More than a third of the advertising tied to the presidential race has been funded by nonprofit groups that will never have to reveal their donors, suggesting that a significant portion of the 2012 elections will be wrapped in a vast cloak of secrecy.

The bulk of the secret money spent so far has come from conservative groups seeking to propel a Republican into the White House, advertising data shows. The flow of funds is part of a wave of spending by outside groups that has quickly come to dominate the 2012 presidential contest, particularly by so-called "super PACs" that have few limits on their activities.

But unlike super PACs, politically minded nonprofit groups are under no obligation to disclose the corporations, unions or wealthy tycoons bankrolling their advertising.

"I don't think we've seen these kind of groups acting so aggressively in election-related activity as we see now," said Richard Hasen, an election law expert at the University of California in Irvine.

Nonprofit "social welfare" organizations and other tax-exempt groups with confidential donors have spent more than $24 million in the 2012 cycle on political ads naming President Barack Obama or, less frequently, his Republican rivals, according to a Washington Post analysis of data supplied by Kantar Media/CMAG, which tracks ad spending. That accounts for about 40 percent of the money estimated to have been spent so far on advertising related to the presidential candidates.

Crossroads GPS, a nonprofit group backed by GOP political guru Karl Rove, has spent more than $10 million on ads targeting Obama over the federal deficit, energy policies and other issues in the 2012 cycle. American Crossroads, a sister group registered as a super PAC, has spent just $133,000 on such ads, the data show.

Obama has complained loudly about the influence of "secret billionaires" on the political system, and Senate Democrats are reviving efforts to force disclosure by nonprofit groups that run political ads.

But Democrats also enjoy support from many groups that rely on undisclosed contributors. Two super PACs helping Democrats in 2012, American Bridge 21st Century and Priorities USA Action, have accepted transfers of more than $200,000 each from their nonprofit arms - meaning that a portion of their budgets were effectively paid for by secret donors.