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Already the No. 3 seller of smartphones globally, China’s Huawei has ambitions of knocking off both Samsung and Apple within five years’ time.

Richard Yu, head of the company’s device business, told reporters on Sunday that the company thinks it could be No. 2 within two to three years.

“Maybe I am not humble,” Yu said at a meeting in Barcelona. “Four years ago, no one knew who we were, even in China.”

There is no doubting that China’s Huawei has risen quickly — it shipped 100 million devices last year, and has eclipsed established players such as LG, Motorola and HTC. However, surpassing either Apple or Samsung would be quite a challenge, let alone both.

Topping the established leaders would almost certainly require doing better in the U.S., where the company has been selling largely online and remains a bit player. Yu said that the company knows it will also need to establish direct relationships with carriers to gain share.

“We are quite late in the U.S. market,” Yu said. “We will be successful in the future.”

The company hopes to have products on sale with at least one of the top U.S. carriers this year, Yu said.

As for the global slowdown in smartphone sales, Yu was unfazed. “Smartphone is a little bit saturated, but for Huawei there is still growth,” he said.

The products are already good, but Yu said Huawei still has work to do on its image.

“We need time to build our brand,” Yu said. “Our products are very good, but many people don’t know them.”

Yu did have praise for Apple CEO Tim Cook in his standoff with the U.S. government.

“We agree with that,” Yu said. “Privacy is very important.”

However, when pressed further, Yu declined to say whether Huawei would similarly resist government requests if put in a similar situation.