\r\n\tThis book will introduce research findings which are important in supporting the development of engineering curricula, creating a sustainable engineering education, designing an innovative technique and enhancing a flip base learning approach in the long term viability of world’s engineering education, all with a purpose to improve and ensure the standards and quality of engineering education. It will provide resources and case studies of engineering education in the area of problem based learning, technology enhanced and flip based engineering approach, integration of blended e-learning, sustainable and social innovation in engineering learning experiences. In addition, the chapters will provide guidelines, benefit and the effectiveness of the evaluating engineering curricula based on learning outcomes and graduate attributes. \r\n\tThis edited book aims to present a number of chapters focusing on cutting edge research work as well as on key issues and current developments in engineering education. It will provide the reader with a broad overview of the current state-of-the-art in the development of engineering design, curriculum and integration in learning and teaching, and pedagogical aspects of engineering education.
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Díaz Martín",authors:[{id:"81752",title:"Dr.",name:"Rosa Patricia",middleName:null,surname:"Arias Llorente",fullName:"Rosa Patricia Arias Llorente",slug:"rosa-patricia-arias-llorente"},{id:"88980",title:"Prof.",name:"Carlos",middleName:"GarcÃa",surname:"Bousoño",fullName:"Carlos Bousoño",slug:"carlos-bousono"}]},{id:"34295",title:"Improving the Likelihood of Success in Trials and the Efficiency of Delivery of Mucolytics and Antibiotics",slug:"improving-the-likelihood-of-success-in-trials-and-efficiency-of-delivery-of-mucolytics-and-antibioti",signatures:"Carlos F. Lange",authors:[{id:"87618",title:"Prof.",name:"Carlos",middleName:"Frederico",surname:"Lange",fullName:"Carlos Lange",slug:"carlos-lange"}]},{id:"34296",title:"Airways Clearance Techniques in Cystic Fibrosis: Physiology, Devices and the Future",slug:"airway-clearance-techniques-in-cystic-fibrosis-physiology-devices-and-the-future",signatures:"Adrian H. Kendrick",authors:[{id:"81571",title:"Dr.",name:"Adrian",middleName:"H.",surname:"Kendrick",fullName:"Adrian Kendrick",slug:"adrian-kendrick"}]},{id:"34297",title:"The Physiotherapist's Use of Exercise in the Management of Young People with Cystic Fibrosis",slug:"the-physiotherapist-s-use-of-exercise-in-the-management-of-young-people-with-cystic-fibrosis",signatures:"Allison Mandrusiak and Pauline Watter",authors:[{id:"84089",title:"Dr",name:"Allison",middleName:null,surname:"Mandrusiak",fullName:"Allison Mandrusiak",slug:"allison-mandrusiak"},{id:"87978",title:"Dr.",name:"Pauline",middleName:null,surname:"Watter",fullName:"Pauline Watter",slug:"pauline-watter"}]},{id:"34298",title:"Exercise Performance and Breathing Patterns in Cystic Fibrosis",slug:"exercise-performance-and-breathing-patterns-in-cystic-fibrosis",signatures:"Georgia Perpati",authors:[{id:"79721",title:"Dr.",name:"Georgia",middleName:null,surname:"Perpati",fullName:"Georgia Perpati",slug:"georgia-perpati"}]}]}]},onlineFirst:{chapter:{type:"chapter",id:"64741",title:"A New Cross-Layer FPGA-Based Security Scheme for Wireless Networks",doi:"10.5772/intechopen.82390",slug:"a-new-cross-layer-fpga-based-security-scheme-for-wireless-networks",body:'
1. Introduction
Generally, wireless networks consist of low capacity links with nodes that rely on batteries. An efficient communication scheme for such networks should minimize both congestion in the links and control information in the nodes. Security is a critical parameter in wireless applications and any efficient communication scheme has to integrate security vulnerabilities of the system in its implementation. Unfortunately, existing schemes have network security implemented at the upper layer such as the application layer; meanwhile parameters such as congestion, which affect data throughput, are the physical layer. Hence, any attempt to increase the security level in a communication system greatly compromises data throughput. In [1], the authors developed a metric to estimate a timeframe for cyberattacks using the RSA public key cryptography. In the analysis, the authors estimated the attacker’s human time in carrying out a successful attack based on the key length. Such an implementation at the upper layer will curb any security attack at the prescribed time but will greatly compromise data throughput at the physical layer due to the huge modular exponentiation involved in its implementation. In [2], the authors developed a secure and efficient method for mutual authentication and key agreement protocol with smart cards. The implementation, which is based on the constant updating of the password, will involve a considerable amount of control information, which is detrimental to the optimum functioning of the nodes. Research work using different information-theoretic models to develop physical layer security based on the characteristics of the wireless links has been carried out [3, 4]. However, the existing methods for implementing physical layer security under the different information-theoretic security models is expensive and requires assumptions about the communication channels that may not be accurate in practice [5]. Hence any deployment of the physical-layer security protocol to supplement a well-established upper layer security scheme will be a pragmatic approach for robust data transmission and confidentiality [6]. It is in this light that, a new cross-layer approach is presented in this research. Major research efforts have targeted cross-layer implementation of security schemes in wireless networks [7, 8, 9]. In this research, the proposed cross-layer security scheme uses signal processing techniques as well as efficient coding and well-established cryptographic algorithm to implement a security scheme, which greatly enhances security-throughput trade-off, and curb many security threats common to wireless networks.
The rest of the chapter is organized in eight subsequent sections. In Section 2, we present the background knowledge required for the design and implementation of the new cross layer security scheme. This will involve a review of the different techniques used in the development of the new security scheme. The first subsection presents the implementation of the multi-level convolutional cryptosystem. This implementation involves the combination of subband coding and a new non-linear convolutional coding. Next, a review of the residue number system (RNS) with brief description of the Chinese remainder theorem (CRT) is presented. We conclude the section with an overview of RSA public-key cryptography. Section 3 presents the protocol for the implementation of the new cross layer security scheme. The FPGA-based implementation applied to CDMA using the new layered security scheme will be presented in Section 4. In Section 5, cryptanalysis of the cross-layer security scheme will be carried out in order to quantify the security. Quantification of data throughput is performed in section 6 while different security threats which could be circumvented by the cross-layer security scheme are presented in Section 7. We end the chapter in Section 8 with conclusions of our work.
