Security in Computing Character Frequencies (English ...

monoalphabetic cryptanalysis

Common English Digrams and Trigrams Digrams EN RE ER NT TH ON IN TF AN OR

Trigrams ENT ION AND ING IVE TIO FOR OUR THI ONE

3

Pfleeger, Security in Computing, ch. 2

See class example

4


Character Frequencies (English) 14 12

Security in Computing

10

percent

8

Chapter 2

6 4

Elementary Cryptography (part 2)

2 0

A B C D E F G H

I

J

K L M N O P Q R S T U V W X Y Z

characters Pfleeger, Security in Computing, ch. 2

1


2

Vigenere Tableau

Vigenere Cipher

construct a table (a Vigenere tableau)

each row in table is a different shift (alphabet)

sender and receiver agree on sequence of rows

helps to disguise patterns


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

7

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

B C D E F G H I J K L M N O P Q R S T U V W X Y Z A

cryptanalysts use properties of plaintext

what can be cryptographers' counter-moves?

F G H I J K L M N O P Q R S T U V W X Y Z A B C D E

G H I J K L M N O P Q R S T U V W X Y Z A B C D E F

H I J K L M N O P Q R S T U V W X Y Z A B C D E F G

I J K L M N O P Q R S T U V W X Y Z A B C D E F G H

J K L M N O P Q R S T U V W X Y Z A B C D E F G H I

K L M N O P Q R S T U V W X Y Z A B C D E F G H I J

L M N O P Q R S T U V W X Y Z A B C D E F G H I J K

M N O P Q R S T U V W X Y Z A B C D E F G H I J K L

N O P Q R S T U V W X Y Z A B C D E F G H I J K L M

O P Q R S T U V W X Y Z A B C D E F G H I J K L M N

P Q R S T U V W X Y Z A B C D E F G H I J K L M N O

Q R S T U V W X Y Z A B C D E F G H I J K L M N O P

R S T U V W X Y Z A B C D E F G H I J K L M N O P Q

S T U V W X Y Z A B C D E F G H I J K L M N O P Q R

T U V W X Y Z A B C D E F G H I J K L M N O P Q R S

U V W X Y Z A B C D E F G H I J K L M N O P Q R S T

V W X Y Z A B C D E F G H I J K L M N O P Q R S T U

W X Y Z A B C D E F G H I J K L M N O P Q R S T U V

X Y Z A B C D E F G H I J K L M N O P Q R S T U V W

Y Z A B C D E F G H I J K L M N O P Q R S T U V W X

Z A B C D E F G H I J K L M N O P Q R S T U V W X Y

8

polyalphabetic ciphers

multiple possible output characters for an input character

polygram ciphers –

5

use multiple alphabets

homophonic ciphers –


E F G H I J K L M N O P Q R S T U V W X Y Z A B C D

Hiding Patterns –

D E F G H I J K L M N O P Q R S T U V W X Y Z A B C


cryptographer's counter-move

C D E F G H I J K L M N O P Q R S T U V W X Y Z A B

encipher groups of letters at once


6

Don't Need to Construct the Table

More on Vigenere Keys

usually think of choice of rows as a keyword example: keyword “BASE” row order is b,a,s,e,b,a,s,e, ...

a b c d e f g h i j k l m n o p q r s t u v w x y z


























11



–

suppose we agree on the key{1,5,9,16,21,22} encrypt: –

char 1 with row 1

–

'

2 '

' 5

–

'

3 '

' 9

...

– –

char 6 with row 22

–

char 7 with row 1

–

char 8 with row 5

–

etc.


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25















equivalent K={1, 17, 0, 10, 4}

plaintext “I am sick of school”

convert to numeric vals

add to K mod 26

+

I 8

A M 0 12

S I C K 18 8 2 10

O F 14 5

S C H O O L 18 2 7 14 14 11

B 1

R A 17 0

K E B R 10 4 1 17

A K 0 10

E B R A K E 4 1 17 0 10 4

9

17 12

2 12 3 1

14 15

22 3 24 14 24 15

12


Vigenere Example

Vigenere Example

keyword = BRAKE











9



M = “Chappelle” K = 1,5,9,16,21,22 EK(M) = DMJFKAMQN

note: our key is in ascending order. this isn't required


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

























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Homophonic Example Plaintext

Homophonic Ciphers (cont'd)

Homophones

A B C D E F G

624 5 919 414 8 61 413

18 333 14 309 13 422 2

329 511 67 238 12

...

...

...

...

19

4

83 71

15

6

16

...

... ...

So “cabbage” could be encrypted as: –

14 329 511 5 624 2 8 15



Don't Need to Construct the Table

Are there disadvantages to this?

