1 embedding compression in chaos- based cryptography 嵌入壓縮功能到混亂加密法 ieee...

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Embedding Compression in Chaos-Based Cryptography嵌入壓縮功能到混亂加密法

IEEE Transactions on Circuits and Systems—II: Express Briefs, VOL. 55, NO. 11, NOV. 2008

Kwok-Wo Wong, Senior Member, IEEE, and Ching-Hung Yuen

Adviser：鄭錦楸 , 郭文中教授 Reporter：林彥宏

2

Outline

Introduction

Proposed ApproachEncryption Procedures

Decryption Procedures

Simulation Results

Conclusions

3

Introduction(1/4)

Entropy codingArithmetic coding

Huffman coding

Baptista-type Chaotic cryptosystem

One-Dimensional Logistic Map:

)1(1 nnn XbXX

]1 ,0[nX

4

Introduction(3/4)

trajectory

5

Introduction(2/4)

SXmin

1)-(SXmin

2)-(SXmin

S

S-1

S-2

S-3

.

.

.

4

3

2

1%

a

b

c

$

#

@

.

Alphabet unit Sit number

3)-(SXmin

minX

minX

2Xmin

3Xmin

4Xmin

4)-(SXmin

Spacing position

SX ,1)-(SX minmin

S

X-X minmax

6

Introduction(4/4)

3626420.44486572X

4471360.44160905X

4471360.44160905X

)X-(1bXX iteration

0000000.23232300X

0000000.44609375 000000,0.44375000interval i

0000000.44375000 000000,0.44140625

0.002343751040.2 ,0.002343751)-(1040.2intervalh

105ACII i

104ACIIh

50.000234370.2)/256-(0.8

256S , 0.8]X 0.2,[Xlimit , 8.3

hi :EX

364

'0

1713

nn1n

0

maxmin

b

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Proposed Approach

Number of Occurrence for

SymbolMap Function

Search Mode

Mask Mode

Huffman Tree

Regenerate Chaotic

TrajectoryExtract Mask Bit

Find Out Iteration Number

Lookup Table

Encryption

Decryption

MaskIntermediate

Sequence

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Proposed Approach

(A,B,C,D)=(0.5 , 0.25 , 0.125 , 0.125)

phase space [0 , 1] is divided into 256 partitions

A=128 B=64 C=32 D=32

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Proposed Approach

more probable symbols are encrypted by searching in the dynamic lookup table

less probable symbols are masked by a pseudorandom bitstream

10

Encryption Procedures

Step1) Scan the whole plaintext sequence once

Step2)M,...s,ss 21

1)

))

1

M

ii

jj

u(s

u(sNn(s

jj su(s symbol tomapped occurrence ofnumber theis )

jj sn(s symbol tomappedpartition ofnumber theis )

MNN ,number partitions theis

.

.

.

.

.

0

1

1s2s3s

Ms

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Step3) encrypt each plaintext symbol sequentiallyif the number of iterations required is smaller than a preselected maximum value, this symbol is considered as encrypted by the search mode; Otherwise, it will be encrypted by the mask mode

eight masking bits are extracted from the least significant byte of the chaotic map output:

Step4) after all the plaintext blocks have been processed, a Huffman tree is built for all the collected number of iterations, including zero

if intermediate sequence exceeds the plaintext length, this means that no compression is achieved at all; encrypted by the all-mask mode

5251504948474645525121 bbbbbbbb0 b...bbb

12


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Step5) binary mask sequence and the intermediate sequence are divided into 32-bit blocks

3214mod11 2 mod )

1 i-)(L/ircii c m(rci-

bits maskingeight are

bytesin length plaintext theis

sequences teintermedia in theblock bit -32ith theare

ciphertext in theblock bit -32ith theare

i

i

i

m

L

r

c

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Decryption Procedures

key and the plaintext specific information must be delivered to the receiver secretly

secret key includes the parameters and the initial value of the chaotic map and also the initial cipher block

information includes the name and length of the plaintext file, the encryption mode

Step1) using the shared secret parameters and the initial conditions to regenerate the chaotic trajectory

extract the mask bitsif all-mask mode was used in encryption, the output sequence is already the plaintext; Otherwise, it is the intermediate sequence

Step2) Scan the intermediate sequence sequentiallyfind out the number of iterations requirednonzero number of iterations and determine the final partition visited by the chaotic trajectory

15

Simulation Results

Compression Ratio

Encryption and Decryption Speed

Key Space and Sensitivity

Plaintext Sensitivity

)11 nnn -x(bxx

256 into divide is space phase

0.3388, , 13.99999999b 0 x

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Compression Ratio

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Compression Ratio

the compression performance of the second configuration is better for most of the files

scheme is not compression-oriented, but is built on a chaotic cryptosystem

100%LengthPlaintext

Length CiphertextR

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Encryption and Decryption Speed

encryption speed

ranges from 684kB/s

to 4.81MB/s

decryption speed

varies from 955 kB/s

to 2.37MB/s

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Key Space and Sensitivity

Key Space

encryptions using all-mask mode were performed with a small change in only one of the parameters

the ciphertext is very sensitive to the key

130bits324652

32bitsc , 52bits , 46bits 1-0

xb

50.01%, 49.97% , 50.05% 1-0 cxb

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Plaintext Sensitivity

The results are 50.00% (bit change at the beginning of plaintext), 50.04% (middle), and 50.01% (end), respectively.

They are all close to 50%, which imply that the ciphertext is very sensitive to the plaintext.

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Conclusions

The key space of the proposed cryptosystem is equivalent to 130 bits

Simulation results show that all the standard test files are compressed to a satisfactory degree, and the ciphertext is very sensitive to a tiny change in the key or the plaintext

the compression capability is achieved while the security is maintained

scheme also guarantees that the ciphertext is not longer than the plaintext

1 embedding compression in chaos- based cryptography 嵌入壓縮功能到混亂加密法 ieee...

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