lec 6-Cryptography -- Block Ciphers

Cryptography -- Block Ciphers

DES

Overview

• _{terms and principles} • _{Claude Shannon}

A few terms

• _{block cipher}

• _{block of plaintext is treated as a whole & used to}

produce a ciphertext block of equal length

• _{typical size: 64 bits}

• _{most modern ciphers are block ciphers} • _{stream cipher}

• _{digital data is encrypted one bit (or one unit) at a time}



Block vs Stream Ciphers



Q: What is a block cipher we have already

seen?



A: Playfair cipher. What is its block size?



A: 2 characters



Q: What are some stream ciphers we have

already seen?

Symmetric ciphers

Symmetric implies

ONE

key

Block Ciphers Features

•

Block size: in general

larger block

sizes mean greater security.

•

Key size:

larger key size means

greater security

(larger key space).

•

Number of rounds: multiple rounds

offer increasing security.

•

Encryption modes: define how

Basis of modern Block ciphers

• _{Claude Shannon- information theory} • _{product cipher}

• _{perform two or more ciphers in sequence so that}

result (product) is cryptographically stronger than any component cipher

• _{alternate confusion & diffusion}

• _{virtually all significant symmetric block ciphers currently}

Shannon’s strategy

• _{thwart cryptanalysis that is based on statistical analysis} • _{hacker has some knowledge of statistical characteristic of}

plaintext

• _{if statistics are reflected in ciphertext, then analyst may be}

able to deduce encryption key, or part of it

• _{in Shannon’s ideal cipher, statistics of ciphertext are}

Shannon’s building blocks

• _confusion

• _{make relation between statistics of ciphertext and the}

value of the encryption key as complex as possible, to thwart attempts to discover the key.

• _diffusion

• _{diffuse statistical property of plaintext digit across a}

range of ciphertext digits

• _{i.e. each plaintext digits affects value of many}

Shannon’s building blocks

• _{Shannon proposed product ciphers with two}

components

• _{S-Boxes -- substitution}

• _{providing confusion of input bits} • _{P-Boxes -- permutation}

Feistel cipher

• _{input plaintext of 2w bits}

• key K = n sub-keys: K₁, K₂, …, K_n

• sequence of n “rounds” each using K_i

• _{substitution followed by a permutation}

• apply function F(K_i) to right half of data, then

exclusive-OR it to left half of data

• _{permutation: interchange two result halves of data}

Feistel cipher

•

Multiple rounds

•

round i input is L

, R

L

= R

R

= (L

XOR

F(R

, K

))

Feistel

Cipher

plaintext (2w bits)

w bits w bits

L₀ R0

Round 1

K₁

L₁ R₁

F +

K_n

L_n R_n

F +

Round n

. . .

. . .

L_n+1 R_n+1

Feistel cipher dependencies

• _{block size – increasing size increases security – 64 bits}

common

• _{key size – increasing size improves security, – 128 bits}

common

• _{number of rounds – 16 is typical}

• _{subkey generation – complex generation makes}

cryptanalysis harder

• _{round function – complex function is stronger}

Feistel decryption

• _{same as encryption, except} • _{ciphertext is input}

• _{use keys in reverse order}

• _{at each round the output is equal to the corresponding}

value of the encryption process with the two halves of the value swapped

History of DES

• _{DES – Data Encryption Standard}

• _{Horst Feistel at IBM developed LUCIFER} • _{about 1971, sold to Lloyds of London}

• _{Nat’l Bureau of Standards issued request for national}

cipher standard

• _{IBM submitted (refined) LUCIFER}

DES Characteristics

• _{Plaintext is 64 bits long} • _{16 rounds}

• _{Key length is 56 bits}

Initial Permutation IP



first step of the DES



IP reorders the input data bits



even bits to LH half, odd bits to RH half



quite regular in structure (easy in h/w)



no cryptographic value

DES cipher

• round i input is L_i-1, R_i-1

L

= R

<----32 bits--->

L_i-1

exp/perm to 48

S-box

permutation

R_i-1

<----32 bits--->

xor

L_i Ri

--- 48 bits

--- 48 bits

--- 32 bits

--- 32 bits

One DES Round

Encryption (Round) (cont.)

32 1 2 3 4 5

4 5 6 7 8 9

8 9 10 11 12 13

12 13 14 45 16 17

16 17 18 19 20 21

20 21 22 23 24 25

24 25 26 27 28 29

Encryption (Round) (cont.)

F

S-box

Key Generation (cont.)

• Original Key: Key₀

• _{Permuted Choice One: PC_1( )} • _{Permuted Choice Two: PC_2( )} • _{Schedule of Left Shift: SLS( )} •

• •

0

0

0

(

C

,

D

)



PC

_ 1(

Key

)

1

1

(

C D

i

,

i

)



SLS C

(

i



,

D

i



)

1

1

_ 2(

(

,

))

i

i

i

Decryption

• _{The same algorithm as}

encryption.

• _{Reversed the order of key}

(Key₁₆, Key₁₅, … Key₁).

• _{For example:}

• _{IP undoes IP}-1 step of

encryption.

• _{1st round with SK16}

undoes 16th encrypt round.

Key property

• _avalanche

• _{small change in plaintext or in key produces}

significant change in ciphertext

• _{test for avalanche}

DES controversy

• _{DES choice was intensely criticized:}

• _{original LUCIFER key length was 128 bits, and DES}

used 56 bit key (to fit on chip, they said)

• _{critics feared brute force attacks}

• _{design criteria for the S-boxes was classified, so users}

DES status

• _{no weak points have surfaced} • _{DES is widely used}

• _{1994, NIST reaffirmed DES for federal use}

• _{NIST recommends DES use for all except classified}

information

• _{generally considered a sound standard} • _{Need more security: use Triple DES}

Cryptanalysis of DES

• _{increased computing speed has made a 56 bit key}

susceptible to exhaustive key search

• _{demonstrated breaks:}

• _{1997 – taking a few months, a large network of}

computers broke DES

• _{1998 – Electronic Frontier Foundation broke DES in a}

few days on dedicated hardware

1997 break

• _{RSA issued reward of $10,000 for finding a DES key, given}

ciphertext for known and unknown plaintext

• _{solution found in 96 days – involved 70,000 computers on}

the Internet

• _{an embarrassingly parallel problem – just divide the key}

space being searched (brute force) each time a new computer joins in

References & Detailed readings

• _{Book: Cryptography and Network Security}

by william stalling chapter 3

• _{Book: Cryptography and Network Security}