
Briefing
A foundational problem in decentralized systems concerns whether permissionless consensus can provide economically meaningful security while maintaining a design that allows for the free entry of operators. This research introduces the Stubborn Nakamoto protocol, a construction that modifies the original Nakamoto consensus rules to guarantee economic security by design. The new protocol operates within the same synchronous environment as Bitcoin, yet its security is decoupled from the reliance on constant monetary payments to miners or immense electricity consumption as the primary deterrent. This breakthrough establishes the theoretical feasibility of a new generation of permissionless systems that are both economically robust and resource-efficient, fundamentally altering the security-cost trade-off for decentralized architecture.

Context
The established Nakamoto consensus model, which underpins Bitcoin, relies on Proof-of-Work (PoW) to provide Sybil resistance and economic security. This security is maintained by ensuring the cost of acquiring 51% of the network’s hash power exceeds the potential profit from an attack. This reliance necessitates massive, continuous energy consumption and a system of monetary block rewards to incentivize honest behavior. The prevailing theoretical limitation is the assumption that permissionless design and robust economic security are intrinsically linked to this high-cost, resource-intensive model, raising questions about long-term sustainability and efficiency.

Analysis
The core mechanism of the Stubborn Nakamoto protocol involves a modification of the original protocol’s chain selection and block acceptance rules. This new protocol operates identically to the Nakamoto protocol in the absence of an attack, preserving the characteristics of anonymity and free entry for all nodes. The key innovation lies in the protocol’s capacity to enforce an economic security guarantee.
This is achieved by altering the consistency rules such that a successful attack, which attempts to deceive a node into accepting a false transaction state, results in a provable loss of value or confiscation of the attacker’s specialized capital. This mechanism shifts the security burden from external resource expenditure (electricity) to an internal, capital-based commitment, making the attack cost endogenous to the protocol’s design.

Parameters
- Permissionless Design ∞ Preserved, allowing all nodes to serve equivalent roles, join, and leave at any time.
- Security Reliance ∞ Decoupled from the necessity of monetary payments or immense electricity consumption.
- Protocol Basis ∞ A modification of the original Nakamoto protocol, designed for the synchronous environment with late joiners.
- Consistency Guarantee ∞ Ensures that any transaction finalized by a merchant following the protocol must be accepted by any honest node.

Outlook
The theoretical proof of the Stubborn Nakamoto protocol opens a critical new avenue for research into resource-efficient, economically secure permissionless systems. Over the next three to five years, this work will likely inform the design of next-generation layer-one blockchains and modifications to existing PoW systems. The strategic implication is the potential for a truly sustainable and decentralized financial rail that achieves the security properties of Bitcoin without its environmental and monetary overhead, leading to the development of new consensus primitives that prioritize economic finality over computational effort.

Verdict
The Stubborn Nakamoto protocol provides a rigorous theoretical construction that redefines the foundational security model, proving that permissionless consensus can be economically secure without relying on massive energy expenditure.