We know that Linear A was an ancestral form of Linear B used on Crete in the Middle–Late Minoan period. It was used alongside another, related undeciphered script called Cretan hieroglyphics. There are just over 1,400 extent texts, but most of these consist of just a handful of characters on seals, so the entire corpus isn't very big. From it we know of about 800 distinct characters.
Like Linear B, Linear A is a syllabary – each character represents a spoken syllable and can be used to spell out words phonetically. Unlike Linear B, it also has a lot of logograms mixed in. These characters represent whole words, e.g. "wheat" might be represented by an abstract version of a bushel of wheat.
The main barrier to deciphering it is we don't know what language it was used to write. The breakthrough in deciphering Linear B was when Ventris showed that it was recording an archaic form of Greek. There's been no such luck with Linear A. Because of its ancestral similarity to Linear B we can actually make a good guess at the sound-values of a lot of Linear A's characters, but plugging these in gives you words in an unrecognizable language. It's not Greek. It's entirely possible that it's unknown language unrelated to anything we know of. Various attempts to argue that it's a relative of X ancient language have failed to get us any further in deciphering it.
Because of this it's unlikely we'll be able to decipher Linear A using the evidence currently available. You can throw all the fancy statistical and cryptographic techniques at it you want, it won't help if we don't understand what the words mean even when they're "decoded". What is really needed is something like the Rosetta Stone, which provided the breakthrough required to understand Egyptian hieroglyphs: a parallel text in Linear A and a script/language we understand (e.g. Linear B). Until then, the effort seems to be stalled – but you never know.
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