A First Look at “New Cryptarchia”

Summary

This report presents an initial examination of the “New Cryptarchia” (Cryptarchia v2) proposal. We outline its core mechanics, place it in context with Bitcoin, PHANTOM, and Praos, and then sketch a roadmap for completing its security analysis.

Core Protocol Mechanics

Multi-Proposer DAG Construction
- Executors: Every slot, all registered validators may produce a block in parallel.
- Block contents:
  1. A random subset of UTXO transactions to limit tagging attacks.
  2. A maximal antichain of references into the last w slots (default w=30), plus optionally one “long-ref” beyond that window.
  3. Dependency edges capturing UTXO consumption, so that conflicting transactions are never included.
Conflict Resolution & Finality
- Nodes detect forks by locating the Closest Common Ancestor (CCA) and then compare the cumulative weight of each branch—i.e., the total count of window-filtered references in descendants—to pick the “heaviest.”
- Short-range equivocations (e.g., two blocks by the same leader) can be slashed via an on-chain “double-sign proof” transaction.

A Unified Three-Step Comparison

We juxtapose four protocols—Bitcoin, PHANTOM, Ouroboros Praos, and Cryptarchia v2—each in the same three-step format, to highlight how Cryptarchia v2 generalizes Praos just as PHANTOM generalizes Bitcoin.

Protocol	1. Mempool / Setup	2. Mining / Election	3. Broadcast & Selection
Bitcoin (PoW chain)	Collect pending transactions	PoW mining: hash(parent ∥ MerkleRoot ∥ nonce)	Gossip block; adopt longest-(most-work) chain
PHANTOM (PoW DAG)	Gather transactions; identify all tips	PoW mining on multi-parent header (tips ∥ MerkleRoot ∥ nonce)	Gossip block; run GHOSTDAG “blue-set” to totally order the DAG
Ouroboros Praos (PoS chain)	Snapshot stakes; derive fresh epoch randomness	VRF_evaluate(seed ∥ slot) < φ ⇒ slot-win; one leader per slot	Extend best chain with VRF proof; use weight-based fork choice
Cryptarchia v2 (PoS DAG)	UTXO-lock registration; compute each validator’s φ	Up-front Bernoulli draw (per-validator, per-slot) ⇒ eligible slots	Gather txns; select max-antichain refs; assemble block; DAG update

Bitcoin ↔ PHANTOM: single-chain PoW → DAG PoW with antichain ordering
Praos ↔ Cryptarchia v2: slot-election PoS → DAG PoS with antichain ordering

Security Analysis: Roadmap

Instantiating the Ideal Coin-Flip

The notebook currently uses rng.binomial() as a stand-in for an ideal public-coin. To make this provably secure, we must choose and specify one of:

Per-validator VRF (Praos/Algorand style)
- Input = (epoch_seed ∥ slot ∥ validator_ID)
- Publish proof π; verify Hash(π) < φ(f,σ).
- Pros: Unbiasable, publicly verifiable; Cons: reintroduces secret-key proofs.