This is really interesting! I would love to see more on this subject!
EDIT: I found this site: http://indoeuro.bizland.com/project/script/slavi.html
An Arabic traveler in the late 9th century wrote about Eastern Slavs: "…They constructed a monument and wrote the name of their dead leader on it". How could Slavs write a name when there was no Cyrillic yet? Such "lines and curvings" were found on different stone and wooden tablets, and also on rocks, instruments and pots all over Russia and several in East Europe. The first such inscription, consisting of 14 symbols, was discovered in 1897 not far from Ryazan, a city southeast from Moscow.
Later similar symbols were found in Belorussia, Bulgaria, Poland, Crimea; they all probably represent modifications of the same writing system. But no idea exists about what kind of writing it was. The number of symbols makes more than 75, this makes us suppose this was a syllabic script or even a logographic one. Still, as the territory of its usage was very wide, different variant of the same letter can differ from each other and considered now as two different letters.
Several symbols look much like Cyrillic, or remind the Greek alphabet. Hard to say how this happened: either the script originally borrowed from the Greek, or modified later under the influence of Cyrillic. Perhaps the "lines and curvings" were written from the left.