I'm an ESL teacher trying to help my student parse this sentence: 

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> And as they have come together, the imperative among participating countries to cloak their technological capacities and weaknesses has proved irresistible, at times hindering the search, military analysts say.
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My question is about the phrase "at times hindering the search" — I'm not sure what it modifies. It begins with an adverb phrase "at times," before a participial phrase "hindering the search." 

Is it an adjective phrase, modifying "imperative?" Or is it an adverb phrase, modifying "to cloak?"