Hybrid Information Privacy System: Integration of ...

Invited Paper

Hybrid Information Privacy System: Integration of Chaotic Neural Network and RSA Coding Ming-Kai Hsua, Jeff Willeyb, Ting N. Leec, Harold Szua a

Digital Media RF Lab, Dept ECE, GWU, Washington DC USA 20052 b US Naval Research Lab, Washington DC USA 20375 c Dept. ECE, GWU, Washington DC USA 20052

ABSTRACT Electronic mails are adopted worldwide; most are easily hacked by hackers. In this paper, we purposed a free, fast and convenient hybrid privacy system to protect email communication. The privacy system is implemented by combining private security RSA algorithm with specific chaos neural network encryption process. The receiver can decrypt received email as long as it can reproduce the specified chaos neural network series, so called spatial-temporal keys. The chaotic typing and initial seed value of chaos neural network series, encrypted by the RSA algorithm, can reproduce spatial-temporal keys. The encrypted chaotic typing and initial seed value are hidden in watermark mixed nonlinearly with message media, wrapped with convolution error correction codes for wireless 3rd generation cellular phones. The message media can be an arbitrary image. The pattern noise has to be considered during transmission and it could affect/change the spatial-temporal keys. Since any change/modification on chaotic typing or initial seed value of chaos neural network series is not acceptable, the RSA codec system must be robust and faulttolerant via wireless channel. The robust and fault-tolerant properties of chaos neural networks (CNN) were proved by a field theory of Associative Memory by Szu in 1997. The 1-D chaos generating nodes from the logistic map having arbitrarily negative slope a = p/q generating the N-shaped sigmoid was given first by Szu in 1992. In this paper, we simulated the robust and fault-tolerance properties of CNN under additive noise and pattern noise. We also implement a private version of RSA coding and chaos encryption process on messages. Keywords—Hybrid Privacy System, Chaotic Logistic Map, RSA coding, Chaotic Neural Networks, Chaos Encryption Process.

1. INTRODUCTION Electronic mail (e-mail) is the most widely used communication and video mail (v-mail) through third generation cellular phone will soon have a broadband wireless delivery. The e-mail or v-mail is free (paid by means other than users), fast and most convenient to communicate with others. The lack of privacy of email is a prone target to hackers and identity theft. Although recently Digital Bacteria [2] is developed as a beneficial virus to solve the authenticity and the intellectual property right from freebees & hackers. The drawback of DB, if any, is third party license expenditure and lacking of the local control of sender-receiver pairs. To overcome such a third party limitation without any cost, we expounded a hybrid system among (I) a free private version of RSA, described in Sect. 3, (patent expired) in terms of limited size of prime number factorization of two asymmetric keys system in order to send the hidden index parameters of the chaotic typing and the initial seed value described in Sect. 2. (II) We furthermore embed the low dimension chaotic mapping type into a high dimensional fault-tolerant Chaotic Neural Networks forming an collective fixed point of cycle-2 to be cascaded moil forward chaotic image, described in Sect. 2, for private binary

Independent Component Analyses, Wavelets, Unsupervised Smart Sensors, and Neural Networks III, edited by Harold H. Szu, Proceedings of SPIE Vol. 5818 (SPIE, Bellingham, WA, 2005) · 0277-786X/05/$15 · doi: 10.1117/12.610802

