Securing a service's secret

I have a TABLE sec.sec_secret_tab in the SEC schema

and this function:

FUNCTION sec.sec_get_secret (p_service_name VARCHAR2) 
IS
  vc_onwer VARCHAR2(32767); 
  vc_secret VARCHAR2(32767);
BEGIN
  vc_onwer := sec.mystery_func;

  SELECT secret
    INTO vc_secret
    FROM sec.sec_secret_tab
   WHERE service_name = p_service_name
     AND onwer = vc_onwer;

  RETURN vc_secret;

END sec_get_secret;

In the schema alpha, there is this procedure:

PROCEDURE alpha.show 
IS
  vc_secret VARCHAR2(32767);
BEGIN
  vc_secret := sec.sec_get_secret('service_1');

  dbms_output.put_line(vc_secret);

  vc_secret := sec.sec_get_secret('service_2');

  dbms_output.put_line(vc_secret);

END show;

In the schema beta, there is this procedure:

PROCEDURE beta.show 
IS
  vc_secret VARCHAR2(32767);
BEGIN
  vc_secret := sec.sec_get_secret('service_1');

  dbms_output.put_line(vc_secret);

  vc_secret := sec.sec_get_secret('service_2');

  dbms_output.put_line(vc_secret);

END show;

Knowing that

• the alpha and beta schemas have EXECUTE right on sec.sec_get_secret
• the user connected (lets call him OMEGA) has the EXECUTE rights on alpha.show and beta.show

How can I make the function sec.mystery_func to get the following output:

• if OMEGA calls alpha.show, 'A1' and 'A2' are displayed
• if OMEGA calls beta.show, 'B1' and 'B2' are displayed