The usage of Information Technologies (IT), as well as data has increased over the years to improve businesses and human life generally thereby increasing productivity. In the health sector, Electronic Health Records (EHR) has helped in collecting demographic medical data which helps healthcare practitioners to provide quality health care. The EHR generates lots of medical data and are analyzed and processed to form big health data and sent to Agencies, Government to influence decisions in improving quality of life and to predict or prevent premature deaths and disease development. In this research work, we propose a model using lattice-based cryptography to encrypt health big data and deploy a decoy model which will be coined in fog computing facility to serve as honeypot or trap machine to attract attackers.