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message hidden inside as (III) a digital salt-pepper watermarks, simulated in Sect. 4, (IV) wrapped in a convolution error correction free coding, such as viterbi convolution coding [32] (patent expired). Simply we wish to design wireless message in terms of pair-wise privacy chain-saw codec, then one sends an identical message to other N-1 members in different codec. No third party can read the two party senderreceive codec as follows: Sender John:Message ”Hello I’m John” in ASCII = {0,1,1,1,0,1,0,1,1,...}= ”Hello I’m John” by ASCII Chaotic key John for Mary CJM = {0,0,1,0,0,0,1,1,0,...} Coded M’=EXOR(M, CJM)= M+ CJM = {0,1,0,1,0,1,1,0,1,...} Receiver Mary: M’ = {0,1,0,1,0,1,1,0,1,...} Special Chaotic key John send Mary: CJM = {0,0,1,0,0,0,1,1,0,...} Message ”Hello I’m John” in ASCII = {0,1,1,1,0,1,0,1,1,…}=”Hello I’m John” by ASCII This pair-wise privacy scheme would require a total of N2 codec of an identical message. The special chaos binary key has to be appropriately sent to each individual by different salt-pepper (1,0) corrupted images tailored to each receiver as hidden digital watermarks. Image format takes the advantage of visually integrity without relying on the prior knowledge of image shall be, and no worry of potential Internet package delay and dropping. Various techniques must be implemented to ward off real world Internet inadvertent or malicious attacker. We propose such a robust implementation in this paper. Subsequently, an entirely different N2 codec system is used for second message in time. Such a chain-saw broadcasting scheme among m-UAVs becomes robust and secure. When any one m-UAV is inadvertently shot down or taken away from the team by the adversary, no termination of relay happens and the loss to the adversary would be at worst only that piece of message if someone takes many days to crack the pair-wise codec. Traditional security system is not strictly private without a third, administrator, party issuing passwords, PIN, or public and private keys. In 1977, Ronald Rivets, Adi Shamir, and Len Adelman invented a coding system called RSA that is the most successful current commercial cryptosystem.. A public key for encoding is given to anyone, while a private key for decoding is kept secret. The security of the system is based on the idea that factoring large numbers is extraordinarily difficult to do in practice. While the RSA public & private keys codec system seems to be adequate for the security according to NSA, the passwords and biometry PIN scheme supports some degree of the authenticity concern. However, the privacy has not yet widely protected and the public suffers numerous ‘identity thefts’. The paper is organized as follows. In Sect. 1, Chaotic Neural Networks (CNN) is introduced for robust synchronization reasons at sender and receiver ends. We adopt a sub-family of chaotic maps xn=sin2 ( Zn π θ) where Z is a real number studied by Jules-Antoine Lissajous in 1857 independently from early work by Nathaniel Bowditch in 1815. We propose to send the initial seed value and class member choice of Logistic maps by means of the RSA public keys in terms rational Z =2 for the logistic maps of arbitrary negative slope a = p/q embedded within a sigmoid logic in the so-called N-shaped sigmoid neuron by Szu (1992). The background introduction and simulations of chaos neural network is in Sect. 2. The basic concept of electrical mail standard format was defined by RFC 2822 and the extension of electrical mail standard format was defined by RFC 2045. Both RFC 2822 and RFC 2045 are introduced in Sect.3. We also introduce the collective maps of CNN, which produce the deterministic chaotic time series in parallel in image, which appears to be random. It can apply on message codec for cryptograph approach [4-11] in Sect. 3. The simulation results of RSA coding and chaos encryption process (CEP) are in section 4. We conclude this hybrid information security system in Sect. 5. Without the seeds one cannot recover the original message. Yet the seemingly random seeds are generated from deterministic chaos controlled by arbitrary initial conditions and arbitrary class of mapping. For easy implementation on PC and robust reasons, we considered a simple family of 1-D chaotic map generators. We embed it into the N-shaped sigmoid logic of artificial neural networks (ANN). Such a massive Associative Memory of 1,600 nodes can generate a stable chaos collectively, in the so-called Chaotic Neural Networks (CNN) defined by Eqs(2a-h). The initial conditions of an image and the height κ or slope parameter a=p/q are sent by the RSA public key secure communication but unknown to outsiders. 166

Proc. of SPIE Vol. 5818


We choose the family of Lissajous maps consists of multiple value periodic function of which the special case is the logistic mapping of simple convex node. This family of maps is based on the exact analytical solution xn= sin2 ( Zn π θ) where Z = 2 is derived from the logistic map y=f(x)= κx(1-x) at κ=4 with iteration x=y, immediately after a perturbation analysis.

y = f ( x ) ≡ κx( 1 − x ), x = y ; or , X n + 1 = κ X n ( 1 − X n ) ≡ f ( X n ) , n = 1, 2, 3,…

(1)