2. Background
This section presents the background knowledge required for the design and implementation of the new cross layer security scheme. It involves a review of the different techniques used in the development of the new security scheme.
2.1 Multi-level convolutional cryptosystem
The multi-level convolutional cryptosystem constitutes the second stage of implementation at the physical layer. It receives integers from the RNS implemented at the first stage. The multi-level cryptosystem is implemented using subband coding and non-linear convolutional cryptosystem.
2.1.1 Subband coding
The integers from the RNS block are split into different levels of decomposition based on subband coding. Subband coding is implemented using integer wavelet lifting scheme [10, 11]. It is shown in [15] that, a judicious choice of filter banks could result into an integer transform despite the fact that, wavelet transform is an approximation process. A four-tap Daubechies polyphase matrix, which results into integer transforms, is given as follows [15]:
Pnewz=hezgenewzhozgonewzE1
where h and g are filter coefficients with suffix e and o denoting even and odd coefficients. The factorization of the polyphase matrix is as follows [12, 13, 15].
Pz=P˜z=1−3011034+3−24z−111z013+12003−12E2
(Eq. (2)) forms the basis of integer to integer wavelet transform which in effect is progressive transmission. The factored coefficients h1=−3,h2=34,h3=3−24,h4=3+12,h5=3−12 are used to compute the approximate and detail sequences. In such transmission, the original data is split into two portions, namely approximate and detail sequences. The detail sequence is transmitted while the approximate sequence is further split into two halves. The process is repeated until the final data point. Using (Eq. (2)), the approximate, an and the detail, dn sequences could be computed as follows [14, 15]:
where an and dn are the approximation and detail sequences of wavelet coefficients of the nth sample. The subsequent transmissions are fed into the non-linear convolutional coding block as depicted in Figure 1 for the first level kth detail and approximation sequences [14, 15]. The processing blocks (PEs) shown in the figure depicts the computations of (Eq. (3)).
Figure 1.
Synopsis for the computation of the kth coefficients for the 1st and 2nd levels of decomposition.
The final decomposition level which comprises one data point will give one approximation coefficient and one detail coefficient.
At the destination, the inverse wavelet transform is performed to obtain the successive approximation sequences. (Eq. (3)) is used to perform the inverse transform by reversing the operations for the forward transform and flipping signs [14, 15]. The process starts with the approximation and detail coefficients a0 and d0 respectively obtained at the final decomposition level of the forward transform. The first stage of the inverse transform is shown in Figure 2 [14, 15].
Figure 2.
The first stage of the inverse transform.
The (↑2) symbol represents upsampling by 2, which means that zeros are inserted between samples while H2 and H3 are the filter coefficients used in (Eq. (3)).
2.1.2 Nonlinear convolutional cryptosystem
A major advantage of symmetric cryptography is the ability of composing primitives to produce stronger ciphers although on their own the primitives will be weak. Hence, the vulnerable convolutional code block will be cascaded into different stages using the product ciphers obtained from the S-box and P-box to form a non-linear convolutional cryptosystem.
Key generation: The specifications of the private keys used in the implementation of the cascaded convolutional cryptosystem are as follows [14, 15, 19]:
States of each transducer or convolutional code block in the cascade given by the contents of the sub-matrices in the generator matrix;
The transition functions. These are mappings used to compare the input bits and present state and switches to the appropriate next state;
n-bit S-boxes. They are used to shuffle the output bits.
n-bit P-boxes. They are used for the different permutations per level of decomposition.
For illustrative purposes, an (8, 8, 2) convolutional encoder will be considered to demonstrate the keys generation process.
2.1.2.1 States of convolutional code block or transducer
For an 8 × 8 matrix, there are at least 216 ways or keys in which the connections of a register to the modulo-2 adder could be made. A possible key which gives the contents of the 8 × 8 matrix are shown in (Eq. (4))
E4
The generator matrix is used to specify the following set of 8 vectors.
It should be recalled that, for an (n,k,L) convolutional encoder, each vector has Lk dimensions and contains the connections of the encoder to the modulo-2 adder.
The structure of the (8, 8, 2) convolutional encoder is shown in Figure 3 with A2, A3 representing the registers M11,M21 while A1 represents the input data.
Figure 3.
Structure of an (8, 8, 2) convolutional encoder.
2.1.2.2 The transition functions
For an (8,8,2) convolutional code, there are 28 = 256 mappings or keys. There are two sets of transition functions denoted as f1 for the two possible states.
For example, a transition function that compares input data to state 1 and remains in state 1 is given as follows:
In (Eq. (5)), if the input data is any of the sequences {[00000000], [00000001], [00000010], [00000011], [00000100], [00000101], [00000110], [00000111]}, the present state of the transducer which is state 1 is retained.
A transition function that compares input data to state 1 and switches to state 2 is given as follows:
In (Eq. (6)), if the input data is any of the sequences {[00001000], [00001001], [00001010], [00001011], [00001100], [00001101], [00001110], [00001111]}, the present state of the transducer which is state 1 is changed to state 2.
At the destination, the transition functions are similar to those for the encoder at the source but change roles. The transition functions are very critical in the implementation of convolutional cryptosystem since it accounts for its dynamic nature, hence an increase in security level.
2.1.2.3 S-box entries
For an (8,8,2) convolutional code, using 2-bit shuffling boxes, there are 16 S-boxes or keys. For higher n-bit shuffling boxes, the number of keys increases, for example 8-bit shuffling boxes will give 28 keys. The four 2-bit S-boxes used to illustrate the scheme are shown in Table 1. Given an 8-bit data sequence as [A7, A6, A5, A4, A3, A2, A1, A0], the look-up S-box, Sub1,1 is used to shuffle the first pair of bits, [A7, A6], Sub1,2 is used to shuffle the second pair [A5, A4], Sub1,3 is used to shuffle the third pair [A3, A2], and Sub1,4 is used to shuffle the last pair [A1, A0].
Table 1.
2-bit shuffle look-up-table.
2.1.2.4 P-box entries
The interconnections between inputs and outputs are implemented using a permutation set look-up table. For an (8,8,2) code, the eight (08) inputs and outputs could be permuted or interconnected in at least 77 = 823,543 ways. A permissible permutation is shown in Table 2 [14, 15].
Table 2.
Input–output interconnect look-up-table for encoder.
After the specification of the keys, the vulnerable convolutional code block will be cascaded into different stages using the product ciphers obtained from the S-box and P-box. Using two (02) stages, a non-linear (8, 8, 2) 2-cascaded is as shown in Figure 4.
