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In the situation where the security of a cipher decreases, the
post-cipher with both higher security and compatibility to the
original cipher is required until a totally new cipher will have
spread. In this paper we propose an idea to construct a more secure
cipher with compatibility to the original block cipher. The known
schemes such as triple-DES do not provide the security corresponding
to the key size. Our scheme provides the security corresponding to
both the key size and the number of original-cipher repetitions under
a certain condition. Furthermore we show that breaking our scheme is
at least as hard as breaking the original block cipher.
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