White House National Security Adviser Jake Sullivan figures prominently in a grand jury investigation run by Special Counsel John Durham into an alleged 2016 Hillary Clinton campaign scheme to use both the FBI and CIA to tar Donald Trump as a colluder with Russia, according to people familiar with the criminal probe, which they say has broadened into a conspiracy case.

Sullivan is facing scrutiny, sources say, over potentially false statements he made about his involvement in the effort, which continued after the election and into 2017. As a senior foreign policy adviser to Clinton, Sullivan spearheaded what was known inside her campaign as a “confidential project” to link Trump to the Kremlin through dubious email-server records provided to the agencies, said the sources, who spoke on condition of anonymity.

Last week, Michael A. Sussmann, a partner in Perkins Coie, a law firm representing the Hillary Clinton campaign and the Democratic National Committee, was indicted by a federal grand jury on charges of making false statements to the FBI about his clients and their motives behind planting the rumor, at the highest levels of the FBI, of a secret Trump-Russia server. After a months-long investigation, the FBI found no merit to the rumor.

The grand jury indicated in its lengthy indictment that several people were involved in the alleged conspiracy to mislead the FBI and trigger an investigation of the Republican presidential candidate—including Sullivan, who was described by his campaign position but not identified by name.

The Clinton campaign project, these sources say, also involved compiling a “digital dossier” on several Trump campaign officials—including Lt. General Michael Flynn, Paul Manafort, George Papadopoulos, and Carter Page. This effort exploited highly sensitive, nonpublic Internet data related to their personal email communications and web-browsing, known as Internet Protocol, or IP, addresses.

To mine the data, the Clinton campaign enlisted a team of Beltway computer contractors as well as university researchers with security clearance who often collaborate with the FBI and the intelligence community. They worked from a five-page campaign document called the “Trump Associates List.”

The tech group also pulled logs purportedly from servers for a Russian bank and Trump Tower, and the campaign provided the data to the FBI on two thumb drives, along with three “white papers” that claimed the data indicated the Trump campaign was secretly communicating with Moscow through a server in Trump Tower and the Alfa Bank in Russia. Based on the material, the FBI opened at least one investigation, adding to several others it had already initiated targeting the Trump campaign in the summer of 2016.