They won't make a sound no matter how many of them you try to toss in a bucket, and you can't pitch them in a fountain and wish for good luck. But make no mistake, bitcoins are getting big.

The online alternative currency, previously little more than a curiosity in financial markets since its 2009 inception, has zoomed in trading value since the Cyprus banking crisis erupted two weeks ago.

With fears spreading that even insured deposits might not be safe in similar nations hit by banking crises, those looking for a haven to store their wealth have fled to the complicated world of digital cash.

"Incremental demand for bitcoin is coming from the geographic areas most affected by the Cypriot financial crisis—individuals in countries like Greece or Spain, worried that they will be next to feel the threat of deposit taxes," Nicholas Colas, chief market strategist at ConvergEx, said in a report on the startling trend.

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Bitcoins operate on a network that, at least on the surface, resembles a typical exchange on the capital markets. Buyers can exchange their paper currencies for bitcoins and use them wherever they are accepted. Sellers can exchange their bitcoins back for their original currency.

But the value of the currency has been anything but typical.