Figure 4.
Initial structure of the cascade before encoding.
In Figure 4, Sub1,1, Sub1,2, Sub1,3 and Sub1,4 are S-boxes used for pairwise bit shuffling and the input vector to the first transducer, {X7, X6, X5, X4, X3, X2, X1, X0} is the output set from the subband encoding block while the output vector {Y7, Y6, Y5, Y4, Y3, Y2, Y1, Y0} is the ciphertext from the second transducer stage.
It is worth noting that the security level could be greatly increased by increasing the number of stages to be cascaded.
2.2 Residue number system (RNS)
The residue number system uses the Chinese remainder theorem (CRT) to compute unknown values from the remainders left or residues when unknown values are divided by known numbers.
The modular Chinese remainder theorem states that [16, 17]:
Assume m1, m2, …, mN are positive integers, relatively prime pairs: (mi, mk) = 1 if i # k. Let {b1, b2, …, bN} be arbitrary integers, then the system of simultaneous linear congruence
x1=b1modm1−−−xN=bNmodmNE7
has exactly one solution modulo the product m1, m2, …, mN. The solution to the simultaneous linear congruence is formally given as [14, 16, 17].
xM=∑j=1Lm̂jxjm̂jmj.xjME8
where m̂j=MmjandM=∏j=1Nmj.
(Eq. (8)) establishes the uniqueness of the solution. In this research, the integers Tj=∣xjm̂j∣ often referred to as the multiplicative inverses of m̂j are computed a priori by solving the linear congruence in (Eq. (7)). In other words, if Mj = M/mj, then the multiplicative inverses, Tj are computed by solving the congruence TjMj = 1 (mod mj).
2.3 RSA public-key cryptography
Key creation
◦ Choose secrete primes p and q and compute m = p.q
◦ Choose encryption exponent, e
◦ Compute d satisfying e.d ≡ 1 mod ((p – 1). (q – 1)).
◦ Public key: (m, e) and Private key: d
Security services achieved using RSA cryptography are authentication and non-repudiation based on digital signatures and confidentiality based on encryption. Implementation of these services are summarized in Table 3
Authentication and non-repudiation
Confidentiality
Choose plaintext X. Compute Xs ≡ Xd (mod m) Send (X, Xs) to Alice. Xs is the RSA digital signature of message, X
Choose plaintext X. Use Bob’s public key (m, e) to compute C ≡ Xe (mod m). Send ciphertext, C to Bob
Table 3.
Summary of security services of RSA public-key cryptography.
3. Protocol of implementation of cross-layer security scheme
The new scheme is implemented at the application and physical layers. The detail operations of the application and physical layers at the source and destination are as follows:
Source:
◦ Application layer:
Traditional RSA encryption
◦ Physical layer:
Step 1: Residue number system (RNS) converts the message points into residues based on the moduli set;
Step 2: RNS-based RSA ciphertext is converted into different levels of decomposition using subband coding;
Step 3: Symmetric encryption using Convolutional cryptosystem;
At the destination, the entire process is reversed starting with convolutional decoding at the physical layer and ending with RSA decryption at the application layer.
3.1 Illustrative example
Consider an arbitrary array of integers for plaintext as follows {398, 453, 876, 200, 356, 165, 265, 897}.
Source
◦ Application layer: Traditional RSA encryption
Primes, p = 13; q = 37 ⇒ n = p. q = 481
Encryption key, e = 5
Decryption key: e. d ≡ 1 mod (432) ⇒ d = 173
Array due to RSA encryption is given as {151, 293, 252, 135, 304, 315, 265, 182}
◦ Physical layer:
Step 1: Moduli set of {107, 109, 113} is used to convert the RSA ciphertext into 8-bit data point arrays. The residue set, r1 for m1 = 107 is as follows:
r1 = {44, 79, 38, 28, 90, 101, 51, 75}
Step 2: Subband coding is performed to split residues obtained using moduli set into three levels of decomposition since m = 8 = 23 data points are used. Subband coding is basically down sampling by 2 using (Eq. (3)). The corresponding arrays for the first level of decomposition are as follows:
Note that r11 refers to first level of decomposition array for modulus, m1 = 107 and the first element is obtained using (Eq. (3)) with integer lifting filter coefficients set, h = {2, 0, 0} as follows: r1(1) – 2 × r1(0) = 79–2 × 44 = −9.
The same procedure is performed for the second and third levels of decomposition.
Step 3: Table 4 summarizes the manual computation of the encryption and decryption process of the convolutional cryptosystem for the data r11(0) = −9 from the subband encoding stage based on the entries of the product cipher and combinational logic of the non-linear (8,8,2) 2-cascaded convolutional transducer in Figure 4.
Destination
◦ Physical layer:
The entire process is reversed starting with convolutional decoding at the physical layer which was illustrated in Table 4.
Subband decoding: It involves upsampling and the use of quadrature mirror filter (QMF) bank as depicted in Figure 5 [12, 15]
Table 4.
Manual computation for the first sample of first level of decomposition for modulus 107.
Figure 5.
The first two stages of the wavelet inverse transform.
The (↑2) symbol represents upsampling by 2, which means that zeros are inserted between samples. The QMF bank are the coefficients derived from the 4-tap Daubechies filter bank [12, 15, 20]. Hence, using upsampling and the QMF bank coefficients the residue sets r1, r2 and r3 are retrieved.
Figure 5 will be used to perform a numerical illustration of subband decoding for the first level of decomposition of the array of modulus m1 = 107 to obtain approximation coefficients a1.
The moduli sets obtained from subband encoding for the three levels of decomposition for m1 = 107 are as follows:
For subband decoding, the entire process is reversed with level 3 of encoding becoming level 1 for decoding.
r31 from subband encoding namely a0 = 2 and d0 = 44 is used. From Figure 5, upsampling performed on the approximation, a0 and detail, d0 data points gives the sets y_1 = {2, 0} and z_1 = {44, 0} respectively. Using 4-tap Daubechies integer lifting filter coefficients set, h = {2, 0, 0} we have.
The process is repeated to obtain the second and third levels approximation data points. The third level approximation data points, a3 should be equal to residue set, r1 obtained from the RNS-based RSA ciphertext using the modulus, m1 = 107.
RNS-based Chinese Remainder Theorem (CRT): It is applied to the residue sets r1, r2 and r3.
