As society becomes increasingly digitalized, payment systems are also shifting toward digital solutions. However, in situations where connectivity is limited or unavailable, such as wars, natural disasters or other scenarios that may damage critical infrastructures, offline payment systems become increasingly important. This thesis conducts a systematic literature review of cryptographic algorithms for secure offline payments between mobile devices utilizing NFC or BLE communication. It investigates symmetric, asymmetric, and post-quantum cryptographic approaches in the context of resource-constrained mobile devices. The analysis focuses on key performance metrics, including computational cost, memory usage, communication overhead, and energy consumption, while considering constraints of wireless communication, as well as mobile devices. The aim is to identify, examine, and analyze cryptographical algorithms and determine suitability for offline payment scenarios between mobile devices in bandwidth-constrained environments. The results indicate that AES-128 combined with lattice-based post-quantum algorithms, such as ML-KEM-512 for key exchange and ML-DSA-44 or FN-DSA-512 for signatures, provides a practical, secure, and post-quantum-ready solution for constrained mobile communication.