•In an
ideal block cipher, the relationship
between the input blocks and the output block is completely random. But
it must be invertible for decryption to work.
–Therefore, it
has to be one-to-
one,
meaning that each input block is mapped to a unique output block.
•The
mapping from the input bit blocks to the output bit blocks can also be
construed as a mapping from the integers corresponding to
the input bit blocks to the integers corresponding to the output bit blocks.
•The
encryption key for the ideal block cipher is the codebook
itself, meaning the table that shows the relationship between the input blocks and the
output blocks.
Problems with Ideal Block Cipher
•There
is a
practical problem with the ideal block cipher.
•If a
small block size, such as n = 4, is used, then the system is
equivalent to a classical substitution cipher.
–Such
systems are vulnerable
to a statistical analysis of the plaintext.
–This weakness
is not inherent in the use of a substitution cipher but rather results from the
use of a small block size.
•If n
is
sufficiently large and an arbitrary reversible substitution between plaintext
and ciphertext is
allowed, then the statistical characteristics of the source plaintext are
masked to such an extent that this type of cryptanalysis is infeasible.
•However,
an arbitrary
reversible substitution cipher (the ideal block cipher) for a large block size
is not practical
from an implementation
and performance point
of view.
–Why?
•n=4,
required key length:
(4
bits)*(16
rows) = 64 bits.
–In
general, for an n-bit ideal block cipher, the length of
the key defined in this fashion is n * 2n
bits.
•For a
64-bit block, which is a desirable length to thwart statistical attacks, the
required key length is 64 * 264 = 270 = 1021 bits.
•The
size of the encryption key would make the ideal block cipher an impractical
idea.
–Think
of
the logistical issues related to the transmission, storage, and processing of
such large keys.
•Considering
these difficulties, what we need to do is make an approximation for large value
of n so that it is easily realizable.
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