Integrated Encryption in Dynamic Arithmetic Compressiongrammars.grlmc.com/LATA2017/Slides/Integrated Encryp… · · 2017-03-24Integrated Encryption in Dynamic Arithmetic Compression

Arithmetic CodingProposed Compression Cryptosystem

Empirical Results

Integrated Encryption in

Dynamic Arithmetic Compression

Shmuel T. Klein and Dana Shapira

1Bar Ilan University2Ariel University, Israel

LATA 2017

Klein & Shapira Integrated Encryption in Dynamic Arithmetic Compression


Empirical Results

Introduction

Concerns of Communication over a network:

1 processing speed

2 space savings of the transformed data

3 security



Empirical Results

Introduction


1 processing speed


3 security



Empirical Results

Introduction


1 processing speed


3 security



Empirical Results

Compression Cryptosystem

Data Compression - representation in fewer bits

Encryption - protecting information

⇒ Achieved by removing redundancies.




Empirical Results








Empirical Results








Empirical Results








Empirical Results


Compress then Encrypt

Encrypt then compress

Simultaneous



Empirical Results


Compress then Encrypt

Encrypt then compress

Simultaneous



Empirical Results

Why Arithmetic coding?

Huffman ???

easily breakable

communication errors



Empirical Results


Huffman ???

easily breakable




Empirical Results


Huffman ???

easily breakable




Empirical Results

Static arithmetic codingAdaptive Arithmetic Coding

1 Arithmetic Coding

Static arithmetic coding

Adaptive Arithmetic Coding

2 Proposed Compression Cryptosystem

3 Empirical Results

Compression performance

Uniformity

Cryptographic attacksKlein & Shapira Integrated Encryption in Dynamic Arithmetic Compression


Empirical Results


Outline

1 Arithmetic Coding




3 Empirical Results


Uniformity

Cryptographic attacks



Empirical Results


Arithmetic Coding

0.0

0.2

0.9

1.0

a

b

c

0.2

0.34

0.83

0.9

a

b

c

b

0.2

0.228

0.326

0.34

a

b

c

ba

0.326

0.3288

0.3386

0.34

a

b

c

bac



Empirical Results


Arithmetic Coding

0.0

0.2

0.9

1.0

a

b

c

0.2

0.34

0.83

0.9

a

b

c

b

0.2

0.228

0.326

0.34

a

b

c

ba

0.326

0.3288

0.3386

0.34

a

b

c

bac



Empirical Results


Arithmetic Coding

0.0

0.2

0.9

1.0

a

b

c

0.2

0.34

0.83

0.9

a

b

c

b

0.2

0.228

0.326

0.34

a

b

c

ba

0.326

0.3288

0.3386

0.34

a

b

c

bac



Empirical Results


Arithmetic Coding

0.0

0.2

0.9

1.0

a

b

c

0.2

0.34

0.83

0.9

a

b

c

b

0.2

0.228

0.326

0.34

a

b

c

ba

0.326

0.3288

0.3386

0.34

a

b

c

bac



Empirical Results


Arithmetic Coding


1 compute the new interval

2 update the model by incrementing the frequency of thecurrent character

3 adjust the relative sizes of the partition accordingly



Empirical Results


Arithmetic Coding







Empirical Results


Arithmetic Coding







Empirical Results


Arithmetic Coding

H.A. Bergen, J.M. Hogan, A chosen plaintext attack on an adaptive arithmetic compression algorithm,

Computers and Security, 12(2), (1993) 157–167.

R.S. Katti, A. Vosoughi On the security of key based interval splitting arithmetic coding with respect to

message indistinguishability, IEEE Trans. on Information Forensics and Security, 7(3), (2012) 895–903.

A. Singh, R. Gilhotra, Data security using private key encryption system based on arithmetic coding,

International Journal of Network Security & Its Applications (IJNSA), 3(3), (2011) 58–67.

I.H. Witten, J.G. Cleary, On the privacy afforded by adaptive text compression, Computers and

Security 7(4) (1988) 397–408.



Empirical Results

Outline

1 Arithmetic Coding




3 Empirical Results


Uniformity




Empirical Results

Proposed Compression Cryptosystem

Cryptosystem based on dynamic arithmetic coding

Update the model selectively

Use a secret key K = k0k1 · · · kt−1

The model is updated at step i if and only ifk(i−1) mod t = 1.



Empirical Results








Empirical Results








Empirical Results


encode(M,K)1 n←− |M|2 t ←− |K |3 initialize the interval to be [0, 1) with

uniform distribution of the alphabet symbols4 for i ←− 1 to n4.1 compute the new interval4.2 if k(i−1) mod t = 1 then4.2.1 update the model4.3 else4.3.1 the new partition into intervals is the current one5 return some value in the current interval

⇐= weakness

Precede plaintextby some known text



Empirical Results




⇐= weakness




Empirical Results




⇐= weakness




Empirical Results




⇐= weakness




Empirical Results

Compression Efficiency

Worst Case Example: abababab· · ·

Dynamic AC: uniform probability distribution (12, 1

2) for any

even sized history windowSelected: The probability of uniform distribution:(

nn/2

)(n

n/2

)(2nn

) ' 2√π n

,

by Stirling’s approximation.−→ For a key of size 512, only in 5% of the cases will theexactly uniform model be obtained.