(Eq. (8))will be used to retrieve the RSA ciphertext from the residue sets. Using (Eq. (8)) and moduli set, m = {107, 109, 113} to compute the first data point of the ciphertext set we have.
The same process is repeated to obtain all the other data points of the RSA ciphertext set. The RSA ciphertext set is fed to the RSA decryption block at the application layer.
◦ Application layer: RSA decryption
Decryption of the first data point is given as M = 151d mod n = 151173 mod 481 = 398 which represents the original data which was sent at the source.
The same process is repeated to obtain all the other data points of the plaintext set.
4. FPGA implementation of security scheme applied to CDMA
In this section, FPGA implementation of new scheme applied to CDMA, the new VHDL code package to implement A mod n operations, synthesis report and behavioral simulation results will be presented.
4.1 FPGA implementation of new scheme applied to CDMA
Code division multiple access (CDMA) enables several users to transmit messages simultaneously over the same channel bandwidth in such a way that each transmitter/ receiver user pair has its own distinct signature code for transmitting over the common channel bandwidth. This distinct signature is ensured by using spread spectrum techniques whereby the message from each user is transmitted using orthogonal waveforms. In orthogonal signaling, the residues are mapped to orthogonal waveforms which constitute the CDMA signal [23]. The orthogonal waveforms used in this research are Walsh functions.
Considering an (8, 8, 2) multi-level cryptosystem for illustrative purposes, the mapping process will involve M = 28 = 256 orthogonal waveforms. Using the dynamic range of (−128, 126), a set of M = 28 = 256 orthogonal waveforms is required to completely represent all the integers or symbols. Based on this, the corresponding Hadamard matrix obtained from the procedure elaborated in [21] is as follows:
H256=H128⊗H128=H128H128H128H¯128
The H256 matrix is a large matrix comprising of 256 rows and 256 columns. The Hadamard matrix results into a multi–dimensional array. Multi–dimensional arrays are arrays with more than one index. Multi–dimensional arrays are not allowed for hardware synthesis. One way around this is to declare two one–dimensional array types. This approach is easier to use and more representative of actual hardware. The VHDL code used to declare the two one–dimensional array types is shown in Figure 6 [22].
Figure 6.
VHDL code for synthesizable 256 × 256 Hadamard matrix.
The other operations in the hardware Walsh function generator implementation are trivial since they involve modulo–2 addition with built–in operators in VHDL code to handle such operations.
4.2 New VHDL code package
In this research, a new algorithm is presented which implements modular exponentiation without the use of the Montgomery algorithm. A package is developed in the VHDL code to extract residues similarly to the X mod N operation for any randomly generated data. Meanwhile, the large operand lengths which resulted from the modular exponentiation are reduced using binary exponentiation and the RNS.
The principle used to develop the package is as follows:
To perform the x = X mod N calculation where X has a large operand length of b bits say b = 1024 bits and N is modulus of small operand length of b1 bits say b1 = 8 bits, the following steps are used:
X is converted to binary equivalent;
The b1 least significant bits of the b bits of X are chosen;
The integer equivalent, x1 of the chosen b1 bits is determined;
The residue, x = X mod N is obtained from the following equation;
x=x1+2b1−1−N×X2b1−1E9
If the residue, x is greater than the modulus, N the process is iterated until the residue is less than the modulus.
(Eq. (9)) forms the basis for the x = X mod N calculation.
Based on this new algorithm which implements modular exponentiation without the use of the Montgomery algorithm, the entire physical layer security scheme could fit into a single FPGA chip.
4.3 Behavioral simulation and synthesis report
In order to verify the performance of the proposed architecture, a VHDL programme was written and implemented on a Xilinx Virtex-4 FPGA chip (device: xc4vlx 200, package: ff 1513, speed grade − 11) [22]. Sixteen (16) randomly generated integers were fed into the FPGA. For this value, the number of bonded IOBs is 760 out of 960 resulting to 79% resource used. The behavioral simulation results for array {39,870, 45,378, 87,654, 20,087, 35,689, 16,592, 564, 276,509, 89,732, 56,287, 4527, 89,065, 4321, 7654, 5489, 512} using moduli set {111, 115, 119} are displayed in [14].
In [14], the complete synthesis report showing device utilization summary is presented. Due to the additional implementation of orthogonal signaling compared to the implementation in [14], the following parameters are different compared to results displayed in [14]:
The device utilization summary is as follows:
Number of slices: 5411 out of 89,088 6%
Number of slice flip flops: 60 out of 178,176 0%
Number of four input LUTs: 7452 out of 178,176 4%
Total REAL time to Router completion: 24 min 7 s.
Total REAL time to place and route (PAR) completion: 24 min 41 s.
Pin delays less than 1.00 ns: 21928 out of 30,651 71.5%.
5. Cryptanalysis of cross-layer scheme
The cryptanalysis will be performed separately at the application and physical layers and later combined in the cross-layer scheme to demonstrate the high security level of the new scheme compared to separate implementations.
5.1 Cryptanalysis at the application layer
The RSA public key cryptography is implemented at the application layer. The most successful method to break the RSA cryptosystem is the Number Field Sieve (NFS) method used for partial key exposure attacks. The NFS is based on a method known as “Fermat Factorization”: one tries to find integers x, y, such that x2 ≡ y2 mod n but x ≠ ± y mod n [15]. We assume that the two primes p and q should be close and approximately equal to the square root of n, where n = p.q. If one of the integers could be written as x = (p + q)/2 then number of steps, S1 required to determine the other integer, y could be computed as follows [24].
S1=p+q2−n=q−p22=n−p22pE10
It is partial key exposure attack since the number of steps, S1 required for the attack depends on one of the primes.
Table 5 gives a summary of the number of steps required to break the traditional RSA cryptography implemented at the application layer using Fermat Factorization.
Operand key length
Total number of steps
16-bit
1
32-bit
1
64-bit
1.8 × 108
128-bit
8.0 × 1017
256-bit
1.26 × 1025
512-bit
2.53 × 1063
1024-bit
3.3 × 10140
Table 5.
Number of steps required to break the traditional RSA.
5.2 Cryptanalysis at the physical layer
Security at the physical layer is ensured by the multi-level convolutional cryptosystem which encrypts already encrypted data emanating from the RNS-based RSA. The cryptanalysis of the multi-level convolutional cryptosystem will be based on the ciphertext-only attack whereby, it is assumed that the attacker knows ciphertext of several messages encrypted with the same key and/or several keys. The keys used in the encryption are those mentioned in Section 2.1.2 for the non-linear (8, 8, 2) 2-cascaded convolutional cryptosystem.
