Radio Frequency Identification (RFID) and Near Field Communication (NFC) are wireless technologies applied in several domains, among which, remote education. The communication between different components of this system is unsecured, which may lead to several security and privacy problems. Designing authentication protocols to protect a remote education system in an open environment (e.g. NFC, RFID, and Internet) is a challenging task. Recently, Yang et al. proposed a mutual authentication protocol based on the hash function for RFID systems to secure this system. Yang et al. showed that their protocol is secure and can resist various attacks. This work proves that Yang et al.'s protocol does not achieve reader authentication, location privacy, and security forward. Furthermore, we propose an enhanced authentication protocol for secure remote education systems (EAP-SRES) using NFC technology. Our protocol is based on post-quantum cryptosystem to resist quantum attacks. Security analysis by using CL-AtSe (Constraint Logic based Attack Searcher) tool and Ouafi-Phan privacy model shows that the EAP-SRES protocol achieves the requirements of mutual authentication, untraceability and resists different possible attacks. In addition, EAP-SRES protocol is very efficient in term of performance.