In the last 10 days around 250 blue Stars of David - similar to the one on the Israeli flag - have appeared on buildings in Paris and its suburbs.
They prompted an outcry from French politicians, who presumed the signs were antisemitic.
But from the start investigators were more circumspect.
While politicians made comparisons with Nazi-era graffiti to "out" Jews in their homes, investigators pointed out the Stars of David were randomly distributed, with no obvious Jewish connection in the choice of buildings.
Also the message in the medium was confusing. Conceivably a blue Israeli flag, or what immediately evokes it, could be seen as a pro-Jewish sign. Surely any genuine antisemite would have found a clearer way of expressing their hate.
Having caught and questioned two Moldovan nationals in connection with the first wave of stencils, French police and intelligence services now suspect the operation may be a classic piece of Russian dezinformatsiya (disinformation).
According to a statement from the prosecutor's office on Wednesday, the graffiti was put up on the two nights in late October by two separate couples. From telephone tracking, they believe both couples were taking orders from the same person.
"At this stage it is not excluded that the [graffiti] was carried out under the express orders of a person living abroad," the prosecutor's office said.
Some 250 Stars of David were tagged on buildings in Paris and its suburbs
French media outlets that have had access to the investigation go further. They point to a pro-Russian businessman from Moldova.
According to Le Monde newspaper, the graffiti operation is linked to a longstanding Russian propaganda network known as Doppelgänger.
In June Le Monde wrote a series of articles about Doppelgänger, which it said used computer bots to deluge social media with fake news postings. At the time the main purpose was to undermine faith in Western policy on Ukraine.
According to Le Monde, both couples who stencilled the Star of David graffiti were accompanied by a photographer whose job was to put the images straightaway online. The newspaper says the images first appeared only on accounts linked to the Doppelgänger network.
French police say the first couple - who were arrested - claimed to have been on holiday in Paris when they were approached by a man who heard them speak Russian and offered them a small sum of money to put up the tags.
That couple is currently awaiting deportation. The second couple left the country before they could be detained. The photographer or photographers remain unidentified.
Quoting sources in the investigation, Le Monde said the cut-price modus operandi - using poorly-paid proxy freelancers - was typical of today's Russian intelligence, which was hit hard by the expulsion of spies from Western capitals after the outbreak of the Ukraine war.
As for the purpose of Operation Star of David, like all dezinformatsiya it seems to have been to sow confusion and anxiety. The fact that the symbol could be either pro- or anti-Israeli made it all the more interesting: that way both sides would be suspicious.
By Hugh Schofield