SINAPAD is a premier national wide network of high performance supercomputing centers (CENAPADs) distributed across Brazil. In order to ease and optimize the use of the computational resources offered, SINAPAD is developing a computational grid under the acronym GRADPAD. One of the key components of the functionality of the grid refers to security and user authentication. We present an overview of the scheme we propose for secure authentication, privilege management and accounting. It is based on the national Public Key Infrastructure for the Brazilian academia (ICP-EDU) proposed by RNP (Rede Nacional de Pesquisa) and the project Diretórios based on the LDAPS (LDAP+SSL) protocol.