It is shown in [15] that, for an (n, k, L) convolutional code, each generator matrix reveals at most p – k – 1 values of a private parameter, using Gaussian elimination for p blocks of input data. Hence, if q is the number of states, then to completely break the (k, k, L) N-cascaded cryptosystem, the minimum number of plaintext-ciphertext pairs (u, v) required is [15].
S2=p.q.2kp−k−1×q.2kp×k!p×1p×k22×22NE11
For an (8, 8, 2) 2-cascaded cryptosystem, k = 8 and the least number of plaintext-ciphertext blocks required is p = 10 due to the number of rows and columns in the generator matrix. Assuming q = 2 states, S2 could be as
Table 6 gives a summary of the number of steps required to break the (8, 8, 2) 2-cascaded cryptosystem using ciphertext-only attack.
Operand key length
Total number of steps
8-bit
7.8 × 1034
16-bit
2.1 × 1057
32-bit
1.4 × 1057
64-bit
1.5 × 1062
128-bit
6.1 × 1071
256-bit
9.87 × 1087
512-bit
2.68 × 10112
1024-bit
1.42 × 10134
Table 6.
Number of steps required to break the (8, 8, 2) 2-cascaded cryptosystem.
5.3 Cryptanalysis of the new cross-layer security scheme
At the upper layer, huge key lengths such as 1024 bits and 2048 bits are used to implement the RSA. Such implementations will greatly compromise throughput at the physical layer due to modular exponentiation. Hence, the main objective of the new cross-layer security scheme is to increase security level at the physical layer despite the small valued data points transmitted derived from the RNS-based RSA in order to enhance throughput. Cryptanalysis is performed on the small residue RSA encrypted values. The analysis will be based on partial key exposure and ciphertext-only attacks at the physical layer for eavesdropper who could wiretap the transmitted data. The number of steps, S required to break the new cross-layer security scheme should be a product of S1 and S2 given as [15].
S=S1.p.q.2kp−k−1×q.2kp×k!p×1p×k22×22NE13
Table 7 gives a summary of the number of steps required to break the new cross-layer security scheme by using partial key exposure attack and ciphertext-only attacks for different cascaded stages.
Operand key length
Total number of steps
N = 2
N = 3
N = 4
16-bit
2.1 × 1057
9.6 × 1085
4.4 × 10114
32-bit
1.4 × 1057
5.2 × 1085
1.9 × 10114
64-bit
1.5 × 1062
1.8 × 1093
2.3 × 10124
128-bit
6.1 × 1071
4.8 × 10107
3.7 × 10143
256-bit
9.87 × 1087
9.8 × 10131
9.7 × 10175
512-bit
2.68 × 10112
4.4 × 10168
7.2 × 10224
Table 7.
Number of steps required to break the cross-layer security scheme.
Comparing Tables 5–7, it can be seen that high security levels comparable to the traditional 1024-bit RSA implemented at the upper layer could be attained using short operand key lengths of 128 bits and 256 bits for cross-layer security implemented at the physical layer. It is worth noting that, the security level could be much higher compared to the values displayed in Table 7 if the S-boxes were implemented using 4-bit and 8-bit shuffling instead of the aforementioned 2-bit shuffling.
where Pe is the bit error probability, N is the number of bits in the block length and R is a fixed transmission rate for the frames. For Pe << 1, the throughput could approximate to
T≅R1–NPeE15
From (Eq. (15)) it could be seen that, for a fixed transmission rate, R the throughput, T could be increased by either minimizing N or Pe. In this section, it will be shown how convolutional coding could be used to achieve both conditions through orthogonal signaling and forward error correction respectively.
6.1 Coded orthogonal signaling
It is shown in [18, 19] that, for coded orthogonal signaling, the bit error probability to transmit k-bit symbols is as follows:
Pb≤2k‐12k−1∑32kad41+kLγ¯b2+kLγ¯b2LE16
where ad denotes the number of paths of distance d from the all-zero path which merge with the all-zero path for the first time and dfree = 3 in this case, is the minimum distance of the code. dfree is also equal to the diversity, L. γ¯b is the average signal-to-noise ratio (SNR) per bit [18]. For each convolutional code, the transfer function is obtained and the sum of the coefficients {ad} calculated.
For illustrative purposes, the transfer function, T(D) of smaller convolutional codes such as (2, 2, 2) and (4, 4, 2) will be used.
The transfer function T(D) for the (2, 2, 2) code is given as follows [19]:
TD=D3+2D4+−−−E17
The transfer function for the (4, 4, 2) code is given as follows [19]:
For both the (2, 2, 2) code and the (4, 4, 2) code, dfree = L = 3. Using the values of L and {ad}, the probability of a binary digit error, Pb as a function of the SNR per bit, γ¯b is shown in Figure 7 for k = 2 and 4 [19].
Figure 7.
Performance of coded orthogonal signaling for k = 2 and k = 4.
The curves illustrate that, the error probability increases with an increase in k for the same value of SNR. Hence, better performance for wireless transmission should involve lower order codes and many independent parallel channels rather than higher order codes with fewer independent parallel channels. Hence, high data throughput could be attained by using small number of bits in the block length, N.
6.2 Forward error correction (FEC) code
The Viterbi algorithm [18] is the most extensively decoding algorithm for Convolutional codes and has been widely deployed for forward error correction in wireless communication systems. In this sub-section Viterbi algorithm will be applied to the non-linear convolutional code. The constraint length, L for a (n,k,m) convolutional code is given as L = k(m-1). The constraint length is very essential in convolutional encoding since a Trellis diagram which gives the best encoding representation populates after L bits. Hence to encode blocks of n bits, each block has to be terminated by L zeros (0 s) before encoding.
For illustrative purposes, a non-linear (4,2,3) convolutional code will be used to demonstrate encoding and Viterbi decoding. A possible non-linear (4,2,3) convolutional code showing mod-2 connections and the product cipher is shown in Figure 8.
Figure 8.
2-stage non-linear (4,2,3) convolutional code.
6.2.1 Example: encode/decode the message M = 10,011
Encoding process
The constraint length, L = k(m-1) = 2(3–1) = 4.
