The Soft Encrypting Channel Based on Turbo-code En-decoders for Wireless Data

TransmissionYang Xiao, Member, IEEE

Ying Zhao, Yu-ming Xie and Moon Ho Lee , Senior Member, IEEE

Abstract Turbo-code has been applied in many fields exceptfor the field of secret communication since its appearance. Thispaper presents a method on designing soft encrypting wirelesschannel based on turbo-code. The method utilizes existingwireless transmitting channel to realize secret communicationbased on turbo-code en-decoders. This paper also presents theencrypting method, which has the compositive elements ofturbo-code en-decoders as secret key to realize encryption. Thestructures of encrypting system and decrypting system and theidea of encryption are also discussed in the paper. This papersimulates on the method with audio and image signal to checkthe effect of encryption and the validity of the methodaccording to the designed program. This paper shows that theencrypting method can be extended into the design of channelcodecs for wireless data transmission.Index Terms turbo-code en-decoder, soft encryptingchannel, secret communication

I. INTRODUCTIONs the performance of turbo-code's error correction

is excellent [1-7], it has been used in many fields, suchas source coding, channel coding, digital watermark,

and so on [8-11]. But it doesn't relate to secretcommunication yet. Though Ref. [10] explored theinformation hiding through low density parity check codes,presented techniques of secret communication don't makeuse of turbo-code and seldom have taken anti-jamming intoaccount. In secret wireless transmission, most techniquescan't recover the encrypting file if it is interfered by noisebadly. In this paper, we present an encrypting method basedon turbo-code en-decoders to realize secret datatransmission in Wireless applications and it also has theperformance of anti-jamming.To the technologies of encryption, the algorithm and

secret key determines the encrypting effect and anti-decryption. As we all know, interleaver and recursivesystematic convolutional (RSC) en-decoder are the main

* This project was supported by Brain Program of Korea under grant:051 S-3-5 and the National Natural Science Foundation of China undergrant: 69971002.

Y. Xiao, Y. Zhao and Y. Xie are with the Institute of InformationScience, Beijing Jiaotong University, Beijing 100044, China (phone: 0086-10-62587017; fax: 0086-10-62245826; e-mail: yxiaoAcenter.njtu.edu.cn).

M. H. Lee is with R Division of Electronics and InformationEngineering College of Engineering, Chonbuk National University, Jeonju561-756, Korea (e-mail: moonhoAmoak.chonbuk.ac.kr).

compositive elements of turbo-code en-decoder. We canform secret key through the structures of interleaver andRSC en-decoder because their structures can becomplicated. Simultaneously, it can correct error codeswhen the encrypted file is in transmission, namely it has theperformance of anti-jamming. In order to constructcomplicated algorithm, we have pseudorandom interleaverand larger interleaving size as the key of our encryptingalgorithm [11]. We also use the interleaver to disturb thedata before its encryption to reach much better encryptingeffect. In this paper the encrypting method can be appliedin multimedia Wireless communications and mobile value-added service of wireless communications. In this paper weverify that it can encrypt multimedia data effectively.

II. SOFT TURBO ENCRYPTING CHANNEL

A. The Structure ofEncrypting SystemThe structure of encrypting system is shown in Fig. 1.

Here, we call the encrypting channel is soft because wemake use of present existing communication channel totransmit encrypted file and encrypt and decrypt data atserver and client respectively by means of software orprogram. We don't construct a new channel tocommunicate.

Binary Outer Turbo EncryptedInforma tion odl u InterleavingEncryption Data

Disturbance (TE)(OID) II

ii Secre t Key tSecret KeyManagement L4

Control of Interface uInterleavinp, (SKMI)

Fig. I Structure of Encrypting SystemIn Fig. 1, the function of module Outer Interleaving

Disturbance (OID) is to reduce the redundancy ofinformation. In this paper we utilize pseudorandominterleaver and disturb the information in this module, so wecan improve the effect of encryption.

The module TE is main body of the encrypting method. Itis a turbo-code encoder in nature. Its structure is shown inFig. 2 [1-6].

mod. 2 c=0,1.

