YPC-27 Checksums | YAKMESH Documentation

Overview

YPC-27 is a checksum algorithm that protects YAKMESH packets from forgery. Unlike traditional CRC or hash-based checksums, YPC-27 operates in ternary space using a 27-trit finite field F_{3^27}.

YPC-27² (Power) adds a multivariate quadratic layer: three input field elements (a, b, c) are mixed linearly, twisted through a 27×27 SST-derived matrix, then amplified through polynomial powers (T²) and cross products (a·b, b·c, a·c). The result is a genuine MQ (multivariate quadratic) structure over F_3 — the same hardness basis as post-quantum multivariate signature schemes.

27

Trits

7.6T

Possible States (3²⁷)

MQ

Quadratic Structure

Why 27 Trits?

Mathematical Properties

• 27 = 3³ — perfect cube in the ternary domain
• 3²⁷ ≈ 7.6 trillion possible checksum values
• Ring structure: F_3[x]/(f(x)) where f is irreducible of degree 27
• Polynomial operations provide algebraic mixing (avalanche)

Security Properties

• MQ structure: Polynomial powers + cross products = multivariate quadratic
• Avalanche effect: Single bit flip → ~60% of trits change
• Non-degenerate: 10K+ random inputs → all distinct outputs
• Non-linear: Hash-to-field + quadratic powers break linearity
• Matrix twist: 27×27 SST-derived matrix mixes all trits
• Domain separation: SST 24-cycle gives 24 unique configurations
• Large state space: 3²⁷ ≈ 7.6T possible checksums

Balanced Ternary

YPC-27 uses balanced ternary with values {-1, 0, +1}:

T

-1 (negative)

0

0 (neutral)

1

+1 (positive)

Example checksum: 1T011T0... (27 trits total)

Usage

Basic Checksum

import { ypc27, YPC27Checksum } from 'yakmesh/oracle/ypc27';

// Compute checksum for any data
const data = new TextEncoder().encode('Hello, YAKMESH!');
const checksum = ypc27(data);          // Poly27 — 27-trit field element
// → digestBytes() / digestHex() / digestWire() for transport

// Verify checksum
const isValid = YPC27Checksum.verify(data, checksum);
// → true

Domain-Separated Checksums

import { PacketChecksum, PROTOCOL_DOMAIN } from 'yakmesh/oracle/packet-checksum';

// Same data, different domain → different checksums
const data = { content: 'test' };

const stupa = new PacketChecksum(PROTOCOL_DOMAIN.STUPA, myNodeId);
const nakpak = new PacketChecksum(PROTOCOL_DOMAIN.NAKPAK, myNodeId);

const stupaChecksum = stupa.compute(data);
const nakpakChecksum = nakpak.compute(data);

// Domain separation — same bytes, different field elements
console.log(stupaChecksum.equals(nakpakChecksum)); // false

Wrap & Unwrap Helpers

import { wrapWithChecksum, unwrapWithChecksum } from 'yakmesh/oracle/packet-checksum';

// Wrap data with checksum
const wrapped = wrapWithChecksum(myData, 'STUPA');
// → { data: myData, ypc27: 'YPC27:v1:abc123...' }

// Unwrap and verify
const { data, valid } = unwrapWithChecksum(wrapped, 'STUPA');
if (!valid) {
  console.error('Checksum mismatch - packet may be corrupted or tampered!');
}

Wire Format

YPC-27 checksums use a versioned wire format. Two encodings are in use: v1 (int8-packed trits, packet-checksum fields) and v2 (compact 5-trits-per-byte, digestWire() / wrapWithChecksum):

YPC27:v1|v2:<base64-encoded-trits>

Part	Description	Example
`YPC27`	Algorithm identifier	`YPC27`
`v1\|v2`	Encoding version — v1 int8-packed, v2 5-trits/byte compact	`v2`
`<trits>`	Base64-encoded 27 trits	`YXBjZGVm...`

Protocol Integrations

STUPA Broadcasts

Beacon messages now include ypc27 field. Verified on deserialize.

mesh/beacon-broadcast.js

NAKPAK Packets

Routed packets include checksum. Computed during padToFixedSize().

mesh/nakpak-routing.js

KHATA Protocol

ANNOUNCE, REQUEST, RESPONSE, REVOKE messages all include checksums.

security/khata-protocol.js

SHERPA Discovery

Peer discovery messages protected against tampering.

mesh/sherpa-discovery.js

Security Analysis

Attack Resistance

Attack	Difficulty	Notes
Brute Force	3²⁷ ≈ 7.6T operations	Infeasible for online attacks
Collision (Classical)	3²⁷ ≈ 7.6T	Large output space, hash collision resistance
Collision (Quantum)	No known speedup	Large output space, no Shor/Grover advantage
Cross-Protocol Replay	Prevented	Domain separation ensures uniqueness

API Reference

oracle/ypc27.js

Export	Description
`ypc27(data)`	Compute 27-trit checksum for any data (returns Poly27)
`YPC27Checksum.verify(data, expected)`	Verify checksum matches data
`tritsToBytes(trits)` / `bytesToTrits(bytes)`	Trit array ↔ byte conversion

oracle/ypc27.js helpers & oracle/packet-checksum.js

Export	Description
`wrapWithChecksum(data, domain)`	Wrap data with domain-separated checksum
`unwrapWithChecksum(wrapped, domain)`	Unwrap and verify checksum
`PacketChecksum` + `PROTOCOL_DOMAIN`	Per-domain checksum engines (STUPA, NAKPAK, KHATA, MANTRA, SHERPA, ANNEX, LAMA, KARMA, MANI)

Provenance full version history →

Introduced in v2.7.1 — Initial release of YPC-27 checksums with STUPA, NAKPAK, KHATA integrations.

v3.5.0 — YPC-27 v2.0 — verified-irreducible F₃²⁷ polynomial replaces degenerate x²⁷−1 ring; YPC-27² power-magnified checksum (27×27 F₃ matrix); v2 compact wire encoding