I want to create a URL shortener service where you can write a long URL into an input field and the service shortens the URL to \"http://www.example.org/abcdef\
Not an answer to your question, but I wouldn't use case-sensitive shortened URLs. They are hard to remember, usually unreadable (many fonts render 1 and l, 0 and O and other characters very very similar that they are near impossible to tell the difference) and downright error prone. Try to use lower or upper case only.
Also, try to have a format where you mix the numbers and characters in a predefined form. There are studies that show that people tend to remember one form better than others (think phone numbers, where the numbers are grouped in a specific form). Try something like num-char-char-num-char-char. I know this will lower the combinations, especially if you don't have upper and lower case, but it would be more usable and therefore useful.