Is the Kurihara algorithm really what it purports to be (dramatically faster but equally secure replacement for Shamir Secret Sharing)?
Shamir's secret sharing algorithm has the desirable properties of information theoretic security (possessing shares fewer than the threshold is no better than random data) and minimal storage (each distributed share is the same size as the original secret). However, it's very slow to compute, to the point that when dispersing a large file with Shamir you would typically use ordinary symmetric encryption for the file at large and protect only the symmetric key with Shamir.
As of around the year 2007 industrial researchers in Japan (Kurihara et alia at KDDI and others at Toshiba) and academics in China (Chunli et alia) have published papers showing how to use random numbers with simple XOR operations to accomplish the same level of information theoretic security and minimal storage, with performance hundreds of times better than Shamir Secret Sharing. Some of the algorithms offer arbitrary "(k, n)", aka "(threshold, sharecount)" flexibility, as Shamir also does.
Is there any reason to continue using Shamir versus the new XOR based threshold secret sharing algorithms?