You need to fulfill a couple of steps. Firstly change login configuration:

Edit config file located here: exo-tomcat/webapps/rest.war/WEB-INF/web.xml

Replace

<login-config>                                                                                                                                          
  <auth-method>BASIC</auth-method>                                                                                                                     
  <realm-name>eXo REST services</realm-name>                                                                                                           
</login-config>

for

<login-config>                                                                                                                                          
  <auth-method>DIGEST</auth-method>                                                                                                                     
  <realm-name>eXo REST services</realm-name>                                                                                                           
</login-config>

More information about tomcat configuration can be found at Apache Tomcat Configuration Reference.

Secondly you also need to specify new login module for JAAS:

Edit config file located here: exo-tomcat/conf/jaas.conf

Replace

exo-domain {
  org.exoplatform.services.security.j2ee.TomcatLoginModule required;
};

for

exo-domain {
  org.exoplatform.services.security.j2ee.DigestAuthenticationTomcatLoginModule required;
};