Empirical Results


Worst Case Example: abababab· · ·Dynamic AC: uniform probability distribution (1

2, 1

2) for any


nn/2

)(n

n/2

)(2nn

) ' 2√π n

,

by Stirling’s approximation.

−→ For a key of size 512, only in 5% of the cases will theexactly uniform model be obtained.



Empirical Results


Worst Case Example: abababab· · ·Dynamic AC: uniform probability distribution (1

2, 1

2) for any


nn/2

)(n

n/2

)(2nn

) ' 2√π n

,

by Stirling’s approximation.−→ For a key of size 512, only in 5% of the cases will theexactly uniform model be obtained.



Empirical Results

Compression performanceUniformityCryptographic attacks

Outline

1 Arithmetic Coding




3 Empirical Results


Uniformity




Empirical Results


Empirical Results

Data Sets

1 ebib - the Bible (King James version) in English

2 ftxt - the French version of the European Union’s JOCcorpus, a collection of pairs of questions and answers onvarious topics used in the arcade evaluation project

3 sources - formed by C/Java source codes obtained byconcatenating .c, .h and .java files of the linux-2.6.11.6distributions

4 English - the concatenation of English text files selectedfrom the collections of the Gutenberg Project



Empirical Results


Empirical Results


File full size compressed size absolute loss relative lossMB MB bytes

ftxt 7.6 4.2 316 7× 10−5

sources 200.0 136.6 436 3× 10−6

English 1024.0 579.3 437 7× 10−7



Empirical Results


Empirical Results



ftxt 7.6 4.2 316 7× 10−5

sources 200.0 136.6 436 3× 10−6

English 1024.0 579.3 437 7× 10−7



Empirical Results


Empirical Results



ftxt 7.6 4.2 316 7× 10−5

sources 200.0 136.6 436 3× 10−6

English 1024.0 579.3 437 7× 10−7



Empirical Results


Empirical Results



ftxt 7.6 4.2 316 7× 10−5

sources 200.0 136.6 436 3× 10−6

English 1024.0 579.3 437 7× 10−7



Empirical Results


Uniformity

Probability of occurrence of substrings as function of value

0.0036

0.0037

0.0038

0.0039

0.004

0.0041

0.0042

0 50 100 150 200 250

8-bit with random key8-bit without a key

8-bit

0.0072

0.0074

0.0076

0.0078

0.008

0.0082

0.0084

0 50 100 150 200 250

7-bit with random key7-bit without a key

7-bit



Empirical Results


Uniformity

Probability of occurrence of substrings as function of value

value standard arithmetic selective updatesm = 3 m = 2 m = 1 m = 3 m = 2 m = 1

0 0.12503 0.25002 0.50011 0.12507 0.25010 0.5000050041 0.12498 0.25009 0.49989 0.12503 0.24991 0.4999949962 0.12510 0.25009 0.12491 0.249913 0.12499 0.24981 0.12499 0.250094 0.12498 0.125035 0.12511 0.124886 0.12499 0.124997 0.12482 0.12499



Empirical Results


Uniformity

Ratio σµ

of standard deviation to averagewithin the set of 2m values for m = 1, . . . , 8.

m 8 7 6 5 4 3 2 1standard 0.00383 0.00251 0.00164 0.00125 0.00094 0.00072 0.00053 0.00030selective 0.00135 0.00042 0.00207 0.00182 0.00059 0.00013 0.00003 0.00001



Empirical Results



Overlapping intervals

a b c d e

a b c d e

0

0 1

1

Cumulative size of boldfaced sub-intervals = 0.714



Empirical Results



Overlapping intervals

a b c d e

a b c d e

0

0 1

1

Cumulative size of boldfaced sub-intervals = 0.714



Empirical Results



Size of overlapping intervals as a function of the number ofprocessed characters.

0

0.2

0.4

0.6

0.8

1

0 2000 4000 6000 8000 10000

size of overlap

Probability for a correct guess after 10 characters ≤ 0.00006



Empirical Results



Size of overlapping intervals as a function of the number ofprocessed characters.

0

0.2

0.4

0.6

0.8

1

0 2000 4000 6000 8000 10000

size of overlap

Probability for a correct guess after 10 characters ≤ 0.00006Klein & Shapira Integrated Encryption in Dynamic Arithmetic Compression


Empirical Results


sensitivity to variations in the secret key

The Normalized Hamming distance: Let A = a1 · · · an andB = b1 · · · bm be two bitstrings and assume n ≥ m.

The normalized Hamming distance: 1n

∑ni=1(ai xor bi).



Empirical Results


sensitivity to variations in the secret key

Normalized Hamming distance

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0 100 200 300 400 500 600 700 800 900 1000

0.52 different keys

keys differing only in first bitkeys differing only in last bit



Empirical Results



Documents

Integrated Encryption in Dynamic Arithmetic Compressiongrammars.grlmc.com/LATA2017/Slides/Integrated Encryp… · · 2017-03-24Integrated Encryption in Dynamic Arithmetic Compression