rs? The answer is that there is an unlim- ited number of ways to proceed, even in the simplest cases. Instead of 26 symbol char- acters, we now have only two symbols, namely 0 and 1. Since each group of seven bits (ASCII) represents one plaintext character, there is a wide variety of possible schemes for transposition, substitution, or permutations. The number of ways in which any single seven-bit word can be modified into any other seven-bit word is 27=128, as opposed to only 26 with the ordinary alphabet. But the interesting feature of the binary system is that now we can code the bits not only within a single seven-bit block, but over the entire message sequence, which scrambles the blocks between themselves. For instance, the (four bit per character) sequence can be transformed by switching the bit positions by pairs, which gives Alternatively, we can take characters by pairs and swap their center bits, i.e., for five bit per character sequences: Clearly, the decryption algorithms consist of performing the reverse substitutions from the above ciphertexts. Let us see now what these two approaches produce as cipher texts (CT). Consider the example in Tables 25.1 and 25.2 (ASCII, seven-bit characters), noting that we can now use capital characters in the alphabetical plaintext (PT). In the first case, we observe that the last bit (ao) of each character is unchanged (since the number of bits is odd), and that the character y is invariant. In the second case, the first two characters, I and m, are invariant. But if we were to swap more bits up 25.2 Encryption and decryption with binary numbers to a complete permutation algorithm, we would achieve most perfect scrambling. For an eight-character or 56-bit codeword, the number of possible permutations is 56! = 7.1 X 1074. although with a sufficiently complex substitution algorithm, this approach would seemingly yield undecipherable messages. But the drawback is that its key (the scrambling algorithm) is fixed once and for all. No matter how complex, a fixed-key crypt