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DATA ENCRYPTION

STANDARD(DES)

by Engr. Khurram Hashmi

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Cryptography

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Block Ciphers

Block ofplain Text

Size: (M)

CipherEncryption

Algorithm

Block ofcipher Text

Size : (M)

Secret key

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Background

The Data Encryption Standard (DES) is a blockcipher that uses shared secret encryption.

It was selected by the National Bureau of Standards asan official Federal Information Processing

Standard (FIPS) for the United States in 1976 Has subsequently enjoyed widespread use

internationally.

The algorithm was initially controversial because

of classified design elements DES consequently came under intense academic

analysis which motivated the modern understandingof block ciphers and their cryptanalysis.

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Shortfalls

DES is now considered to be insecure for many applications.Chiefly due to the 56-bit key size being too small.

The basic method of attack is brute force trying everypossible key in turn.

The length of the key determines the number of possiblekeys.

DES has a small key size 56-bits and this approach isfeasible for breaking it

Questions were raised about the adequacy of DES key sizeeven before it was adopted as a standard, and it was thesmall key size, rather than theoretical cryptanalysis, whichdictated a need for a replacement algorithm

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Data Encryption Standard

It is a block Cipher

Data is encrypted block by block i.e. 64 bits each

time

plain Text64 bit blocks

CipherEncryptionAlgorithm

16 cycles

Cipher Text64 bit blocks

Secret key64 bits

N Blocks N Blocks

56 bits used

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Encryption Algorithm

Data is processed as 32 bithalf-blocks

Takes 16 rounds to complete

In each round, a new sub-key from the key schedulerisutilized

Data is swapped after each

round except the last Initial and final permutations

are Inverses of each other

48 bitSub-key

48 bitSub-key

32bit32bit

XOR

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Structure

BinaryInput

One Dimensional arrays.

For loops

While loops

Function calling

Sub function calling

1 2 3 4 5 6 ... ... ... N

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Main

A=round(rand(1,64))

B=P1(A);

[l,r]=LR(B);

[l,r]= mnalgo(l,r);

C=LRbk(l,r);

D=P2(C)

64 elements (random)

32 elements 32 elements

64 elements (permuted)

Expansionkey XOR

Compression (S-Box)

P-Box

64 element final permt

L

Script file

64 element (cipher text)

R

16 cycles

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Initial Permutation: P1( )

function [b]= P1(a)

Shif=[58 50 42 34 26 18 10 2;

60 52 44 36 28 20 12 4;

62 54 46 38 30 22 14 6;

64 56 48 40 32 24 16 8;

57 49 41 33 25 17 9 1;

59 51 43 35 27 19 11 3;

61 53 45 37 29 21 13 5;

63 55 47 39 31 23 15 7;];

l=1; % extra counter

for i= 1:8, %rows

for j= 1:8, %columns

b(1,l)=a(1,Shif(i,j)); %the actual guided shifting

l=l+1; % extra counter increment

end

end

1 2 3 4 5 . . 58 . 64

58 50 42 34 26 . . . . 7

58

a original array

b shifting / swapping

b shifted / swapped array

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16 cycles: Main algorithm ( )

function[l,r]= mnalgo(l,r)

cnt=0; %counter intialization

while cnt

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Left Right Breaking: LR( )

function[l,r]=LR(c)

l(1,1:32)=c(1,1:32); %the first 32 of the input elements

r(1,1:32)=c(1,33:64); %the next 32 of the input elements

1.32 33..64

1.64

left right

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Expansion and key XOR ( )

function [b]= E(a)

Ex=[32 1 2 3 4 5;

4 5 6 7 8 9;

8 9 10 11 12 13;

12 13 14 15 16 17;

16 17 18 19 20 21;

20 21 22 23 24 25;

24 25 26 27 28 29;

26 29 30 31 32 1;];

l=1; %extra variable

for i= 1:8, %rows

for j= 1:6, %columns

b(1,l)=a(1,Ex(i,j)); %the actual guided shifting

l=l+1; %extra increment

end

end

Duplication of two columns

Expansion Table

32 1

1 2 .. . .. 32

32 1 2 3 4 5 4 5 6

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Expansion and key XOR (b)

key=[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1

0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0]; %48 bitkey

b= xor (b,key);1 2 3 48

1 1 1 0 1

XOR

1 2 3 48

keyExpanded array

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S-Box Compression

function [b]= S(a)

% where a is a 48 element binary array

t=[14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7;

0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8;

4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0;

15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 14]; %S-box Table

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S-Box Compression

6bit 6bit 6bit 6bit

011011

01

1101

1

13

rows

columns

temp

cnv( )

cnv4( ) S-Box Tableref

Binary to decimal

91001Decimal to Binary

4bit

32 bit

4 bit

Replacement element

48 bit

+1

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S-Box Look up table

S5Middle 4 bits of input

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

Outer

bits

00 0010 1100 0100 0001 0111 1010 1011 0110 1000 0101 0011 1111 1101 0000 1110 100101 1110 1011 0010 1100 0100 0111 1101 0001 0101 0000 1111 1010 0011 1001 1000 0110

10 0100 0010 0001 1011 1010 1101 0111 1000 1111 1001 1100 0101 0110 0011 0000 111011 1011 1000 1100 0111 0001 1110 0010 1101 0110 1111 0000 1001 1010 0100 0101 0011

Input: 011011 Output: 1001

Non Linear Transformation

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4bit

S-Box: While loop

i=1; j=1; l=1; cn=1; %initializing counterswhile i

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P-Box permutation

%P-Box permutation

P=[16 7 20 21 29 12 28 17 1 15 23 26 5 18 31 10;

2 8 24 14 32 27 3 9 19 13 30 6 22 11 4 25]; % P-box table

l=1; % extra counter

for i= 1:2, %rows

for j= 1:16, %columns

b(1,l)=c(1,P(i,j)); %the actual guided shifting

l=l+1; % extra counter increment

end

end

32 bit Array

P-Box permuted array

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Final Permutation: P2( )

function [b]= P2(a)

ip= [58 50 42 34 26 18 10 2;

60 52 44 36 28 20 12 4;

62 54 46 38 30 22 14 6;

64 56 48 40 32 24 16 8;

57 49 41 33 25 17 9 1;

59 51 43 35 27 19 11 3;

61 53 45 37 29 21 13 5;

63 55 47 39 31 23 15 7;];

The initial permutation table

Generating a reverse permutation array that reverses the initial permutation

58 50 42 34 26 18 10 2

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Final Permutation: P2( )c=1;

for x= 1:64

l=1;

for i= 1:8,

for j= 1:8,

ifip(i,j) = = x;

iprev(1,c) =l;

c=c+1;

else

;

end

l=l+1;

end

end

end

%iprev

for j= 1:64, %coloumns

b(1,j)=a(1,iprev(1,j)); %the actual guided shifting

%l=l+1; % extra counter incrementend

58 50 y

7

Reverse Reference index iprev

Reverse permuted array

Initialpermutationtable

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Binary to Decimal conversion

function[b]=cnv(a)

%where a is a 2 bit array

c=0000;

c=(a(1,1)*10)+c;

c= a(1,2)+c;

b=int2str(c);

b=bin2dec(b);

1 1

c=0000

0010

0011

3

0011

int2str( )

bin2dec ( )

10

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Encryption

plain Text64 bit blocks

CipherEncryptionAlgorithm

16 cycles

Cipher Text64 bit blocks

Secret key64 bits

N Blocks N Blocks

56 bits used

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Questions are Welcome

Thank You