Hence 4 zeros will be appended to message M before encoding. The modified message becomes M’ = 10110000. Transition tables in appendix are used to encode the modified message.
Using transition tables in appendix, the transmitted sequence from the 1st stage is given as Tin = 10 01 01 11
S-box output is given as S = 00 11 11 01
P-box output is given as P = 00 11 11 10
Transmitted sequence into the 2nd stage is given as P = 00 11 11 10
Using transition tables in appendix, the final transmitted sequence which is the output bits from the 2nd stage is given as Tout = 0000 1111 0101 1001
Viterbi decoding process
In performing the Viterbi algorithm, a bit in the sequence Tout will be altered. Let the received sequence be TR = 1000 1111 0101 1001 instead of Tout = 0000 1111 0101 1001. The Viterbi algorithm applied to the 2nd stage is summarized in Table 8.
Table 8.
Viterbi algorithm applied to 2nd stage of (4,2,3) code.
The bits above the arrows will constitute the retrieved sequence from the 2nd stage. Hence, the retrieved sequence is given as, R1 = 00 11 11 10. This sequence is fed to the P-box.
P-box output is given as P1 = 00 11 11 01. Sequence, P1 is fed to the S-box
S-box output is given as S1 = 10 01 01 11
Sequence, S1 is fed into the 1st stage to retrieve the final correct message. The Viterbi algorithm applied to the 1st stage is summarized in Table 9.
Table 9.
Viterbi algorithm applied to 1st stage of (4,2,3) code.
For a good trellis, the final state is the all-zero state as seen in the winning path in Table 9. The final received sequence is identical to the original transmitted message of M’ = Rfinal = 10110000 despite the first bit error. Hence, using the non-linear convolutional code, the error bit was identified and corrected. The forward error correction capability will therefore enhance throughput, since the bit error rate, Pe is reduced.
7. Security attacks in wireless networks
Most attacks in wireless networks are classified into two categories: passive and active. Passive attacks such as eavesdropping and traffic analysis do not interfere with normal network operations as opposed to active attacks. Some of the attacks could be circumvented by the cross-layer security scheme presented in this research due to the following characteristics inherent in its implementation:
RSA cryptographic algorithm at the upper layer: Table 3 summarized the security services, which could be achieved by implementing RSA cryptography such as authentication, non-repudiation and confidentiality. These services are essential network security requirements which are vital in curbing attacks such as eavesdropping, masquerade attack and information disclosure since there will be a possibility of not attaining the final all-zero state if message is modified.
Convolutional cryptosystem at the physical layer: The different keys generated are essential in ensuring confidentiality while the forward error correction capability is essential in curbing message modification attack.
Other attacks such as denial of service and replay attack could be circumvented if the cross-layer security scheme is associated with Transmission Control Protocol (TCP).
8. Conclusions
In this chapter, we have described a new cross-layer security scheme which has the advantage of enhancing both security and throughput as opposed to existing schemes which either enhances security or throughput but not both. The new scheme is implemented using the residue number system (RNS), non-linear convolutional coding and subband coding at the physical layer and RSA cryptography at the upper layers. By using RSA cryptography, the scheme could be used in encryption, authentication and non-repudiation with efficient key management as opposed to existing schemes, which had poor key management for large wireless networks since their implementation, was based on symmetric encryption techniques. Results show that, the new algorithm exhibits high security level for key sizes of 64, 128 and 256 bits when using three or more convolutional-cascaded stages. The security level is far above the traditional 1024-bit RSA which is already vulnerable. The vulnerability of 1024-bit RSA has led to the proposal of implementing higher levels such as 2048-bit and 4096-bit. These high level RSA schemes when implemented will greatly compromise throughput due to modular exponentiation. Hence the usefulness of a scheme such as the one presented in this chapter. In addition, Viterbi algorithm was performed for the new non-linear convolutional code in order to highlight the error correction capability. It was shown that, by using error correction codes on many small block lengths compared to one huge block length, throughput increases. Hence non-linear convolutional code is very critical in the implementation of the new scheme, since it contributes in enhancing both security and throughput. The entire scheme could be implemented at different access points in a wireless network since it fits in a single FPGA. Finally, the new cross-layer security scheme is essential in circumventing some attacks in wireless and computer networks.
A. Appendix: transition tables
\n',keywords:"residue number system (RNS), RSA cryptography, field programmable gate array (FPGA), subband coding, convolutional coding, CDMA",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/64741.pdf",chapterXML:"https://mts.intechopen.com/source/xml/64741.xml",downloadPdfUrl:"/chapter/pdf-download/64741",previewPdfUrl:"/chapter/pdf-preview/64741",totalDownloads:48,totalViews:0,totalCrossrefCites:0,dateSubmitted:"July 10th 2018",dateReviewed:"November 5th 2018",datePrePublished:"December 11th 2018",datePublished:null,readingETA:"0",abstract:"This chapter presents a new cross-layer security scheme which deploys efficient coding techniques in the physical layer in an upper layer classical cryptographic protocol system. The rationale in designing the new scheme is to enhance security-throughput trade-off in wireless networks which is in contrast to existing schemes which either enhances security at the detriment of data throughput or vice versa. The new scheme is implemented using the residue number system (RNS), non-linear convolutional coding and subband coding at the physical layer and RSA cryptography at the upper layers. The RNS reduces the huge data obtained from RSA cryptography into small parallel data. To increase the security level, iterated wavelet-based subband coding splits the ciphertext into different levels of decomposition. At subsequent levels of decomposition, the ciphertext from the preceding level serves as data for encryption using convolutional codes. In addition, throughput is enhanced by transmitting small parallel data and the bit error correction capability of non-linear convolutional code. It is shown that, various passive and active attacks common to wireless networks could be circumvented. An FPGA implementation applied to CDMA could fit into a single Virtex-4 FPGA due to small parallel data sizes employed.