# CS代考计算机代写 algorithm Excel Understanding Cryptography – A Textbook for

Understanding Cryptography – A Textbook for

Students and Practitioners by Christof Paar and Jan Pelzl

www.crypto-textbook.com

Chapter 3 – The Data Encryption Standard (DES)

ver. Nov 26, 2010

These slides were prepared by Markus Kasper, Christof Paar and Jan Pelzl

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Some legal stuff (sorry): Terms of Use

• The slides can used free of charge. All copyrights for the slides remain with the authors.

• The title of the accompanying book “Understanding Cryptography” by Springer and the author’s names must remain on each slide.

• If the slides are modified, appropriate credits to the book authors and the book title must remain within the slides.

• It is not permitted to reproduce parts or all of the slides in printed form whatsoever without written consent by the authors.

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Content of this Chapter

• Introduction to DES

• Overview of the DES Algorithm

• Internal Structure of DES

• Decryption

• Security of DES

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Content of this Chapter

• Introduction to DES

• Overview of the DES Algorithm

• Internal Structure of DES

• Decryption

• Security of DES

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Classification of DES in the Field of Cryptology

Symmetric Ciphers Asymmetric Ciphers Protocols

Block Ciphers

Stream Ciphers

You are here!

Cryptology

Cryptography Cryptanalysis

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DES Facts

• Data Encryption Standard (DES) encrypts blocks of size 64 bit.

• Developed by IBM based on the cipher Lucifer under influence of the National

Security Agency (NSA), the design criteria for DES have not been published • Standardized 1977 by the National Bureau of Standards (NBS)

today called National Institute of Standards and Technology (NIST)

• Most popular block cipher for most of the last 30 years.

• By far best studied symmetric algorithm.

• Nowadays considered insecure due to the small key length of 56 bit.

• But: 3DES yields very secure cipher, still widely used today.

• Replaced by the Advanced Encryption Standard (AES) in 2000

• For a more detailed history see Chapter 3.1 in Understanding Cryptography

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Block Cipher Primitives: Confusion and Diffusion

• Claude Shannon: There are two primitive operations with which strong encryption

algorithms can be built:

1. Confusion: An encryption operation where the relationship between key and ciphertext is obscured.

Today, a common element for achieving confusion is substitution, which is found in both AES and DES.

2. Diffusion: An encryption operation where the influence of one plaintext symbol is spread over many ciphertext symbols with the goal of hiding statistical properties of the plaintext.

A simple diffusion element is the bit permutation, which is frequently used within DES.

• Both operations by themselves cannot provide security. The idea is to concatenate confusion and diffusion elements to build so called product ciphers.

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Product Ciphers

• Most of today‘s block ciphers are product ciphers as they consist of rounds which are applied repeatedly to the data.

• Can reach excellent diffusion: changing of one bit of plaintext results on average in the change of half the output bits.

Example:

single bit flip many bit flips

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Content of this Chapter

• Introduction to DES

• Overview of the DES Algorithm

• Internal Structure of DES

• Decryption

• Security of DES

Overview of the DES Algorithm x

DES 64

k

y

64

• Encrypts blocks of size 64 bits.

• Uses a key of size 56 bits.

• Symmetric cipher: uses same key for encryption and decryption • Uses 16 rounds which all perform the identical operation

• Different subkey in each round derived from main key

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56

The DES Feistel Network (1) • DES structure is a Feistel network

• Advantage: encryption and decryption differ only in keyschedule

• Bitwise initial permutation, then 16 rounds

1.Plaintext is split into 32-bit halves Li and Ri

2.Ri is fed into the function f, the output of which is then XORed with Li 3.Left and right half are swapped

• Rounds can be expressed as:

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The DES Feistel Network (2)

• L and R swapped again at the end of the cipher, i.e., after round 16

followed by a final permutation

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Content of this Chapter

• Introduction to DES

• Overview of the DES Algorithm

• Internal Structure of DES

• Decryption

• Security of DES

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Initial and Final Permutation

• Bitwise Permutations.

• Inverse operations.

• Described by tables IP and IP-1.

Initial Permutation Final Permutation

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The f-Function

• main operation of DES

• f-Function inputs: Ri-1 and round key ki

• 4 Steps:

1.Expansion E 2.XOR with round key 3.S-box substitution 4. Permutation

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The Expansion Function E 1.Expansion E

• main purpose: ! increases diffusion

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Add Round Key

2.XOR Round Key

• Bitwise XOR of the round key and the output of the expansion function E

• Round keys are derived from the main key in the DES keyschedule (in a few slides)

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The DES S-Boxes 3.S-Box substitution

• Eight substitution tables.

• 6 bits of input, 4 bits of output.

• Non-linear and resistant to differential cryptanalysis.

• Crucial element for DES security!

• Find all S-Box tables and S-Box design criteria

in Understanding Cryptography Chapter 3.

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The Permutation P

4. Permutation P

• Bitwise permutation.

• Introduces diffusion.