* RSC code C2

Fig. 2 Structure of Turbo Encryption (TE) (rate= 1/3)

Consider a binary rate R=1/2 convolutional encoder withconstraint length K and memory M=K-1. The input to the encoder

at time k is a bit dk and the corresponding codeword Ck is the

binary couple ( Xk , Yk ) withK-1

x = glidik-i mod. 2 g1i =0,1

i=oK-1

Yk =Y 2idk-i mod. 2 g2i = 0,1

i=o

(la)

(lb)

where G1 :{g1j }, G2 :g2i } are the two encoder generators,

generally expressed in octal formIt is well known that the BER of a classical Non Systematic

Convolutional (NSC) code is lower than that of a classicalSystematic code with the same memory M at large SNR. At lowSNR, it is in general the other way round. The new class ofRecursive Systematic Convolutional (RSC) codes, proposed in thispaper, can be batter than the best NSC code at any SNR for highcode rates.A binary rate R=1/2 RSC code is obtained from a NSC code by

using a feedback loop and setting one of the two

outputs Xk or Yk equal to the input bit dk For an RSC code, the

shift register (memory) input is no longer the bit dk but is a new

binary variable ak. If Xk = dk (respectivelyYk = dk ), the

output Yk (resp. Xk) is equal to equation (Ib) (resp. la) by

substituting ak for dk and the variable ak is recursively

calculated asK-1

ak =dk + Ey lak-i mod. 2 (2)

where Yi is respectively equal to g1i if Xk = dk and to g2if Yk = dk Equation (2) can be rewritten as

K-1

dk =Yiak-ii=O

mod. 2

One RSC encoder with memory M=4 obtained from an NSCencoder defined by generators Gi=37, G2=21 is depicted in Fig. 2.

Generally, we assume that the input bit dk takes values 0 or 1

with the same probability. From equation (2), we can show that

variable ak exhibits the same statistical property

P{ lak =0/a1 =1 .... ak1 =8k-I I=Prdk =8}=1/2

(4)

with £ is equal to

Thus the trellis structure is identical for the RSC code and theNSC code and these two codes have the same free distance df .

However, the two output sequences { Xk } and { Y4 } do not

correspond to the same input sequence { dk } for RSC and NSC

codes. This is the main difference between the two codes.The function of Secret Key Management Interface (KMI) is

to manage the setting and store of secret key that isincluding the infornation of interleaver and RSC encoder.

B. The Structure ofDecrypting System

The structure of decrypting system matching with theencrypting system is shown in Fig. 3.

Data Decryption De-interleaving Data Display

(TD) Disturbance And Record

Secret Key The Information ofInterleaving Disturbance

Secret KeyManagement

Interface(SKMI)

Fig. 3 Structure of Decrypting SystemIn Fig. 3, the module TD is a turbo-code decoder in

nature. Its structure is shown in Fig. 4.

Fig. 4 Structure of Turbo Decryption (TD)

The decoder DEC depicted in Fig.4, is made up of twoelementary decoders (DECI and DEC2) in a serial concatenationscheme [1-6]. The first elementary decoder DEC1 is associatedwith the lower rate RI encoder Ci and yields a soft (weighted)decision. The error bursts at the decoder DEC1 output are

scattered by the inteleaver and the encoder delay LI is inserted totake the decoder DEC1 delay into account. Parallel concatenationis a very attractive scheme because both elementary encoder anddecoder use a single frequency clock.

For a discrete memoryless gaussian channel and a binarymodulation, the decoder DEC input is made up of a couple Rk of

two random variables Xk and Yk, at time k

Xk = (2dk 1)+ik n (7a)

(7a)

where ik and qk are two independent noises with the same

variance oT The redundant information Yk is demultiplexed

K-1

£ = Yicii=l

(5)

and sent to decoder DECI when Y. = Y., and toward decc

DEC2 when Y. = Y2,. When the redundant information

given encoder (Cl and C2) is not emitted, the correspondecoder input is set to zero. This is performed byDEMUX/INSERTION block.