Homophonic Ciphers

keyword = BRAKE –

equivalent K={1, 17, 0, 10, 4}

plaintext “I am sick of school”

convert to numeric vals

add to K mod 26

+

Encrypts to: J RM CMDB OP WDYOYP

A M 0 12

S I C K 18 8 2 10

O F 14 5

S C H O O L 18 2 7 14 14 11

B 1

R A 17 0

K E B R 10 4 1 17

A K 0 10

E B R A K E 4 1 17 0 10 4

9

17 12

2 12 3 1

14 15

22 3 24 14 24 15


I 8

16

13

Try to hide plaintext patterns Map each plaintext character m to any of a set of ciphertext characters set of possible ciphertext characters that map to a single plaintext character m called homophones


14

Playfair Cipher

Playfair Encryption

1850s. named after Playfair

actually invented by his friend Wheatstone

write keyword without dups. into 5x5 matrix

treat I and J as the same character example: –

keyword “MACARONI”

M N F P V

A I/J G Q W

C B H S X

R D K T Y

divide plaintext into pairs

O E L U Z


double characters separated by dummy character (e.g. x)

mi ss is si pp i becomes

–

mi sx si sx si px pi

ciphertext longer than the plaintext

How many homophones per plaintext char? – –

fixed number variable: more for frequent plaintext characters


only 3 possibilities –

same row

–

same column

–

different row and col.

20

Polygram Ciphers

Are there disadvantages to this? –


Homophonic Ciphers (cont'd)

encrypt plaintext pairs

if plaintext has odd number of chars, append dummy char.

19

–

17

simple substitution ciphers, e.g. shift ciphers, keyword mixed alphabet, (even Vigenere tableau) ... substitute one character for another character polygram ciphers substitute a group of characters for another group of characters goal: make frequency analysis more difficult examples: –

playfair cipher

–

hill cipher


18

One time pad

One time pad

Idea: –

Take a stream of random data (keystream)

–

used to be physically on a pad. rip out as many random pages as you need.

Combine it with plaintext to form ciphertext

Message receiver uses same keystream to recover plaintext

Take a stream of random data (keystream)

–

Combine it with plaintext to form ciphertext

Message receiver uses same keystream to recover plaintext

If the stream is truly random perfect security

Why don't we use this all the time?

If the stream is truly random perfect security

–

How do we get unlimited truly random stream?

Why don't we use this all the time?

–

If we could get it, how do we distribute it?

–

What if sender and receiver aren't synchronized?

23

same row –

substitute with chars to right

–

examples: MCAR, RMOA,SUTP

same col –

substitute with chars below

–

examples: EULZ, GWQA

M N F P V

A I/J G Q W

C B H S X

Playfair – different row and col R D K T Y

O E L U Z

M N F P V

different row and col tricky


24


Playfair encryption (cont'd)

–


Idea:

21

substitute plaintext letter with letter that –

is in its own row

–

and is in the column of the other plaintext letter

example, AT becomes RQ

A C R O I/J B D E G H K L Q S T U W X Y Z


M

A

C R O D K T Y

P

A I/J G Q W

S

T U

22

Reusing the stream

Combining Plaintext with Keystream

So why can't we just reuse the DVD? –

It's very insecure: more on this later

27


Can do it a different ways: –

XOR

–

If text, can add to key (mod 26)

Quick Quiz

28


Quick Quiz

I have:

I have:

–

DVD ( 5 GBytes) of random data

–

DVD ( 5 GBytes) of random data

–

a 1.5 Mbps DSL

–

a 1.5 Mbps DSL

If I copy the DVD and give it to a friend, how long can we use it as a one-time pad?

If I copy the DVD and give it to a friend, how long can we use it as a one-time pad?

5GBytes1024MBytes/GByte8bits/byte =27,306secs.=about 7.5hours 1.5Mbps Pfleeger, Security in Computing, ch. 2

25


26

XOR (cont'd)

XOR (cont'd)

a a=?

a a=0

a b b=?

a b b=a XOR is an involution 31


XOR

XOR

Review: XOR logic operator

A

B

A XOR B

FALSE FALSE TRUE TRUE

FALSE TRUE FALSE TRUE

FALSE TRUE TRUE FALSE


32


29

XOR often denoted

Don't have to write the words TRUE, FALSE

The following are equivalent:

A

B

FALSE FALSE TRUE TRUE

FALSE TRUE FALSE TRUE

A B FALSE TRUE TRUE FALSE


A

B

0 0 1 1

0 1 0 1

A B 0 1 1 0 30

XOR Example

XOR in Java

can encrypt by XORing plaintext with keystream Example: plaintext = “Chappelle”

XOR it the keystream with the ciphertext.


35

System.out.println(plaintext.charAt(i) + "\t" + Integer.toBinaryString((int)plaintext.charAt(i)) + "\t" + key[i] + "\t" + Integer.toBinaryString(key[i])+ "\t" + Integer.toBinaryString((int)plaintext.charAt(i) ^ key[i]));


–

f a bijection (11, onto) from S to S (i.e. f: S S)

can encrypt by XORing plaintext with keystream

Example: plaintext = “Chappelle”

c C h a p p e l l e c(bin) 01000011 01101000 01100001 01110000 01110000 01100101 01101100 01101100 01100101 key 33 72 31 79 82 74 126 89 2 key(bin) 00100001 01001000 00011111 01001111 01010010 01001010 01111110 01011001 00000010 c XOR k 01100010 00100000 01111110 00111111 00100010 00101111 00010010 00110101 01100111

f is an involution if f = f -1 –

i.e. f(f(x)) = x

So XOR is an involution


36

XOR Example

Let: S be a finite set

Code that produced the example: for (int i=0; i

Security in Computing Character Frequencies (English ...

Security in Computing Character Frequencies (English ...

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