U.S. election laws date back to Article 1 of the Constitution which outlines the structure of America's federal government. It also guarantees the states and people certain rights. Many constitutional amendments and federal laws have passed to help protect the right to vote and to make it easier for citizens to exercise that right.
"No right is more precious in a free country than that of having a voice in the election of those who make the laws under which, as good citizens, we must live. Other rights, even the most basic, are illusory if the right to vote is undermined." ~Justice Hugo Black, Wesberry v. Sanders, 376 U.S. 1,17 (1964)