It is well known that soft decoding is better than tdecoding, therefore the first decoder DEC1 must deliver tosecond decoder DEC2 a weighted (soft) decision. The Logarinof Likelihood Ratio (LLR), A1 (dk ) associated with e

decoded bit dk by the first decoder DECI is a relevant piec

information for the second decoder DEC2

Al (d ) = LogPr {dk = 1 / observation}()= Log Pr {dk = 0 / observation}where Pr {dk = i / observation}, i=0, 1 is the a postef

probability (APP) of the data bit dkThe function of module ODD is to de-interleave

disturbance corresponding to the module OID. The type cthe de-interleaver is suited with the interleaver of OID.

The module SKMI in Fig. 3 is the same with the one inFig. 1. Here, we can adopt the secret key that is prearrangby server and client.

B. C. The Idea ofConstructing the Encrypting Channel

In this paper, we present a concept of soft tuencrypting channel, which is formed by means of presexisting communication channel and transmits encrypdata package in nature.

The method of realizing encryption is through progranLsoftware, which is named after the soft modifier.The process of encryption can be divided as three stepsFirst, the binary digital information is encrypted by

encrypting system. The information is disturbed by OIDencrypted by TE. In this step, the information is encryptwice in fact. The OID disturbs the information and gre;changes the character of the information because of its lasize and pseudorandom interleaver, which can be regaras first encryption. Then TE encrypts the first encrypinformation for second time in order to realize beencrypting effect.

Second, the twice-encrypted information is transmittecthe communication channel. Because the information ikind of encrypted data package by turbo-code encodefcan resist the interference of strong noise and othertransmitted in the channel. This can guaranteeinformation transmit in the channel well. Theencrypting channel comes into being in this way.At last, the received data package is decrypted by

decrypting system.Through the steps above, we can construct a soft tu

encrypting channel and it can be applied in the fieldinformation and network security and secret ctransmission.

III. ENCRYPTING AND DECRYPTING OF INTERLEAVER

With given length, the interleaver with encrypting fundtshould be as randomized as possible, so that the users who d(

know the Secret Key can not decode the received information data.This paper offers a family of encrypting interleavers with optimalor quasi-optimal Hamming correlation for encrypting Turbosystems.

The design of family of encrypting interleaver indexsequences can be concluded the following steps.1) Suppose interleaver length to be prime number q;2) Construct a nonrepeating natural number random sequenceR = {r(m)} whose length is q, where 1 < r(m),m < q;3) According to prime sequence design method [11-14], obtainq -1 sequences forming a family {XI, X2,*..., Xq l }, which

can be rewritten as follow,X1 x Xlq

(8) X= 2 X21 X2,2 *. X2,q

riorn

xq-1 Xq_ll1 Xq-l12 * * Xql,q _

Every row vector of X is an index sequence.

4) According to the value of element in every row of X,rearranged sequence R to obtain matrix

r(x1j) r(xl,2 ) r(xl, ) RI-r(x21) r(x2,2 ) r(x2,) R2

r(xq _1) r(Xq 1,2) r(Xq-1,q)_ _Rq(10)

q -1 row vectors of matrix T form a new family of indexsequences, every sequence represents an interleaver.The family of interleaver index sequences has optimal Hamming

correlation [11].For any two row vectors in matrix T, if

HRiRj (r) 0 ( 0< r < q-1)then there must be

r(xi1) = r(xa I+T )

where xi1 E Xi, xj l+E X * denotes arithmetic

modulo q for the encrypting system.

There is a one-to-one mapping relationship between the

elements of sequence R and Xi (1 < i < q -1), hence,

r(xil) = r(xa I+T )is equivalent to

xi I = xj +By the characteristic of prime sequences and finite field [11-13],

we know the condition XiI = xj l+T is equivalent to

|iax = Ij(a +r)e E GF(q) (wherea E X0),namely,

|a(i- j)| = Ifr| E GF(q) (1 1)

For given sequences X, Xi and certain shift r, i j |r|and (i - j) are constants, and the (11) has only solution

aE GF(q).From above all, we know that the q -1 sequences obtained in

step 4) form a family of sequences with optimal Hammingcorrelation. At the same time, for every element of random

( 9)

sequence Ri , the mapping between Ri and Xi is equivalent,hence, every row of matrix T is still a random sequence suitablefor the design of random interlever for encrypting Turbo systems,which can be used by different users in communication.

