A discrete mathematical framework for security and cryptographic analysis of Ethereum smart contracts
Satpal Kushwaha, Sonam Gupta, Lipika Goel, Abhay Agarwal, Prashant Hemrajani · Journal of Information and Optimization Sciences · 2026
Ethereum smart contracts execute immutable and financially critical logic, making post-deployment security flaws especially expensive to remediate.Existing protection mechanisms typically depend on either static code inspection or dynamic execution-based testing, often lacking formal security assurances.This paper introduces a discrete mathematics based hybrid static and dynamic security and encryption analysis framework for Ethereum smart contracts that is both formally rigorous and practically deployable.Smart contracts are represented as discrete transition systems composed of finite states, executable actions, and security invariants, enabling formal reasoning about contract behavior.Static analysis derives control-flow and state-transition relationships to identify invariant violations before deployment, while dynamic analysis validates runtime execution traces against the discrete mathematical model.The framework additionally incorporates an encryption aware access control mechanism defined through key-dependent discrete transitions.Experimental evaluation on vulnerable Ethereum smart contracts shows enhanced vulnerability detection coverage and a reduction in false positives compared to standalone analysis approaches.The proposed framework provides a scalable, mathematically grounded solution for improving the security, encryption assurance, and reliability of Ethereum smart contracts.