The work is not an original composition by Mendelssohn's violinist Ferdinand David, or some kind of hoax perpetuated by him. The original is a "Parte [Partite-"variations"?] del Tomaso Vitalino," Ms Mus 2037/R-1 in the Sächsische Landesbibliothek in Dresden (olim MS Cx 1145 in the Kgl. Musikalien-Sammling des Königs von Sachsen, a private library until 1898). The manuscript probably originated in Dresden, since it is copied by a principal music scribe at the Hofkapelle named Jacob Lindner (he copied many of the Vivaldi works in Dresden). The title Ciaconna is David's, and indeed the four-measure descending tetra chord is typical of chaconnes, but since the harmonies are not consistently the same, some have classified it as a passacaglia.
David, who edited and published other baroque violin works from the Dresden library, transformed the chaconne into a virtuoso 19th-century piece by adding an idiomatic accompaniment for Konzertflügel. The violin part is expanded with multiple stops, octave doublings, and 19th-century violinistic figuration (one passage "borrowed" from Mendelssohn's concerto!), and even a cadenza-flourish at the end. The whole is recast into a dynamic arch form, and Romantic dynamics and bowings abound.
The generally Romantic cast of the work has caused some to suggest that it is a hoax. And surely the scheme of keys causes one to raise an eyebrow. The work is in G minor (using a modal signature of one flat), but soon is in B flat minor, A minor, and even E flat major/against D sharp minor!! Not the usual scheme of most early 18th century baroque pieces. But one is reminded of that enharmonic modulation that Dresden lutenist S. L. Wiess penned. Dresden resident Heinrich Heinichen has a prelude through all the keys, and there is a beautiful one by lutenist Adam Falkenhagen (recorded by Paul Beier-20 minutes in length). And Tomaso's father in 1689 published a passagallo that begins in E flat major, and ends many measures later in E major, or as he titles it "Passagallo, che principia per B molle, E finischere per diesis." The same collection has a balletto that uses simultaneously meters of C, 12/8 and ¾, and another balletto ingenuously uses both F sharp and G flat. And in the university library at Rostock is a viola da gamba piece with a key signature that uses B flat, and the octave below a B natural. Experimentation was very much in the air back then, too.
There are scores of the original in facsimile (Zentralantiquariat der DDR), modern editions with realized figured bass, and virtuoso transformation for solo piano by Carlo Salina (dedicated to Busoni). Respighi orchestrated it also.
Some works have been identied as hoaxes, when they are genuine works by the named composer. That is the case of the famous Vitali Chaconne which has falsely been attributed to Ferdinand David, the famous 18th-century violin virtuoso. The original score with the name of Vitalino (son of the composer Vitali) is in a library in Dresden, and is available in facsimile edition. The composer's father was somewhat of a Charles Ives, and composed works with adventuresom harmonic relations. The son picked up some of these, when for example his harmonies move from B flat to D sharp major, suggesting to some observors a the harmonic vocabulary if a 19th-century composer! The 18th-century copyist has been identified with a music copyist employed at the Dresden court, and is known by name (Landsman or something like that).