According to some reports, the US National Security Agency would have suffered in 2015 a leak of information in which documents have been leaked which details, among other things, how the United States infiltrates into foreign computer networks and how it defends itself from cyber attack not knowing this theft until the beginning of 2016. The leak of information caused by an employee of the Agency who transferred these documents to his personal computer in which Kaspersky antivirus was installed, this being an element whose role is not clear in the leak of information.
According to some experts, Kaspersky may be able to collaborate directly with the Russian government, facilitating access to that information in some way. Kaspersky sources have denied this possibility by stating that it does not work jointly with any government, either its own or any foreigner.
Other experts also talk about the possibility that the role of Kaspersky was not intentional, but that it occurred through an incident recognized by the company between 2014 and 2015 in which his network was compromised by sophisticated malware or that attackers will take advantage of a vulnerability discovered in 2015 by Tavis Ormandy in the mechanisms of SSL transmission of information from clients with Kaspersky to their servers. In both cases the attackers could have accessed Kaspersky's information about the clients running their antivirus and then locate and access the NSA data that the agency worker had on their computer.
[Update 10/10/2017]: According to the US newspaper "The New York Times", the Israeli cyber intelligence service may have noticed how the Russian government was looking at names belonging to United States programs and classified documents on Kaspersky servers. After this event, last summer the government of Israel proceeded to warn the American, which vetoed Kaspersky in all its computer systems.