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PRAGTHOS:Practical Game Theoretically Secure Proof-of-Work Blockchain

Varul Srivastava, Sujit Gujar

TL;DR

This paper interrogates the security of Proof-of-Work blockchains under realistic, dynamic economic conditions that prior cryptographic and game-theoretic analyses overlook. It introduces Practical Rational Protocol Design (pRPD) to model altrust miners, adversaries, and rational deviators, incorporating external market effects via a signaling factor and dynamic rewards/difficulty. Building on this, it identifies new attack vectors—including Difficulty Altering, Quick Fork, Selfish Mining with Bribing, and Transaction Withholding—that can threaten even honest-majority systems. To counter these, the authors propose PRAGTHOS, a framework that couples protocol modifications (PC-MOD, PoI-based deterrence, and transaction-inclusion gating) with inflationary reward schemes to achieve strong attack-payoff security under plausible conditions. They show PRAGTHOS is secure against a computationally bounded adversary with inflationary rewards, and provide bounded-security guarantees under deflationary regimes, thereby offering a practical path to robust PoW design and laying a foundation for future incentive-aware blockchain security analyses.

Abstract

Security analysis of blockchain technology is an active domain of research. There has been both cryptographic and game-theoretic security analysis of Proof-of-Work (PoW) blockchains. Prominent work includes the cryptographic security analysis under the Universal Composable framework and Game-theoretic security analysis using Rational Protocol Design. These security analysis models rely on stricter assumptions that might not hold. In this paper, we analyze the security of PoW blockchain protocols. We first show how assumptions made by previous models need not be valid in reality, which attackers can exploit to launch attacks that these models fail to capture. These include Difficulty Alternating Attack, under which forking is possible for an adversary with less than 0.5 mining power, Quick-Fork Attack, a general bound on selfish mining attack and transaction withholding attack. Following this, we argue why previous models for security analysis fail to capture these attacks and propose a more practical framework for security analysis pRPD. We then propose a framework to build PoW blockchains PRAGTHOS, which is secure from the attacks mentioned above. Finally, we argue that PoW blockchains complying with the PRAGTHOS framework are secure against a computationally bounded adversary under certain conditions on the reward scheme.

PRAGTHOS:Practical Game Theoretically Secure Proof-of-Work Blockchain

TL;DR

This paper interrogates the security of Proof-of-Work blockchains under realistic, dynamic economic conditions that prior cryptographic and game-theoretic analyses overlook. It introduces Practical Rational Protocol Design (pRPD) to model altrust miners, adversaries, and rational deviators, incorporating external market effects via a signaling factor and dynamic rewards/difficulty. Building on this, it identifies new attack vectors—including Difficulty Altering, Quick Fork, Selfish Mining with Bribing, and Transaction Withholding—that can threaten even honest-majority systems. To counter these, the authors propose PRAGTHOS, a framework that couples protocol modifications (PC-MOD, PoI-based deterrence, and transaction-inclusion gating) with inflationary reward schemes to achieve strong attack-payoff security under plausible conditions. They show PRAGTHOS is secure against a computationally bounded adversary with inflationary rewards, and provide bounded-security guarantees under deflationary regimes, thereby offering a practical path to robust PoW design and laying a foundation for future incentive-aware blockchain security analyses.

Abstract

Security analysis of blockchain technology is an active domain of research. There has been both cryptographic and game-theoretic security analysis of Proof-of-Work (PoW) blockchains. Prominent work includes the cryptographic security analysis under the Universal Composable framework and Game-theoretic security analysis using Rational Protocol Design. These security analysis models rely on stricter assumptions that might not hold. In this paper, we analyze the security of PoW blockchain protocols. We first show how assumptions made by previous models need not be valid in reality, which attackers can exploit to launch attacks that these models fail to capture. These include Difficulty Alternating Attack, under which forking is possible for an adversary with less than 0.5 mining power, Quick-Fork Attack, a general bound on selfish mining attack and transaction withholding attack. Following this, we argue why previous models for security analysis fail to capture these attacks and propose a more practical framework for security analysis pRPD. We then propose a framework to build PoW blockchains PRAGTHOS, which is secure from the attacks mentioned above. Finally, we argue that PoW blockchains complying with the PRAGTHOS framework are secure against a computationally bounded adversary under certain conditions on the reward scheme.
Paper Structure (69 sections, 14 theorems, 69 equations, 4 figures)

This paper contains 69 sections, 14 theorems, 69 equations, 4 figures.

Key Result

Theorem 3.1

When $\tau_{min}<\frac{1}{2}$, an adversary can fork a PoW blockchain using Difficulty Altering attack w.p. $> 1- negl(\Theta\varepsilon)$ if $\beta_{a} \geq \underline{\beta_{a}}$. (i) expected time to mine a block by any party is $\propto \Theta$, (ii) $2\varepsilon$ is the difference in time betw

Figures (4)

  • Figure 1: Difficulty Altering Attack
  • Figure 2: Successful Quick Fork Attack
  • Figure 3: Pragthos Framework
  • Figure 4: Environment $Z_{1}$

Theorems & Definitions (46)

  • Definition 2.1: Round
  • Definition 2.2: Epoch
  • Definition 2.3: Phase
  • Claim 2.1: Eyal-2014-Selfish, Observation 1
  • Definition 2.4: Front-Running, Def. 2, Badertscher-2018-BitcoinRPD
  • Theorem 3.1: Difficulty Altering Attack
  • proof
  • Corollary 3.1: Bitcoin-Difficulty Altering
  • Definition 3.1: Quick Fork
  • Theorem 3.2: Quick Fork Attack
  • ...and 36 more