If you do not have the means to do a web authorization you will need to include the third party decryption with you application.
This is what you could try
1) Write a standalone program only to create a password hash one time. (This program should not be a part of your app). Make a note of the hash that was generated.
http://www.mindrot.org/projects/jBCrypt/
// Hash a password for the first time.
String hashed = BCrypt.hashpw(password, BCrypt.gensalt(12));
2) Store this password hash as a String constant in you APK.
3) Then every time you need to check the password, compare with the hashed password, using bcrypt.
// Check that an unencrypted password matches one that has
// previously been hashed
if (BCrypt.checkpw(candidate, hashed))
System.out.println("It matches");
else
System.out.println("It does not match");
jBCrypt is a single java file and it can be directly included in your application. It is considered one of the strongest encryption algorithms for passwords.
Even through the decryption algorithm is present in you APK, trying to break this is very time consuming details of which can be read in the article below.
Read this article for details and security of bcrypt.
http://codahale.com/how-to-safely-store-a-password/
Again, use this only if you do not have the means to do web based authentication.