# Chapter 6 Block Ciphers

# 6.1 Block Ciphers

In many classical cryptosystems, changing one letter in the plaintext changes exactly one letter in the ciphertext. In the shift, affine, and substitution ciphers, a given letter in the ciphertext always comes from exactly one letter in the plaintext. This greatly facilitates finding the key using frequency analysis. In the Vigenère system, the use of blocks of letters, corresponding to the length of the key, makes the frequency analysis more difficult, but still possible, since there is no interaction among the various letters in each block. Block ciphers avoid these problems by encrypting blocks of several letters or numbers simultaneously. A change of one character in a plaintext block should change potentially all the characters in the corresponding ciphertext block.

The Playfair cipher in Section 2.6 is a simple example of a block cipher, since it takes two-letter blocks and encrypts them to two-letter blocks. A change of one letter of a plaintext pair always changes at least one letter, and usually both letters, of the ciphertext pair. However, blocks of two letters are too small to be secure, and frequency analysis, for example, is usually successful.

Many of the modern cryptosystems that will be treated later in this book are block ciphers. For example, DES operates on blocks of 64 bits. AES uses blocks of 128 bits. RSA sometimes uses blocks more than 1000 bits long, depending on the modulus used. All of these block lengths are long enough to be secure against attacks such as frequency analysis.

Claude Shannon, in one of the fundamental papers on the theoretical foundations of cryptography [Shannon1], gave two properties that a good cryptosystem should have in order to hinder statistical analysis: **diffusion** and **confusion**.

Diffusion means that if we change a character of the plaintext, then several characters of the ciphertext should change, and, similarly, if we change a character of the ciphertext, then several characters of the plaintext should change. This means that frequency statistics of letters, digrams, etc. in the plaintext are diffused over several characters in the ciphertext, which means that much more ciphertext is needed to do a meaningful statistical attack.

Confusion means that the key does not relate in a simple way to the ciphertext. In particular, each character of the ciphertext should depend on several parts of the key. When a situation like this happens, the cryptanalyst probably needs to solve for the entire key simultaneously, rather than piece by piece.

The Vigenère and substitution ciphers do not have the properties of diffusion and confusion, which is why they are so susceptible to frequency analysis.

The concepts of diffusion and confusion play a role in any well-designed block cipher. Of course, a disadvantage (which is precisely the cryptographic advantage) of diffusion is error propagation: A small error in the ciphertext becomes a major error in the decrypted message, and usually means the decryption is unreadable.

The natural way of using a block cipher is to convert blocks of plaintext to blocks of ciphertext, independently and one at a time. This is called the electronic codebook (ECB) mode. Although it seems like the obvious way to implement a block cipher, we’ll see that it is insecure and that there are much better ways to use a block cipher. For example, it is possible to use feedback from the blocks of ciphertext in the encryption of subsequent blocks of plaintext. This leads to the cipher block chaining (CBC) mode and cipher feedback (CFB) mode of operation. These are discussed in Section 6.3.

For an extensive discussion of block ciphers, see [Schneier].