• Output bits of one S-Box effect several S-Boxes in next round

• Diffusion by E, S-Boxes and P guarantees that after Round 5 every bit is a function of each key bit and each plaintext bit.

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Key Schedule (1)

• Derives 16 round keys (or subkeys) ki of 48 bits each from the

original 56 bit key.

• The input key size of the DES is 64 bit: 56 bit key and 8 bit parity:

• Parity bits are removed in a first permuted choice PC-1:

(note that the bits 8, 16, 24, 32, 40, 48, 56 and 64 are not used at all)

!

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Key Schedule (2)

• Split key into 28-bit halves C0 and D0.

• In rounds i = 1, 2, 9 ,16, the two halves are each rotated left by one bit.

• In all other rounds where the two halves are each rotated left by two bits.

• In each round i permuted choice PC-2

selects a permuted subset of 48 bits of Ci and Di as round key ki, i.e. each ki is a permutation of k!

• Note: The total number of rotations: 4×1+12×2=28 ⇒D0=D16 andC0=C16!

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Content of this Chapter

• Introduction to DES

• Overview of the DES Algorithm

• Internal Structure of DES

• Decryption

• Security of DES

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Decryption

• In Feistel ciphers only the keyschedule

has to be modified for decryption.

• Generate the same 16 round keys in reverse order.

(for a detailed discussion on why this works see Understanding Crptography Chapter 3)

• Reversed key schedule:

As D0=D16 and C0=C16 the first round key can be generated by applying PC-2 right after PC-1 (no rotation here!).

All other rotations of C and D can be reversed to reproduce the other round keys resulting in:

• No rotation in round 1.

• One bit rotation to the right in rounds

2, 9 and 16.

• Two bit rotations to the right in all other rounds.

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Content of this Chapter

• Introduction to DES

• Overview of the DES Algorithm

• Internal Structure of DES

• Decryption

• Security of DES

Security of DES

• After proposal of DES two major criticisms arose:

1. Key space is too small (256 keys)

2. S-box design criteria have been kept secret: Are there any hidden analytical attacks (backdoors), only known to the NSA?

• Analytical Attacks: DES is highly resistent to both differential and linear cryptanalysis, which have been published years later than the DES. This means IBM and NSA had been aware of these attacks for 15 years!

So far there is no known analytical attack which breaks DES in realistic scenarios.

• Exhaustive key search: For a given pair of plaintext-ciphertext (x, y) test all 256 keys until the condition DES -1(x)=y is fulfilled.

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⇒ Relatively easy given today’s computer technology!

k

History of Attacks on DES

Year 1977 1990 1993

Proposed/ implemented DES Attack

1993

Jun. 1997 Feb. 1998 Jul. 1998

Matsui proposes linear cryptanalysis (243 chosen ciphertexts) DES Challenge I broken, 4.5 months of distributed search DES Challenge II–1 broken, 39 days (distributed search)

Jan. 1999

DES Challenge III broken in 22h 15min (distributed search assisted by Deep Crack)

2006-2008

Reconfigurable key search machine COPACOBANA developed at the Universities in Bochum and Kiel (Germany), uses 120 FPGAs to break DES in 6.4 days (avg.) at a cost of $10 000.

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Diffie & Hellman, (under-)estimate the costs of a key search machine

Biham & Shamir propose differential cryptanalysis (247 chosen ciphertexts)

Mike Wiener proposes design of a very efficient key search machine: Average search requires 36h. Costs: $1.000.000

DES Challenge II–2 broken, key search machine Deep Crack built by the Electronic Frontier Foundation (EFF): 1800 ASICs with 24 search engines each, Costs: $250 000, 15 days average search time (required 56h for the Challenge)

Triple DES – 3DES

• Triple encryption using DES is often used in practice to extend the effective key length of DES to 112. For more info on multiple encryption and effective key lengths see Chapter 5 of Understanding Cryptography.

• Alternative version of 3DES:

Advantage: choosing k1=k2=k3 performs single DES encryption.

• No practical attack known today.

• Used in many legacy applications, i.e., in banking systems.

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Alternatives to DES

Algorithm AES / Rijndael

I/O Bit 128

key lengths 128/192/256

remarks

Triple DES Mars RC6 Serpent Twofish IDEA

64

128

128

128

128

64

112 (effective) 128/192/256 128/192/256 128/192/256 128/192/256 128

conservative choice AES finalist AES finalist AES finalist AES finalist patented

DES ”replacement”, worldwide used standard

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Lessons Learned

• DES was the dominant symmetric encryption algorithm from the mid-1970s to the mid-1990s. Since 56-bit keys are no longer secure, the Advanced Encryption Standard (AES) was created.

• Standard DES with 56-bit key length can be broken relatively easily nowadays through an exhaustive key search.

• DES is quite robust against known analytical attacks: In practice it is very difficult to break the cipher with differential or linear cryptanalysis.

• By encrypting with DES three times in a row, triple DES (3DES) is created, against which no practical attack is currently known.

• The “default” symmetric cipher is nowadays often AES. In addition, the other four AES finalist ciphers all seem very secure and efficient.