Nowadays, big data becomes widespread. Big data has great value, but it faces many challenges. One of these challenges is security. Many classic security techniques exist, but these mechanisms are not appropriate for big data security. To secure big data, it is necessary to secure many aspects such as infrastructure, data privacy, data management, and integrity and reactive. Securing computations in distributed programming frameworks and protecting non-relational data stores are two requirements for infrastructure protection. This survey will highlight securing MapReduce as one of the most popular distributed programming frameworks. Security of MapReduce computation is an important consideration when a MapReduce computation is performed on a public or hybrid cloud. When a MapReduce job is executed on public cloud or hybrid cloud, an integrity check of its result is required. In this survey, a set of previous techniques that check the result integrity of MapReduce will be explained. In addition to discussion of the advantages and disadvantages of each technique.