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 show. Millions of dollars in additional spending from both sides has poured into legislative races, such as the Senate contest in Massachusetts, that could help determine which party controls Congress in 2013.

The flow of funds is part of a wave of spending by outside groups — particularly super PACs, which have few limits on their activities — that has quickly come to dominate the 2012 presidential contest.

But unlike super PACs, politically minded nonprofit groups are under no obligation to disclose the corporations, unions or wealthy tycoons bankrolling their advertising, much of which is almost indistinguishable from regular political ads run by campaigns.

The result is a race heavily influenced by such organizations and their funders, who will remain largely in the shadows.

“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 at Irvine. “This is pure secret money. . . . The goal is to avoid disclosure.”

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 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 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.

The disparity means that nearly all of the broadcast messages that voters have encountered from the Crossroads groups were paid for by persons unknown. The super PAC side of the operation reported taking in $18.2 million in 2011, including $7 million from Texas billionaire Harold Simmons and his company; the nonprofit side raised almost twice as much from unidentified donors.

For donors, ‘a choice’

Spokesman Jonathan Collegio said Crossroads GPS is no different than tens of thousands of other nonprofits, from ideological groups to charities, that are entitled to keep their contributors confidential.

“Private organizations don’t have to disclose their donor lists to the government at their beck and call,” Collegio said. “Those who want to support the Crossroads groups have a choice of whether they want to give to a more political- or issue-oriented effort, and they make their decisions according to their tastes and preferences.”

Another top spender is Americans for Prosperity, a Washington-based group that has ties to two conservative brothers who run the Koch Industries oil-and-gas conglomerate; David Koch is chairman of the group’s foundation.

Americans for Prosperity has spent nearly $7 million on ads targeting Obama, including a spot criticizing his administration’s handling of a government loan guarantee to failed solar firm Solyndra; the spot prompted a response ad from the Obama campaign. Tim Phillips, Americans for Prosperity’s president, said he expects that the organization will exceed $50 million in total spending, including ads and grass-roots organizing, in 2012.

Phillips defended the ability to keep donors under wraps, saying that the group “works in the public policy arena more than the political arena.” He also cited concerns that donors could be targeted for harassment by the Obama administration and liberal groups.

“This administration, and politicians in general, want to seek retribution with people who disagree with them,” Phillips said.

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, including unions and environmental groups. Two super PACs helping Democrats in 2012, American Bridge 21st Century and Priorities USA Action, have each accepted transfers of more than $200,000 from their nonprofit arms — meaning that a portion of their budgets were effectively paid for by secret donors.

Officials with both super PACs said the transfers were made to cover administrative expenses as part of cost-sharing agreements with their affiliated nonprofit groups.

Unlimited dollars

A general surge in spending by outside groups, first seen during the 2010 elections, is due in part to a series of court rulings, including Citizens United v. Federal Election Commission , that have made it easier for corporations and wealthy individuals to spend unlimited amounts of money on elections.

That environment led to the rise of super PACs — more than 300 are now registered with the FEC — that can raise and spend unlimited amounts as long as they do not coordinate directly with candidates. The catch is that such PACs must disclose their donors — leading an increasing number of publicity-shy contributors to use nonprofits to cloak their political spending, experts say.

Under U.S. tax laws, certain types of nonprofit groups can keep contributors confidential as long as their “primary purpose” is not politics, a definition that is the focus of fierce dispute in legal circles. The Internal Revenue Service has been cautious about treading too heavily, leaving many groups to, in effect, police themselves, many experts say.

The rule of thumb for social-welfare groups, business groups and other nonprofits is that they must spend less than half their budget on election activities to avoid disclosure of donors. Many nonprofits contend that that leaves them free to spend the rest of their budget on “issue ads,” which often include scathing and pointed attacks on individual politicians but don’t explicitly tell viewers how to vote.

Crossroads GPS — which is awaiting IRS approval of its nonprofit status — is currently on the air with an ad attacking Obama for the administration’s loan guarantee to Solyndra, calling it a “big-government fiasco” that left “laid-off workers forgotten.” But the ad never urges viewers to vote a certain way.

“Tell President Obama we need jobs, not more insider deals,” the spot concludes.

Donald Tobin, a tax-law professor at Ohio State University’s Moritz College of Law, said political advocacy groups are taking advantage of a murky legal landscape between tax and election laws.

He argues that many of the social-welfare groups now spending big on campaigns are flouting the intent of tax laws, which did not envision groups formed solely to dance on the line between issue advocacy and direct participation in elections.

“There’s no way that Congress expected groups like Crossroads GPS to be social-welfare organizations,” Tobin said. “They used to be groups that were focused on social welfare and did a little politics on the side. This has turned that idea on its head.”

Staff writer T.W. Farnam contributed to this report.