A linear perturbation methodology decomposes Eq(1) into two displacements x =X+x', which yield a pair of equations: equilibrium X = κ X (1-X), and fluctuation x' = κ (1-2X) x’ = f’ (X) x' in terms of the slope f’ (X) at the equilibrium. It implies two possible equilibrium roots: X=0, and X= 1 - 1/κ of which the convergence occurs beside the origin X=0 if the slope |f'(X)|=|κ-2κX| a=p/q > 0, which is bounded with a unit norm. One can choose a time series of any pixel or a set of pixels and the threshold to be furthermore the variable seeds, one seed per each data to be sent by a simple binary projection EXOR algorithm. For a limited scalar data set, one can choose any pixel or region of interest; say eyes, of the fuzzy set of image membership function to be the seeds for codec. A fastest codec trick is applying a projection operator defined by PxP = I. For binary data P=ExOR is a binary addition without carrier, Given a message set, say m = 9 = 1x23+ox22+0x21+1x20= (1, 0, 0, 1) and a corresponding chaotic seed (usually having more than 100 decimals), e.g. s = 7 = (0, 1, 1,1). Then one sends the encoded message e = ExOR (m,s) = (1,0,0,1)+(0,1,1,1)=(1,1,1,0). Since receiver knows by RSA of the class of chaos generator and the original seed to reproduce a corresponding seed s, one recovers the message ExOR (e,s)=(1,1,1,0)+(0,1,1,1)=(1,0,0,1)=m

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We will apply the public keys of RSA to send the prime numbers to select a open set of membership of chaotic node and initial seed for a specific message. Since the prime numbers are also adopted for the patent public key RSA coding, and thus better security than those in terms of the RSA public keys based on prime numbers factorization alone may be desirable. We propose to implement the communication cryptology in massively parallel for robustness and stability, according to early theorem proved by Szu for a fully connected network of neurons coupled by the bi-linear Hebbian learning dynamics that is reducible and thus equivalent exactly to a single neuron embedded in the mean filed proportional to other neurons for the return slops [25]. 3.4 Convolution error correction coding The package losses and bit errors occur during the wireless transmission is inevitable no matter how advanced current communication technology is. When a user sends or receives a message, be text, image or video, the message can be transmitted wirelessly or on wire lines. A third generation cellular phone can sends email or v-mail, the bit error is not limited to single bit. It tends to be burst because the wireless channel is both time and space variant. There are several well-known error correction algorithms, such as Viterbi convolution coding [32], ReedSolomon coding [33]. In May 1993, Claude Berrou, Alain Glavieux and Punya Thitimajshima announced a new class convolution codes called Turbo Coding [34]. The performance of Turbo Coding in terms of bit error rate is close to the Shannon limit. Berrou adopts two Recursive Systematic Convolutional (RSC) codes concatenated in parallel through a non-uniform interleaver to build Turbo-Code encoder. The associated decoder is implemented as P pipelined identical elementary decoders. Today, Turbo Codes are considered as the most efficient coding algorithm for Forward Error Correction (FEC) [34]. The major advantages of Turbo codes are that it makes possible to increase available bandwidth without increasing the power of a transmission, or they can be used to decrease the amount of power used to transmit at a certain data rate. The main drawback of Turbo codes is its relatively high latency. To understand error correction coding, we need to understand three basic characteristics of codes. These characteristics are dimension, length and minimum distance. The dimension, k, is the actual information bits contained in the code word. The length, n, is the number of bits in each code word. The minimum distance, d, of code word is the minimum bit differences in each code word. For example, Reed-Solomon codes are liner block codes and they often denoted as RS(n, k) with s-bit symbols. Reed-Solomon codes can correct up to t bits errors and 2t=n-k. The maximum code size of Reed-Solomon is n=2^s-1. For Viterbi algorithm, it is a method to decode bit streams encoded by convolution encoders. The Viterbi algorithm can be implemented on a 4-state optimal rate convolutional code system. It can be expressed in Eq(3ab). The x(n) is the input and the G0 ( n) and G1 ( n) are the outputs [32].

