Tahoe-LAFS[1] is a storage system that works similarly. It splits data into n fragments, of which any k fragments are enough to restore the data. This leads to a replication factor of only DATA_SIZE/k*n, while you can still lose n-k pieces without data loss. Additionally all data is encrypted, signed and optionally deduplicated.
One of the authors of Tahoe-LAFS started a company that ported the whole system over to cloud storage providers.[2] It's still in alpha, but it's definitly worth a look if you want secure, encrypted storage without relying on a single cloud provider.