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/64741",risUrl:"/chapter/ris/64741",signatures:"Michael Ekonde Sone",book:{id:"8368",title:"Computer and Network Security",subtitle:null,fullTitle:"Computer and Network Security",slug:null,publishedDate:null,bookSignature:"Prof. Jaydip Sen",coverURL:"https://cdn.intechopen.com/books/images_new/8368.jpg",licenceType:"CC BY 3.0",editedByType:null,editors:[{id:"4519",title:"Prof.",name:"Jaydip",middleName:null,surname:"Sen",slug:"jaydip-sen",fullName:"Jaydip Sen"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Background",level:"1"},{id:"sec_2_2",title:"2.1 Multi-level convolutional cryptosystem",level:"2"},{id:"sec_2_3",title:"2.1.1 Subband coding",level:"3"},{id:"sec_3_3",title:"Table 1.",level:"3"},{id:"sec_3_4",title:"2.1.2.1 States of convolutional code block or transducer",level:"4"},{id:"sec_4_4",title:"2.1.2.2 The transition functions",level:"4"},{id:"sec_5_4",title:"Table 1.",level:"4"},{id:"sec_6_4",title:"Table 2.",level:"4"},{id:"sec_9_2",title:"2.2 Residue number system (RNS)",level:"2"},{id:"sec_10_2",title:"2.3 RSA public-key cryptography",level:"2"},{id:"sec_12",title:"3. Protocol of implementation of cross-layer security scheme",level:"1"},{id:"sec_12_2",title:"3.1 Illustrative example",level:"2"},{id:"sec_14",title:"4. FPGA implementation of security scheme applied to CDMA",level:"1"},{id:"sec_14_2",title:"4.1 FPGA implementation of new scheme applied to CDMA",level:"2"},{id:"sec_15_2",title:"4.2 New VHDL code package",level:"2"},{id:"sec_16_2",title:"4.3 Behavioral simulation and synthesis report",level:"2"},{id:"sec_18",title:"5. Cryptanalysis of cross-layer scheme",level:"1"},{id:"sec_18_2",title:"5.1 Cryptanalysis at the application layer",level:"2"},{id:"sec_19_2",title:"5.2 Cryptanalysis at the physical layer",level:"2"},{id:"sec_20_2",title:"5.3 Cryptanalysis of the new cross-layer security scheme",level:"2"},{id:"sec_22",title:"6. Data throughput quantification",level:"1"},{id:"sec_22_2",title:"6.1 Coded orthogonal signaling",level:"2"},{id:"sec_23_2",title:"6.2 Forward error correction (FEC) code",level:"2"},{id:"sec_23_3",title:"Table 8.",level:"3"},{id:"sec_26",title:"7. Security attacks in wireless networks",level:"1"},{id:"sec_27",title:"8. Conclusions",level:"1"},{id:"sec_29",title:"A. Appendix: transition tables",level:"1"}],chapterReferences:[{id:"B1",body:'Patterson W, Sone ME. A metric to assess cyberattacks. In: Proceedings of the AHFE 2018 International Conference on Human Factors in Cybersecurity; AISC 782; Florida, USA. 2018. pp. 33-43'},{id:"B2",body:'Guo C, Chang C-C, Chang S-C. A secure and effcient mutual authentication and key agreement protocol with smart cards for wireless communications. International Journal of Network Security. 2018;20(02):323-331'},{id:"B3",body:'Bloch M et al. Wireless information-theoretic security. IEEE Transactions on Information Theory. 2008:2515-2534'},{id:"B4",body:'Wyner AD. The wire-tap channel. Bell System Technical Journal. October 1975;54(8):1355-1387'},{id:"B5",body:'Lin F, Oggier F. Coding for wiretap channels. In: Physical Layer Security in Wireless Communications. Auerbach Publications, CRC Press, Taylor & Francis Group. 2013'},{id:"B6",body:'Shui Y-S, Cheng SY, Wu H-C, Huang SC-H, Chen H-H. 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College of Technology, University of Buea, Buea, Cameroon
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The company was founded in Vienna in 2004 by Alex Lazinica and Vedran Kordic, two PhD students researching robotics. While completing our PhDs, we found it difficult to access the research we needed. So, we decided to create a new Open Access publisher. A better one, where researchers like us could find the information they needed easily. The result is IntechOpen, an Open Access publisher that puts the academic needs of the researchers before the business interests of publishers.
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We started by publishing journals and books from the fields of science we were most familiar with - AI, robotics, manufacturing and operations research. Through our growing network of institutions and authors, we soon expanded into related fields like environmental engineering, nanotechnology, computer science, renewable energy and electrical engineering, Today, we are the world’s largest Open Access publisher of scientific research, with over 4,000 books and 54,000 scientific works including peer-reviewed content from more than 116,000 scientists spanning 161 countries. Our authors range from globally-renowned Nobel Prize winners to up-and-coming researchers at the cutting edge of scientific discovery.
\\n\\n
In the same year that IntechOpen was founded, we launched what was at the time the first ever Open Access, peer-reviewed journal in its field: the International Journal of Advanced Robotic Systems (IJARS).
\\n\\n
The IntechOpen timeline
\\n\\n
2004
\\n\\n
\\n\\t
Intech Open is founded in Vienna, Austria, by Alex Lazinica and Vedran Kordic, two PhD students, and their first Open Access journals and books are published.
\\n\\t
Alex and Vedran launch the first Open Access, peer-reviewed robotics journal and IntechOpen’s flagship publication, the International Journal of Advanced Robotic Systems (IJARS).
\\n
\\n\\n
2005
\\n\\n
\\n\\t
IntechOpen publishes its first Open Access book: Cutting Edge Robotics.
\\n
\\n\\n
2006
\\n\\n
\\n\\t
IntechOpen publishes a special issue of IJARS, featuring contributions from NASA scientists regarding the Mars Exploration Rover missions.
\\n
\\n\\n
2008
\\n\\n
\\n\\t
Downloads milestone: 200,000 downloads reached
\\n
\\n\\n
2009
\\n\\n
\\n\\t
Publishing milestone: the first 100 Open Access STM books are published
\\n
\\n\\n
2010
\\n\\n
\\n\\t
Downloads milestone: one million downloads reached
\\n\\t
IntechOpen expands its book publishing into a new field: medicine.
\\n
\\n\\n
2011
\\n\\n
\\n\\t
Publishing milestone: More than five million downloads reached
\\n\\t
IntechOpen publishes 1996 Nobel Prize in Chemistry winner Harold W. Kroto’s “Strategies to Successfully Cross-Link Carbon Nanotubes”. Find it here.
\\n\\t
IntechOpen and TBI collaborate on a project to explore the changing needs of researchers and the evolving ways that they discover, publish and exchange information. The result is the survey “Author Attitudes Towards Open Access Publishing: A Market Research Program”.
\\n\\t
IntechOpen hosts SHOW - Share Open Access Worldwide; a series of lectures, debates, round-tables and events to bring people together in discussion of open source principles, intellectual property, content licensing innovations, remixed and shared culture and free knowledge.