G0 (n) = x(n) + x (n − 1) + x(n − 2) G1 (n) = x(n) + x(n − 2)

(3a) (3b)

Prior Turbo coding, Reed-Solomon encoder with Viterbi decoder combination was the best-known error correction codes. We will adopt modified version so that it becomes cost free.

4. SIMULATIONS In simulations, the chaos neural series (CNS) are generated from one dimension logistic map. From equation (1), the initial values of CNS we need to transmit and encrypted by RSA are initial value of X and K. The initial value of X and K are 0.3 and 4 respectively. To illustrate how RSA works, the prime numbers are chosen to be simple to understand. Moreover, p and q have to be larger than the message that is going to be encrypted. Besides, the prime numbers should be chosen very large up to 256 bits in practical.



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(1) First, we choose two prime numbers p and q respectively. P = 5, q = 13 (2) Let m = (p-1)*(q-1). m = (5-1)*(13-1) = 48 (3) Let n = p*q, n = 5*13 = 65 (4) We need to choose a small number, d, relatively prime to m. If d = 2, is it prime to m? No, since the greatest common divisor is 2. If d = 3, is it prime to m? No, since the greatest common divisor is 2. If d = 4, is it prime to m? No, since the greatest common divisor is 4. If d = 5, is it prime to m? Yes, since the greatest common divisor is 1! It is what we want. (5) Find an integer e so that d*e = 1 (mod m). The equation above can be rewritten as e = (1+l*m)/d where l is any integer number. If n = 0, e = 1/5. It is not integer. If n = 1, e = 49/5. It is not integer. If n = 2, e = 97/5. It is not integer. If n = 3, e = 145/5 = 29. It is integer! It is what we want. Now, we have public key and private key. They are (65, 5) and (65, 29) respectively. The initial value of logistic map will be encrypted by public key. The encrypted initial value can be recovered by private key. 4.1 RSA Encryption In RSA algorithm, there is a restriction that the message must be less than p and q. In practical, p and q should be chosen with lower bound of the messages. In this simulation, we know that the initial value of X and K are 0.3 and 4 respectively. Since X is bounded between 0 and 1, we use 3 instead of 0.3 in simulation of RSA coding. However, in CEP simulation, we still use 0.3 to generate chaos neural series. E (X) = X ^ d (mod n) = 3 ^ 5 (mod 65) = 243 (mod 65) = 48 D (E (X)) = E (X) ^ e (mod n) = 48 ^ 29 (mod 65) = 48 * (48 ^ 28) (mod 65) = 48 * ((48 ^ 4) ^ 7) (mod 65) = 48 * (61 ^ 7) (mod 65) = 48 * (61 * (61 ^ 6)) (mod 65) = 48 * (61 * (3721 ^ 3)) (mod 65) = 48 * (61 * (16 ^ 3)) (mod 65) = 48 * (61 * 1) (mod 65) = 3 (mod 65) ! The RSA public key and private key were simulated on MATLAB. In table 2, there are some examples simulated and verified on MATLAB. Public Key is (N, d) (299, 5) (143, 7) (77, 7) (15, 3)

Private Key is (N, e) (299, 53) (143, 103) (77, 43) (15, 3)

Message to be transmit 8 9 6 3

Encrypted message 177 48 41 12

(P, Q) (13, 23) (11, 13) (7, 11) (3, 5)

Table 2. Examples of RSA coding. The last example is simple to show how RSA algorithm works. First, we choice (p, q) = (3, 5) so that n = p*q=15 and m =(p-1)*(q-1) =8. Second, we need to find a small number d and it is relatively prime to m. The equation is mod (m+1, d) = 0 (mod (9, d) = 0) so that d = 3. Third, we need to find integer e, e = (1+l*m)/d, l is any integer. Integer e= (1+1*8)/3=3. Now we get both pubic key and private key, (15, 3) and (15, 3). '

Next, we need to encrypt the message M=3. Encrypted message, M =mod (3^3, 15) =12. To get original message, M = mod (12^3, 15) = mod (1728, 15) =3! It is the original message. Q.E.D. 176



