Permutation and modes of operation

Question

I'm reading the book "Serious Cryptography A Practical Introduction to Modern Encryption" from Jean-Philippe Aumasson, and in the first chapter, it is written this :

We can try to abstract out the workings of a cipher, first by identifying its two main components: a permutation and a mode of operation. A permutation is a function that transforms an item (in cryptography, a letter or a group of bits) such that each item has a unique inverse (for example, the Caesar cipher’s three-letter shift). A mode of operation is an algorithm that uses a permutation to process messages of arbitrary size.

But when I search about "mode of operation", I only found "block ciphers" using it.

Do all ciphers (for instance stream ciphers) have modes of operation?

And do all ciphers use permutation?

Thanks !

Answer 1

if a cipher operates on fixed length blocks it has to be a permutation by definition since a one to one function is automatically a permutation on the finite domain $\{0,1\}^n.$

This gives the Electronic Codebook Mode, which uses a key to choose which pseudorandom permutation to use, but it leaks information, so modes of operation were invented for block ciphers, to stop equal messages resulting in equal ciphertexts.

Stream ciphers are not permutations in general. Stream ciphers don't have modes of operation in general.

Permutations play a significant role in asymmetric ciphers as well, and the discrete log map over the multiplicative group $Z_{p}^{\ast}$, for example, is a permutation.