Edit config file located here: exo-jboss/server/default/deploy/exo.jcr.ear.ear/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-confi

You also need to edit login configuration file located here: exo-jboss/server/default/conf/login-config.xml

<application-policy name="exo-domain">
    <authentication>
        <login-module code="org.exoplatform.services.security.j2ee.DigestAuthenticationJbossLoginModule"
                      flag="required">
            <module-option name="usersProperties">props/jmx-console-users.properties</module-option>
            <module-option name="rolesProperties">props/jmx-console-roles.properties</module-option>
            <module-option name="hashAlgorithm">MD5</module-option>
            <module-option name="hashEncoding">rfc2617</module-option>
            <module-option name="hashUserPassword">false</module-option>
            <module-option name="hashStorePassword">true</module-option>
            <module-option name="passwordIsA1Hash">true</module-option>
            <module-option name="storeDigestCallback">
                org.jboss.security.auth.spi.RFC2617Digest
            </module-option>
        </login-module>
    </authentication>
</application-policy>

You probably should define users.properties and role.properties according to your own needs.

More information about jboss server Digest authentication configuration can be found at JBoss guide chapter.