It is the U.S. Constitution and Bill of Rights that makes election the business of the federal government. By giving all citizens the right to vote.
To insure that every American entitled to vote gets to vote, the Voter Rights Act was passed and other Federal Public Laws cover voter registration,Under Title 42, Chapter 20, Elective Franchise, Subchaper I -H, National Voter Registration Plus.
The Voting Rights Act itself has been called the single most effective piece of civil rights legislation ever passed by Congress.
The United States Department of Justice has a section whose job it is to enforce the VRA 
Here is a short but adequate history of voting rights in the United States.
https://www.justice.gov/crt/introduction-federal-voting-rights-laws
The Voting Rights Act and changes.
https://www.justice.gov/crt/history-federal-voting-rights-laws
https://www.justice.gov/crt/statutes-enforced-voting-section
Alaska Info HAVA
http://www.elections.alaska.gov/doc/info/Fiscal%20Challenges.pdf