: https://security-math.x402tookit.com/birthday-collision?bits=32&probability=0.5

### GET /bloom-filter — $0.02
Bloom filter sizing: bits, bytes and hash count for n items at a false-positive rate, or the rate for a given size.
Params: n: number, p?: number, mBits?: number, k?: integer
Example: https://security-math.x402tookit.com/bloom-filter?n=1000000&p=0.01

### GET /checksum — $0.02
CRC-32, CRC-32C, Adler-32, FNV-1/1a (32 and 64 bit) and MurmurHash3 x86_32 of text or hex bytes. Not cryptographic.
Params: data: string, algorithm?: string, inputType?: string, seed?: number
Example: https://security-math.x402tookit.com/checksum?data=123456789&algorithm=all

### GET /crack-time — $0.02
Time to brute-force a space of N bits (or N guesses) at a guesses-per-second rate: average, worst case, and presets.
Params: bits: number, guessesPerSecond?: number
Example: https://security-math.x402tookit.com/crack-time?bits=56&guessesPerSecond=1000000000000

### GET /encoded-length — $0.02
Encoded length of N bytes in hex, base64, base32, base58, base85, decimal or any base-N alphabet, and bytes per N characters.
Params: bytes: number, alphabetSize?: integer
Example: https://security-math.x402tookit.com/encoded-length?bytes=32

### GET /key-size-equivalence — $0.02
NIST SP 800-57 comparable strengths: RSA, DH, DSA, ECC and AES key sizes to security bits, hash strengths, 2030 status.
Params: algorithm: string, size: string
Example: https://security-math.x402tookit.com/key-size-equivalence?algorithm=rsa&size=2048

### GET /password-entropy — $0.02
Entropy bits for a random password policy, PIN or diceware passphrase from length and alphabet, with crack-time ranges.
Params: length: integer, lower?: string, upper?: string, digits?: string, symbols?: string, poolSize?: integer, words?: string
Example: https://security-math.x402tookit.com/password-entropy?length=4&words=true&poolSize=7776

### GET /shamir-threshold — $0.02
Shamir t-of-n secret sharing maths: qualifying subsets, loss tolerance, recovery and compromise odds. Counts only, no secrets.
Params: n: integer, t: integer, shareSurvival?: number, shareCompromise?: number
Example: https://security-math.x402tookit.com/shamir-threshold?n=5&t=3

## Terms

Educational maths and reference tables computed locally, provided as is. Crack-time figures are illustrative order-of-magnitude assumptions, not benchmarks of any real attacker. NIST tables are summarised from SP 800-57 Part 1 Rev. 5 and may be superseded. NEVER send real passwords, keys, TOTP seeds or secret shares to this or any service: every endpoint takes only lengths, sizes and counts. Not security advice; use a qualified professional for risk decisions.