You dont need to mention the 'real' reason in the resignation letter. You can communicate it verbally to your boss. The letter can be straight an simple. It must have the Date. In case you are serving a notice period mention that too. Make sure you take a signature from your boss and keep a copy with yourself.
Sample resignation letter for notice period of one month.
Its been a pleasant experience to have been working with <company name>. However, I have decided to move on to explore other oppurtunities.
Please accept my resignation letter, and kindly consider the resignation date <date>, as the start of my notice period of one month.
I wish the firm success in the future and I am sincerely proud to have had the opportunity to be with.
If anybody thinks the format is not appropriate, please point out.
1st October 2009 From India, Mumbai