Cryptography and its application, Lecture notes of Cryptography and System Security

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INTRODUCTION TO CRYPTOGRAPHY

Lecture 4: Week 5

Dr. Azni Haslizan bt Ab Halim

CONTENT OF THIS CHAPTER Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 2 / 28

• (^) Overview of the AES algorithm
• (^) Internal structure of AES
  • (^) Byte Substitution layer
  • (^) Diffusion layer
  • (^) Key Addition layer
  • (^) Key schedule
• (^) Decryption
• (^) Practical issues

Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 4 / 28  (^) Some Basic Facts

• (^) AES is the most widely used symmetric cipher today
• The algorithm for AES was chosen by the US National Institute of Standards and Technology (NIST) in a multi-year selection process
• The requirements for all AES candidate submissions were:
  • (^) Block cipher with 128-bit block size
  • Three^ supported^ key^ lengths :^ 128, 192 and 256^ bit
  • Security relative to other submitted algorithms
  • Efficiency in software and hardware

Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 5 / 28  (^) Chronology of the AES Selection

• (^) The need for a new block cipher announced by NIST in January, 1997
• 15 candidates algorithms accepted in August, 1998
• 5 finalists announced in August, 1999:
  • Mars^ – IBM^ Corporation
  • RC6 – RSA Laboratories
  • Rijndael – J. Daemen & V. Rijmen
  • Serpent – Eli Biham et al.
  • Twofish – B. Schneier et al.
• In^ October 2000,^ Rijndael^ was^ chosen^ as^ the^ AES
• AES was formally approved as a US federal standard in November 2001

 (^) AES: Overview

• (^) Iterated cipher with 10/12/14 rounds
• Each round consists of “Layers” Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 7 / 28

CONTENT OF THIS CHAPTER Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 8 / 28

• (^) Overview of the AES algorithm
• Internal structure^ of^ AES
  • (^) Byte Substitution layer
  • (^) Diffusion layer
  • (^) Key Addition layer
  • (^) Key schedule
• Decryption
• Practical^ issues

 (^) Internal Structure of AES

• (^) Round function for rounds 1,2,…, nr -1: Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 10 / 28
• (^) Note: In the last round, the MixColumn tansformation is omitted

 (^) Byte Substitution Layer

• (^) The Byte Substitution layer consists of 16 S-Boxes with the following properties: The S-Boxes are - identical - the only nonlinear elements of AES, i.e., ByteSub( Ai ) + ByteSub( Aj ) ≠ ByteSub( Ai + Aj ), for i,j = 0,…, - bijective , i.e., there exists a one-to-one mapping of input and output bytes  S-Box can be uniquely reversed
• (^) In software implementations, the S-Box is usually realized as a lookup table Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 11 / 28

 (^) ShiftRows Sublayer

• (^) Rows of the state matrix are shifted cyclically: Input matrix Output matrix

B 0 B 4 B 8 B 12

B 1 B 5 B 9 B 13

B 2 B 6 B 10 B 14

B 3 B 7 B 11 B 15

Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 13 / 28

B 0 B 4 B 8 B 12

B 5 B 9 B 13 B 1

B 10 B 14 B

2 B 6

B 15 B

3 B 7

B 11 no shift ← one position left shift ← two positions left shift ← three positions left shift

 (^) MixColumn Sublayer

• (^) Linear transformation which mixes each column of the state matrix
• Each 4-byte column is considered as a vector and multiplied by a fixed 4x4 matrix, e.g., where 01, 02 and 03 are given in hexadecimal notation
• (^) All arithmetic is done in the Galois field GF (2^8 ) (for more information see Chapter 4.3 in Understanding Cryptography )

 ^ 

Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 14 / 28

 3  ^ ^  15 

03 ^ ^ B 10 

(^01)    B 5 

 02 03 01 01  ^ B 0 

03 01 01 02 B

C

 C

2

 C 1    01

 C 0 

Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 16 / 28  (^) Key Schedule

• (^) Subkeys are derived recursively from the original 128/192/256-bit input key
• Each round has 1 subkey, plus 1 subkey at the beginning of AES
• (^) Key whitening: Subkey is used both at the input and output of AES  # subkeys = # rounds + 1
• (^) There are different key schedules for the different key sizes Key length (bits) Number of subkeys 128 11 192 13 256 15

 (^) Key Schedule Example: Key schedule for 128-bit key AES

• (^) Word-oriented: 1 word = 32 bits
• 11 subkeys are stored in W[0]…W[3], W[4]…W[7], … , W[40]…W[43]
• First subkey W[0] … W[3] is the original AES key Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 17 / 28

CONTENT OF THIS CHAPTER Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 19 / 28

• (^) Overview of the AES algorithm
• (^) Internal structure of AES
  • (^) Byte Substitution layer
  • (^) Diffusion layer
  • (^) Key Addition layer
  • (^) Key schedule
• Decryption
• Practical^ issues

 (^) Decryption

• (^) AES is not based on a Feistel network  All layers must be inverted for decryption:
  • (^) MixColumn layer → Inv MixColumn layer
  • ShiftRows layer→^ Inv ShiftRows^ layer
  • Byte Substitution^ layer^ →^ Inv^ Byte Substitution layer
  • Key Addition layer is its own inverse Chapter 4 of Understanding Cryptography by Christof Paar and Jan Pelzl 20 / 28