North Korean leader Kim Jong Un examines a rocket warhead that North Korea says could be equipped with a nuclear weapon. Some South Koreans are suggesting they should develop nuclear arms as well, in response. (Kcna/Reuters)

What would it take for South Korea to develop nuclear weapons? It’s a fringe idea that rears its head every now and then here.

But North Korea’s advances in nuclear weapons technology and the frustration over how to deal with Kim Jong Un’s obstinate regime have led a small but growing number of prominent politicians and academics to wonder: Why not us, too?

The idea has influential backers in the Chosun Ilbo, South Korea’s biggest newspaper, and in Chung Mong-joon, a scion of the Hyundai family and a staunch — and wealthy — advocate for South Korea having nuclear weapons.

And they have one main target in mind: China.

“I don’t think that South Korea actually wants nuclear weapons,” said Park Syung-je, chairman of the Asia Strategy Institute in Seoul. “It’s a way of saying to the Chinese that ‘if you don’t cooperate on North Korea, then we’re going to get nuclear weapons of our own.’ ”

While South Korea’s government has been doing all it can to punish North Korea for its latest nuclear and missile tests, there is a limit to how much pain Seoul can inflict. Instead, all eyes are on China, North Korea’s largest trading partner by far and the closest thing it has to an ally.

There is a great deal of frustration here that China is the country that has almost all the leverage over North Korea, especially given the widespread view that Beijing, while angry, will never risk destabilizing its impoverished and nuclear-armed neighbor.

“North Korea’s nuclear weapons capability power is bound to grow, so it is important for South Korea to keep military and power balance between the two Koreas,” said Cheong Seong-chang, a North Korea expert at the Sejong Institute, a think tank, and one of the most prominent advocates of South Korean nuclear weapons.

“China would object to the idea of South Korea becoming a nuclear state, but it is important for us to find a point where the national interests of both countries meet,” Cheong said.

China is already vehemently objecting to talks between Seoul and Washington over the deployment in South Korea of a sophisticated anti-missile system known as THAAD, for Terminal High Altitude Area Defense.

Thanks to its post-Korean War security alliance with the United States, South Korea is protected by the American nuclear umbrella. It declared in a 1991 deal that it would not “manufacture, possess, store, deploy or use nuclear weapons” and is a signatory to several nonproliferation treaties.

But some politicians are openly wondering why South Korea shouldn’t have its own weapons program.

“We can’t borrow an umbrella from a neighbor every time it rains,” said Won Yoo-cheol, a lawmaker from President Park Geun-hye’s ruling Saenuri party and its floor leader in the National Assembly. “It’s time for us to seriously consider an effective and realistic countermeasure for dealing with North Korea’s nuclear capability.”

This could take the shape of asking the United States, which pulled its nuclear weapons out of South Korea in 1992, to bring them back. Or it could entail South Korea developing nuclear weapons of its own, Won said last month.

In January, an editorial titled “South Koreans Must Discuss Acquiring Nuclear Arms” ran in the conservative Chosun Ilbo.

“The U.S. has passed the buck for taming North Korea to China, and China is doing nothing. Seoul now faces a real need for public discussion of the development of its own nuclear weapons,” the editorial said.

Then last month, the newspaper ran a detailed article in which nuclear experts said it could take only 18 months to turn plutonium from South Korea’s nuclear power plants into a workable bomb. “It would take time to construct a large-scale reprocessing facility, but it can be done [at a smaller scale] even now in laboratories,” the paper quoted Kim Seung-pyong, a professor of nuclear engineering, as saying.

The weapons advocates have a not-insignificant amount of public support. A Korea Research poll published last month found that 53 percent of respondents supported South Korea either developing its own nuclear weapons or considering doing so. Forty-one percent wanted a nuclear-free Korean Peninsula.

But the idea has not gained traction among senior politicians, and President Park has unequivocally dismissed it, saying that the whole peninsula should be free of nuclear weapons.

David Straub, associate director of the Korea Program at Stanford University’s Asia-Pacific Research Center, said the public discussion has so far largely been a media phenomenon that has shown some South Koreans’ frustration with China’s lack of action to punish North Korea. Speaking out publicly, he said, seems to be mostly an attempt to get Beijing’s attention.

“And the Chinese,” he added, “are not stupid.”

Still, American officials have long worried about an arms race in northeast Asia.

Japan has a plutonium reprocessing facility and could use it to develop fissile material for nuclear bombs in as little as three months. It wouldn’t take much for South Korea, with its 24 nuclear power plants and its advanced technology, to get to the same stage. Taiwan might also join in.

U.S. Energy Secretary Ernest Moniz, during a visit to Beijing last week, expressed rare public concern over China’s spent-nuclear-fuel reprocessing plans.

China’s plan for a large-scale plutonium reprocessing facility “certainly isn’t a positive in terms of nonproliferation,” Moniz told the Wall Street Journal.

Henry Sokolski, executive director of the Nonproliferation Policy Education Center in Washington, interpreted Moniz’s words as a sign of concern about discussions such as those taking place in South Korea.

“It’s hard to believe that South Korea would ever go first [in developing nuclear weapons],” Sokolski said. “But it’s getting tougher and tougher to deflect this idea. I think they’re definitely all looking at each other.”

Yoonjung Seo contributed to this report.