\\n
\\n\\n
2012
\\n\\n
\\n\\t
Publishing milestone: 10 million downloads reached
\\n\\t
IntechOpen holds Interact2012, a free series of workshops held by figureheads of the scientific community including Professor Hiroshi Ishiguro, director of the Intelligent Robotics Laboratory, who took the audience through some of the most impressive human-robot interactions observed in his lab.
\\n
\\n\\n
2013
\\n\\n
\\n\\t
IntechOpen joins the Committee on Publication Ethics (COPE) as part of a commitment to guaranteeing the highest standards of publishing.
\\n
\\n\\n
2014
\\n\\n
\\n\\t
IntechOpen turns 10, with more than 30 million downloads to date.
\\n\\t
IntechOpen appoints its first Regional Representatives - members of the team situated around the world dedicated to increasing the visibility of our authors’ published work within their local scientific communities.
\\n
\\n\\n
2015
\\n\\n
\\n\\t
Downloads milestone: More than 70 million downloads reached, more than doubling since the previous year.
\\n\\t
Publishing milestone: IntechOpen publishes its 2,500th book and 40,000th Open Access chapter, reaching 20,000 citations in Thomson Reuters ISI Web of Science.
\\n\\t
40 IntechOpen authors are included in the top one per cent of the world’s most-cited researchers.
\\n\\t
Thomson Reuters’ ISI Web of Science Book Citation Index begins indexing IntechOpen’s books in its database.
\\n
\\n\\n
2016
\\n\\n
\\n\\t
IntechOpen is identified as a world leader in Simba Information’s Open Access Book Publishing 2016-2020 report and forecast. IntechOpen came in as the world’s largest Open Access book publisher by title count.
\\n
\\n\\n
2017
\\n\\n
\\n\\t
Downloads milestone: IntechOpen reaches more than 100 million downloads
\\n\\t
Publishing milestone: IntechOpen publishes its 3,000th Open Access book, making it the largest Open Access book collection in the world
We started by publishing journals and books from the fields of science we were most familiar with - AI, robotics, manufacturing and operations research. Through our growing network of institutions and authors, we soon expanded into related fields like environmental engineering, nanotechnology, computer science, renewable energy and electrical engineering, Today, we are the world’s largest Open Access publisher of scientific research, with over 4,000 books and 54,000 scientific works including peer-reviewed content from more than 116,000 scientists spanning 161 countries. Our authors range from globally-renowned Nobel Prize winners to up-and-coming researchers at the cutting edge of scientific discovery.
\n\n
In the same year that IntechOpen was founded, we launched what was at the time the first ever Open Access, peer-reviewed journal in its field: the International Journal of Advanced Robotic Systems (IJARS).
\n\n
The IntechOpen timeline
\n\n
2004
\n\n
\n\t
Intech Open is founded in Vienna, Austria, by Alex Lazinica and Vedran Kordic, two PhD students, and their first Open Access journals and books are published.
\n\t
Alex and Vedran launch the first Open Access, peer-reviewed robotics journal and IntechOpen’s flagship publication, the International Journal of Advanced Robotic Systems (IJARS).
\n
\n\n
2005
\n\n
\n\t
IntechOpen publishes its first Open Access book: Cutting Edge Robotics.
\n
\n\n
2006
\n\n
\n\t
IntechOpen publishes a special issue of IJARS, featuring contributions from NASA scientists regarding the Mars Exploration Rover missions.
\n
\n\n
2008
\n\n
\n\t
Downloads milestone: 200,000 downloads reached
\n
\n\n
2009
\n\n
\n\t
Publishing milestone: the first 100 Open Access STM books are published
\n
\n\n
2010
\n\n
\n\t
Downloads milestone: one million downloads reached
\n\t
IntechOpen expands its book publishing into a new field: medicine.
\n
\n\n
2011
\n\n
\n\t
Publishing milestone: More than five million downloads reached
\n\t
IntechOpen publishes 1996 Nobel Prize in Chemistry winner Harold W. Kroto’s “Strategies to Successfully Cross-Link Carbon Nanotubes”. Find it here.
\n\t
IntechOpen and TBI collaborate on a project to explore the changing needs of researchers and the evolving ways that they discover, publish and exchange information. The result is the survey “Author Attitudes Towards Open Access Publishing: A Market Research Program”.
\n\t
IntechOpen hosts SHOW - Share Open Access Worldwide; a series of lectures, debates, round-tables and events to bring people together in discussion of open source principles, intellectual property, content licensing innovations, remixed and shared culture and free knowledge.
\n
\n\n
2012
\n\n
\n\t
Publishing milestone: 10 million downloads reached
\n\t
IntechOpen holds Interact2012, a free series of workshops held by figureheads of the scientific community including Professor Hiroshi Ishiguro, director of the Intelligent Robotics Laboratory, who took the audience through some of the most impressive human-robot interactions observed in his lab.
\n
\n\n
2013
\n\n
\n\t
IntechOpen joins the Committee on Publication Ethics (COPE) as part of a commitment to guaranteeing the highest standards of publishing.
\n
\n\n
2014
\n\n
\n\t
IntechOpen turns 10, with more than 30 million downloads to date.
\n\t
IntechOpen appoints its first Regional Representatives - members of the team situated around the world dedicated to increasing the visibility of our authors’ published work within their local scientific communities.
\n
\n\n
2015
\n\n
\n\t
Downloads milestone: More than 70 million downloads reached, more than doubling since the previous year.
\n\t
Publishing milestone: IntechOpen publishes its 2,500th book and 40,000th Open Access chapter, reaching 20,000 citations in Thomson Reuters ISI Web of Science.
\n\t
40 IntechOpen authors are included in the top one per cent of the world’s most-cited researchers.
\n\t
Thomson Reuters’ ISI Web of Science Book Citation Index begins indexing IntechOpen’s books in its database.
\n
\n\n
2016
\n\n
\n\t
IntechOpen is identified as a world leader in Simba Information’s Open Access Book Publishing 2016-2020 report and forecast. IntechOpen came in as the world’s largest Open Access book publisher by title count.
\n
\n\n
2017
\n\n
\n\t
Downloads milestone: IntechOpen reaches more than 100 million downloads
\n\t
Publishing milestone: IntechOpen publishes its 3,000th Open Access book, making it the largest Open Access book collection in the world
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