What was the concept of voting rights based on?

It's based on the Voting Rights Act of 1965. This prohibits the states and various political parties from putting voting qualifications or any other requirements in order to proceed with voting. Take note that this is all for the sake of the Civil Rights of the citizen so that everyone will be able to have a fair way to vote - regardless of status and color. 

Before this happened, take note that only a few African Americans had access to voting. There were even tests conducted to see if they are worthy for voting - indicating a bias in their colored race.