The matrix (2) produces q-1 interleaver sequences, which can

support q-1 users in the communication system. Now, we see howto apply the interleaver sequences. Suppose that the input andoutput of the ith interleaver are

ai(n),n =l.,q-land

bi(n),n = I,..,q-1,according to (2), we have a interlever index sequence

r(xi,n), n = Il, ,q- 1Then the output and input of the ith interleaver have the followingrelationship,

bi (n) = a, (r(xi,n )), n = 1,..., q - 1 (12)It is corresponding to the matrix transformation,

If two users in a communication system support theencrypting Turbo en-decoder, selecting index sequences inTab. 1, we have 16-modes Turbo en-decoder that is used toconstruct 16 Turbo encrypting channels.Suppose there are two users use the encrypting channel 1, theinterlever index sequence from Tab. 1,

[r(xl1), r(X1,2 )... r(xl,15 ), r(X1,16 )]

Then we can get

b1 (1) = a1 (r(x1,1)) = a, (8),b1(2) = a,(r(xl2)) = a,(I5),

bl(15) = a,(r(xll5)) = a,(2).bl(16) = a, (r(xll6)) = a, (1).

The user of every Turbo encrypting channel can use the same

modulation mode. The user capacity of a system is 16 for thedesign. In practice, the length of interleaver is much bigger than17.

bi (1) - 0

bi (2) 0

bi (q - 1) 0

ai (1)

ai (2)

ai(q -1)

*''o Gi(l,r(xi,l)) 0

''0 Gi(2,r(Xi,2)) 0

** 0 Gi(q -1,r(xiq 1)) 0°..

where Gi (n, r(xi,n )) = 1,n =1,...,q -1,

given by (1O).Let

0

0

0

(13)and r(xi,n ) is

0 *..0 Gi(1,r(xi,l)) 0 0

0 *..0 Gi(2,r(xi,2)) 0 0

L0 *.0 Gi(q-1,r(x,q l)) 0... 0

(14)

It is easy to get the original signal ai (n), n = 1,..., q -1 from

the output bi (n), n = 1,..., q -1 of interleaver by an inverse

transformation,

ai (1) bi (1)

a,(2) =G,1 b (2) (15)

a, (q -1)_ b,(q -1)_The transformations of (13) and (15) gave the algorithms of the

interleavers in Fig. 2 and de-interleavers in Fig. 4For the users try to decode the transmitting data processed by

above approach, it is very difficult for them, since they don't knowthe encrypting interleaver sequences and the transformations of(13) and (15).Example: As shown in Tab. 1, by the design method presented inthis paper, we have a family of interleaver index sequences whoselength is 17.

Tab. 1 Family of interleaver index sequences whose length is 17

Ordr Fmfd rekaavciv xseiencesrober

1 8 15 5 9 11 14 10 13 6 3 12 16 7 4 2 12 15 9 14 13 3 16 4 1 8 5 11 10 6 12 7 23 5 14 6 16 2 8 9 10 3 7 1 15 11 13 12 44 9 13 16 1 5 10 12 2 15 14 3 4 8 11 6 75 11 3 2 5 13 7 8 14 12 1 9 6 4 15 10 166 14 16 8 10 7 15 13 4 5 6 2 9 3 1 1 1127 10 4 9 12 8 13 2 11 16 15 6 1 14 7 5 38 13 1 10 2 14 4 11 7 9 16 5 12 15 3 8 69 6 8 3 15 12 5 16 9 7 11 4 14 2 10 1 1310 3 5 7 14 1 6 15 16 1 2 13 8 12 9 4 1011 12 11 1 3 9 2 6 5 4 13 15 7 10 8 16 1412 16 10 15 4 6 9 1 12 14 8 7 13 5 2 3 1113 7 6 11 8 4 3 14 15 2 12 10 5 1 16 13 914 4 12 13 1115 1 7 3 10 9 8 2 16 6 14 515 2 7 12 6 10 11 5 8 1 4 16 3 13 14 9 1516 1 2 4 716 123 6 13 10 14 11 9 5 15 8

IV. SIMULATION AND EXPERIMENTS ONENCRYPTING EFFECT

In this section, we will check the encrypting effectthrough simulation and experiments. In this paper, we takethe audio and image as the encrypting data source. And thedata source can also be other types in practice. In order tocompare the effect of encryption, we assume the encrypteddata package captured in transmission. Through theencrypted data comparing with original data, we can checkthe effect of encryption.

