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This paper extends the provably-secure blockcipher construction proposed at FSE 2009 by Minematsu. Unlike the classical Luby-Rackoff cipher and its variants, the scheme is based on tweakable blockciphers. An advantage of the scheme is that it provides the beyond-birthday-bound security quite efficiently. While FSE 2009 proposal was the case of building a 2n -bit blockcipher using an n -bit tweakable blockcipher, we extend it to shorter and longer block lengths than 2n bits, keeping the security of beyond the birthday bound.