DEPID (Detached Embedded-Proof IDentifiers)

DEPID is a 128-bit identifier specification designed for decentralized applications. It enables mathematically guaranteed instance-to-instance uniqueness and embedded source attribution without the need for a central registry.

Key Features

• Decentralized Attribution: Identify the origin (issuer) of an ID in O(1) time.

• Algebraic Uniqueness: Uses prime-field divisibility to ensure global uniqueness with minimal shared knowledge.

• Collision Resistant: Combines high-entropy "Naked IDs" ($Q$) with algebraic alignment to prevent overlaps.

• Opaque & Secure: Employs Keyed-Folding to protect against GCD and prime-recovery attacks.

• Time-Sortable (v3): Includes an embedded Unix timestamp for native lexicographical ordering.

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How It Works: The Algebraic Basis

The core of DEPID is mapping a high-entropy "Naked ID" ($Q$) into a verifiable prime field based on a source-specific 20-bit prime ($P$).

1. Prime-Field Alignment

A 100-bit (v2) or 64-bit (v3) entropy source is shifted and aligned to the nearest multiple of the issuer's assigned prime :

$D=(Q≪20)−((Q≪20)\mod P)$

This ensures , making the ID mathematically verifiable.

2. Masking (Folding)

To prevent unauthorized parties from identifying the prime, the value is obfuscated using a deterministic XOR mask:

$X=D⊕fold{_L}​(P)$

3. O(1) Verification

Receivers extract an 8-bit Scattered Hint ($H$) to perform subset selection. Instead of checking all primes, they only test the small "bucket" of candidate primes associated with that hint, resulting in constant-time identification.

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Specification & Formats

Binary Layout (128-bit)

Segment	Bits	Description
Hint (H)	0–7	8-bit Keyed Hint for routing.
Version (V)	8–11	4-bit Version identifier.
Payload (K)	12–127	Algebraic/Entropy field (116 bits).

Versioning

• v1 (Algebraic): Unkeyed fixed sets.
• v2 (Hardened): Two-keyed masking for max entropy ().
• v3 (Temporal): Includes 32-bit Unix timestamp for chronological sorting.

String Representation

DEPID uses a 2-1-29 (v2) or 2-1-8-21 (v3) hex-and-dash format:

• v1: HH-1-KKKKKKKKKKKKKKKKKKKKKKKKKKKKK
• v2: HH-2-KKKKKKKKKKKKKKKKKKKKKKKKKKKKK
• v3: HH-3-TTTTTTTT-KKKKKKKKKKKKKKKKKKKKK

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Anti-Collision Fail-safes

To guarantee 100% uniqueness, the generation process utilizes three layers of protection:

1. Progressing Entropy: Use of a CSPRNG and/or progressing counters/timestamps.
2. Cross-Prime Check: A "Bucket Collision" rule ensures the generated ID isn't accidentally divisible by other primes in the same hint bucket.
3. Local DB Check: A final fail-safe check against the local issuance database.

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License

Copyright (c) 2026 Rhendra Networking. Distributed under the MIT License.