In this paper we consider multiple encryption schemes built from conve
ntional cryptosystems such as DES. The existing schemes are either vul
nerable to variants of meet-in-the-middle attacks, i.e., they do not p
rovide security corresponding to the full key length used or there is
no proof that the schemes are as secure as the underlying cipher. We p
ropose a variant of two-key triple encryption with a new method of gen
erating three keys from two. Our scheme is not vulnerable to the meet-
in-the-middle attack and, under an appropriate assumption, we can show
that our scheme is at least about as hard to break as the underlying
block cipher.