The increasing adoption of smart contracts on Ethereum and similar blockchain platforms has brought new security concerns, particularly regarding code-level vulnerabilities and unauthorized intrusions. This paper introduces a hybrid framework for intrusion detection in Ethereum smart contracts, leveraging cryptographic modeling and discrete mathematical structures. The framework formalizes contract behavior using graph theory and logic-based models to detect deviations from predefined secure states. Cryptographic primitives such as hash functions and digital signatures ensure data integrity and transactional authenticity. A temporal logic-based formal verification mechanism validates execution paths, while an embedded intrusion detection module enables real-time monitoring and automatic threat response. Experimental evaluation on Ethereum testnets demonstrates enhanced accuracy in identifying reentrancy attacks, access control violations, and state inconsistencies. The results affirm the effectiveness of discrete structures and cryptographic techniques in strengthening the security and reliability of decentralized applications.