A Stackelberg Model for Hybridization in Cryptography

2026-04-23

AI Summary

This work addresses the challenge of secure communication under resource constraints by formulating, for the first time, a hybrid encryption strategy as a Stackelberg game, wherein the defender acts as the leader by randomly selecting encryption schemes and the attacker, as the follower, optimizes its decryption strategy in response. To solve this game-theoretic model efficiently, the authors propose a conditional optimization framework that employs dynamic programming to solve the attacker’s subgame and linear programming to optimize the defender’s mixed strategy. This approach achieves a strong security guarantee while significantly reducing computational overhead, thereby enabling an effective trade-off between security and operational cost.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Adversarial Search

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Similar to a strategic interaction between rational and intelligent agents, cryptography problems can be examined through the prism of game theory. In this setting, the agent aiming to protect a message is called the defender, while the one attempting to decrypt it, generally for malicious purposes, is the attacker. To strengthen security in cryptography, various strategies have been developed, among which hybridization stands out as a key concept in modern cryptographic design. This strategy allows the defender to select among different encryption algorithms (classical, post-quantum, or hybrid) while carefully balancing security and operational costs. On the other side, the attacker, limited by available resources, chooses cryptanalysis methods capable of breaching the selected algorithm. We model this interaction as a Stackelberg cryptographic hybridization problem under resource constraints. Here, the defender randomizes over encryption algorithms, and the attacker observes the choice before selecting suitable cryptanalysis methods. The attacker's decision is framed as a conditional optimization problem, which we refer to as the ``attacker subgame''. We then propose a dynamic programming approach for the attacker's subgame, while the defender's Stackelberg optimization is formulated as a linear program.

Problem

• cryptography
• hybridization
• Stackelberg game
• resource constraints
• cryptanalysis

Innovation

• Stackelberg game
• cryptographic hybridization
• dynamic programming
• linear programming
• post-quantum cryptography