4.2 CEP Encryption Since the initial value of chaos neural series and chaotic typing can be secured by RSA algorithm, the next step is to generate chaos neural network series and encrypt the message by CEP. In the simulation of CEP encryption, we mixed the encrypted message with an image for security reason. The encrypted message is also protected by the image. We called the image as the carrier or media. To separate the encrypted message from the carrier, we can adopt independent component analysis (ICA) or blind source separation (BSS) on the mixed image. In the simulation, the carrier, the original image, and the mixed image are shown on figure 6. In Matlab, 255th gray scale is white and 0th gray scale is black. In this simulation, I define 1 as 50th and 0 as 150th in 256 gray scales. The watermark includes chaotic typing, initial seed value and messages we want to transmit. The message is composed by binary sequences. Any character can be represented in 8 bits. It follows the ASCII standard. Characters will be enciphered by chaos neural network series. To generate mixed images, the transfer matrix A is as follows.  cos θ

A = 

 sin θ

 I1    I   2



S

   W 

= A ∗ 

− sin θ  , cosθ 

 cosθ

= 

 sin θ

− sin θ  cosθ

S  ∗      W 

The angle θ selection is based on the rule that we want to keep original source or watermark. In the 270 degree ≤ θ ≤ 360 degree interval, I1 contrasts the original image with watermark and I2 is the original mage mixed with message. In ASCII format, unless the character is extended character, the Most Significant Bit (MSB) is always 0. It would be a weak point for hacker to decipher messages. The next step of the simulation is to encrypt the message by Chaos Neural Series (CNS). The M.S.B will no longer always be 0. It is shown on figure 7. The chaotic typing and initial value of the first chaotic encryption key of CEP are extracted from the header of the first data packet. Other chaotic encryption keys will be sequentially generated from the previous ones. The block diagram is on figure 5. An exclusive OR (XOR) operation encrypts the data by using this chaotic encryption key. Since we use 1-dimension logistic map to implement chaos neural series, the seed consists of in initial value Χ and parameter Κ. The equation is as follows.

χ

n +1

= κ * χ

n

* (1 − χ n ),

0 < κ ≤ 4 ,0 < χ

n

< 1

In the simulation of CEP, we choose the initial value X = 0.3 and K = 4. The simulation result of encrypted message is shown on figure 7. The MSB of each character is no longer 0. The encrypted message looks like white Gaussian noise

The mixed image

Original image

the original message

Figure 6. The original image, the original message and the mixed image Proc. of SPIE Vol. 5818


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The mixed image

Messages encrypted by CEP

Figure 7. The encrypted message and the mixed image. The MSB of each character is no longer 0. The encrypted message looks like white Gaussian noise

5. CONCLUSION We proposed a fast, free and private hybrid system to protect the most popular communication media, email, rather than Digital Bacteria [2]. The family of chaotic node and its initial seed value are protected by the RSA public key system, and then apply the fault-tolerance nature of chaotic neural networks (CNN) [1] to make it robust to communication channel propagation error. In this paper, we simulated the properties of robust and fault-tolerance in chaos neural networks in Sect.2. The properties of the sequence produced by the proposed dynamical system were proved or illustrated to be pseudo-random in Sect.4. The generalized logistic map result can be also useful for communication cryptology. It is implemented in parallel by Nshaped sigmoid CNN, of which a group of N-body dynamics is proved to be equivalent to a single body interacting in a group medium in Sect.2. For future work, we are looking for new encryption algorithm to replace RSA coding in this hybrid privacy system. Building a pure privacy system without 3rd party is our goal and further improving the wrapped watermarks as a private envelop applying in the privacy system. The error correction on burst errors in wireless transmission is our concern. The verification and simulations of overcome burst errors by Vitebri convolution coding and Turbo coding will be implemented in our system.

ACKNOWLEDGEMENT The simulation of N-shaped sigmoid neurons, RSA coding and CEP are implemented on the computer in SEAS Computing Facility. I am very appreciated the support from the director of SEAS Computing Facility, Mr. Michael P. White. I also want to thank Dr. Joe DeWitte for the help in RSA coding. Last, I want to thank Dr. Charles Hsu for his encouragement and his early thesis work, cited in references, that is helpful in this paper.

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