Revealing your current salary puts you in a position of negotiating against yourself.
Negotiate at the Right Time
Negotiating your salary after receiving an offer is generally better than during the interview process.
A job with a salary at the lower end of your desired range could come with a very generous employee benefits package. That could influence negotiations.
Consider the Whole Package
If the salary is firm, you can negotiate additional benefits or perks. The company may view benefits as a less costly way of keeping employees happy.