Cryptology II.3 Modes of Operation of Block Ciphers

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Contents

1. ECB = Electronic Code Book [PDF].
2. CBC = Cipher Block Chaining [PDF].
3. Variants of CBC [PDF].
4. CFB = Cipher Feedback [PDF].
5. OFB = Output Feedback (and CTR = Counter Mode) [PDF].

The complete Section II.3 as an PDF file.

Introduction

A bitblock encryption function f : F₂ⁿ → F₂ⁿ is primarily defined on blocks of fixed length n. To encrypt longer (or shorter) bit sequences the sender must

1. split the sequence into n-bit blocks,
2. pad the last block if necessary with
   • zeroes or
   • random values or
   • context information.

Then each block is encrypted by f, but in general one uses some sort of »chaining«. Four chaining procedures, called »modes of operation« were standardized together with DES:

• ECB,
• CBC,
• CFB,
• OFB.

• CTR,
• XTS.

The official web site for these standards is

https://csrc.nist.gov/projects/block-cipher-techniques

For a description of the modes a suitable general framework is a »block alphabet« Σ, with F₂ⁿ as most important example, equipped with a group composition *.

Furthermore we fix an encryption function

f : Σ → Σ.

The dependence on the key doesn't matter in this context and therefore is dropped in the notation.