Because the encrypting method presented in this paperalso has the performance of error correction and anti-jamming, we simulate the situation of strong noise andcompare the decrypted data with the original to check thisperformance.

In the simulation and experiments bellow, theparameters are shown in Tab. 2.Tab. 2 Parameters of simulation

Generate Matrix [15,17]Interleaver Pseudorandom

Interleaver Size[+] 128, 416

[8,15 .... . 2J]

Iteration Number 3Eb/NO 1.5dB

Modulation BPSKPuncture Yes

Size of Interleaving Disturbing 1024( In the parameters of interleaver size, 128 is for audiosignal and 416 is for digital image which is equal to thevalue of the image's pixels in height.)

A. The Encryption to Audio Information

We select a segment of audio signal as data source. Herewe don't disturb the audio signal before encryption in orderto show the function of disturbing in encrypting modelbecause there is interleaver in it also. The original sampledsignal's amplitude curve is shown in Fig. 5. And that of thedecrypting signal is shown in Fig. 6.

From Fig. 7 we can't know the information of originalaudio signal. It indicates that the method has goodencrypting performance.

0.8

0.6-

CD 0.4

0.20

-0.2-

-0.4-

-0.6

-0.8

-1 ,0 50 100 150

Sampled dataFig. 7 Encrypted audio signal

200 250 300

20 40 60 80 100 120sampled data

Fig. 5 Original audio signal

B. The Encryption to Image Information

We select an image that is screened by satellite and itspixels are 438X416 as data source. The original image isshown in Fig. 8, and the decrypting image is shown in Fig.9.From Fig. 8 and 9 we can find the decrypting imagerecovers the most information of original one and loses verylittle information. It verifies that this encrypting method hasexcellent anti-jamming performance because of turbo code'sgood error-correcting performance. Here we consider twokinds of effects of encryption. One is encrypted withoutinterleaving disturbing; the other makes use of it. Theformer is shown in Fig. 10 and the latter is shown in Fig. 1 1.

-0. 08 L0 20 40 60 80

sampled data100 120 140

Fig. 6 Decrypted audio signalFrom the Fig. 5 and 6 we can find that the encrypting

method has good recovered performance in strong noiseenvironment because the SNR is only 1.5dB. The effect ofencrypting is shown in Fig. 7. In Fig. 7 encrypting audiosignal doubles the sampled data because we utilizepuncturing when we encode the original one with turbocode, namely the code rate is 1/2. We use PCM as source

coding. The coded values are +1 and -1 because the mode ofmodulation is BPSK.

Fig. Ur-iginal imageFrom Fig. 10 and 11 we can see that the encrypting

effect is not good when the correlation of information ismuch more, especially for image. But when we disturb theimage before encryption, the encrypting effect is very goodas shown in Fig. 11. Here we don't consider source coding.In order to reduce the correlation and redundancy ofinformation much more, we should consider source codingin practice. But in this experiment the interleavingdisturbance has reduced the correlation and redundancy to a

great extent. By the way, same as the simulation of audiosignal, the data information is doubled.

0.03

0.02

X 0.01.2)v)

.0 0

a) -0.01

°6 -0 .02-

-0 .05

-0 .06

-0 .07

0.06

0.04

-F0.02

cn

0

Q-m 002

-E

X -0.04

0.06

In this paper, we mainly indicate that our presentedencrypting method has two functions. The one is anti-jamming and the other is encrypting. In the experiments werecord the performance of decrypting, and it is shown inFig. 12.

r lg. 9 Diecrypted image

Fig. 10 Encrypted image without interleaving disturbance

Fig. 11 Encrypted image with interleaving disturbance

Fig. 12 Bit error rate of simulation

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100

-10

102

mJm

106

10

Interleaver Size=832Interleaver Size=416

050.5 1 1.5

Eb/NO in dB2.5