The
translation of text from clear form to an encrypted form and back is a common
problem in computing. One simple
technique for encrypting text is based on the mathematical notion of a
permutation. A permutation of the
integers 0 through N-1 is simply a one-to one function whose domain and range
are both the set of integers {0, 1, 2, . . . , N-1}. In other words, a permutation transforms each
integer in the set {0, 1, 2, . . . , N-1} into another integer in the same set,
with no two integers being transformed into the same result. For example, here is a permutation of {0, 1,
2, 3, 4}.
This
permutation can be used to encrypt a sequence of five characters by moving each
character from its original position to the position defined by the
permutation. For example, the sequence
"APPLE" would be translated into the string "PLEAP":
Note that we
number positions starting at zero just as in C++ arrays — that’s a hint of
things to come. What about decrypting
the text above? Well, each permutation
has an inverse, another permutation that does the exact opposite of the
original permutation. For the
permutation given above, the inverse permutation is:
Apply the
inverse permutation to the scrambled sequence "PLEAP"; you should get
back the original sequence "APPLE".
That’s the key point about encryption/decryption using a permutation, apply
the permutation, and then apply its inverse, and you get back where you started.
Data Encryption
Standard (DES)
DES
is the archetypal block cipher — an algorithm
that takes a fixed-length string of plaintext
bits and transforms it through a series of complicated operations into another ciphertext
bitstring of the same length. In the case of DES, the block size is 64 bits. DES also uses a key to customize the transformation, so that
decryption can supposedly only be performed by those who know the particular
key used to encrypt. The key ostensibly consists of 64 bits; however, only 56
of these are actually used by the algorithm. Eight bits are used solely for
checking parity,
and are thereafter discarded. Hence the effective key length
is 56 bits, and it is always quoted as such.The key is nominally stored or
transmitted as 8 bytes,
each with odd parity. According to ANSI X3.92-1981, section 3.5: One bit in
each 8-bit byte of the KEY may be utilized for error detection in key
generation, distribution, and storage. Bits 8, 16,..., 64 are for use in
ensuring that each byte is of odd parity.
