The Italians used Egyptian phone records to make other connections and discovered that the police officer who claimed to have found Regeni’s passport had been in touch with members of the National Security team that had been following Regeni. Suddenly, Regeni’s parents dared to hope the truth might surface. ‘‘The evil is unraveling slowly, like a ball of wool,’’ his parents wrote in a letter published in La Repubblica on the first anniversary of his disappearance.

But although the Egyptians admitted to surveilling Regeni, they insisted they had not abducted or killed him. And even if that could be proved, the core mystery remained: Why had he been ‘‘killed like an Egyptian’’? One common theory pointed to the work of a rogue officer. At the Interior Ministry, which controls National Security, even low-level officers enjoy considerable autonomy yet are rarely held to account, according to Yezid Sayigh, a senior associate at the Carnegie Middle East Center in Beirut. ‘‘Things may happen that Sisi does not approve of,’’ he said. But there was much else that made little sense. Which Egyptian official figured that torturing a foreigner was a good idea? Why dump his body on a busy highway, instead of burying it in the desert where it might never be found? And why produce his body as a high-level Italian delegation arrived in Cairo?

An anonymous letter sent to the Italian Embassy in Bern, Switzerland, last year and later published in an Italian newspaper, offered another explanation: Regeni had been caught in a shadowy turf war between National Security and Military Intelligence, with one group seeking to use his death to embarrass the other. The details suggested that the author of the account was intimately familiar with Egypt’s security apparatus, yet it also seemed improbable that one person could know so much. Senior American officials told me the letter was consistent, however, with broader intelligence reports of the fierce jockeying for power among rival security agencies. ‘‘They try to use cases as a lever to embarrass one another,’’ one said.

The most alarming possibility is that Regeni’s death was a deliberate message — a sign that, under Sisi, even a Westerner could be subjected to the most brutal excesses. In Rome, an official told me that when Regeni’s body was discovered, it was propped up against a wall. ‘‘Did they want him to be found?’’ the official asked. The Obama official said he believed that someone in the ‘‘upper echelons’’ of the Egyptian government may have ordered Regeni’s death ‘‘to send a message to other foreigners and foreign governments to stop playing with Egypt’s security.’’

No senior Egyptian official agreed to speak to me for this article. But Hossam Zaki, the former deputy foreign minister who is now assistant secretary general at the Arab League, told me that Egyptian officials believe that the murder was the work of an unidentified ‘‘third party’’ seeking to sabotage Egypt’s relations with Italy. ‘‘Egyptians do not treat foreigners badly, full stop,’’ he said.

Nonetheless, Regeni’s death cast a chill over Cairo’s shrinking expatriate community. ‘‘Few things have shaken me so deeply,’’ one European diplomat told me. Before we spoke, the diplomat asked me to deposit my cellphone in a signal-blocking box so that our conversation could not be surveilled. Regeni’s death, the diplomat continued, signaled Egypt’s broader direction: Regeni had fallen victim to the paranoia about foreigners that now coursed through Egyptian society; since the revolution, even small interactions could be fraught. During lunch in Cairo’s Islamic Quarter, the diplomat recounted, an agitated man remonstrated loudly with another guest for taking a photo of a meal — beans, bread and tamiyya, the Egyptian falafel. ‘‘He started to shout: ‘You’re a foreigner. You will use this image to show that we only eat beans and bread!’ ’’

In Fiumicello, where Regeni grew up and his parents still live, a banner reading ‘‘Verità per Giulio Regeni’’ hangs in the main church, but few believe that the truth will ever come out. Regeni’s family has closed ranks, appointing a pugnacious lawyer as its gatekeeper, and begun their own investigation into his murder. (His parents declined to be interviewed for this article but answered some questions by email.) At the Rome headquarters of the Carabinieri’s Special Operations Group, which specializes in counterterrorism and anti-mafia operations, Gen. Giuseppe Governale insists that there is still hope of solving the crime. ‘‘The Arab mentality is to procrastinate until everyone forgets,’’ he said. ‘‘But we will not stop until we find an answer. We owe it to his mother.’’