Startseite A privacy-preserving parallel and homomorphic encryption scheme
Artikel Open Access

A privacy-preserving parallel and homomorphic encryption scheme

  • Zhaoe Min EMAIL logo , Geng Yang und Jingqi Shi
Veröffentlicht/Copyright: 6. April 2017
Artikel downloaden (PDF)
Open Physics
Aus der Zeitschrift Open Physics Band 15 Heft 1

Abstract

In order to protect data privacy whilst allowing efficient access to data in multi-nodes cloud environments, a parallel homomorphic encryption (PHE) scheme is proposed based on the additive homomorphism of the Paillier encryption algorithm. In this paper we propose a PHE algorithm, in which plaintext is divided into several blocks and blocks are encrypted with a parallel mode. Experiment results demonstrate that the encryption algorithm can reach a speed-up ratio at about 7.1 in the MapReduce environment with 16 cores and 4 nodes.

Keywords: privacy protection; homomorphic encryption; parallel encryption; parallel homomorphic encryption; cloud computing; MapReduce
PACS: 9.70.-a; 89.70.EG

1 Introduction

Since 2009, cloud servers such as Microsoft, Amazon and Google have experienced security incidents and the security of cloud computing has become the paramount problem constraining its development. In 2011, Cloud Security Alliance (CSA) presented the cloud security model, emphasising the issue of privacy protection in cloud computing. The privacy problem in cloud computing results from the features of data outsourcing and service renting. Users lose their direct control of data while they store the data in the cloud, which can lead to the leakage and abuse of personal privacy data. Some privacy preserving methods are proposed in Papers [1, 2]. Furthermore, it is considered that data privacy can be protected from the two aspects of data encryption and user identity management. The homomorphic encryption (HE) technique supports the management of ciphertext data under the privacy protection, and can directly applied to ciphertexts for retrieval, computation and statistics in the clouds. Afterwards, the results are returned to the user in the form of ciphertexts, in contrast to the conventional encryption algorithm, which can eliminate the need for frequent operations of encryption and decryption between the clouds and the users, thus reducing the communication overhead and computation resources.

Cloud computing clusters possess large numbers of computational nodes, and they can be used for storing and processing mass data. It is easy to construct a cloud computing environment, therefore, many enterprises and research institutes have built private cloud computing platforms. We can conduct encryption on the data which need to be stored in the public clouds using the parallel features of the private cloud clusters and the computational capacities of the various nodes. Therefore, with pertinence to the problem of mass data and the frequent visits and clouds utilization, it is of great importance to speed up the processing capacities of mass data encryption, and then conduct parallel process of data encryption computations in combination with the features of cloud computing and the networks.

2 Related works

HE was first proposed by Rivest et al. in 1978 as a concept of “privacy homomorphism” [3], and is an encryption scheme which can directly conduct computations on the ciphertexts. Subsequently, RSA [4] and the ElGamal algorithm [5] with multiplicative homomorphism as well as Paillier [6] and the BNG algorithm [7] with additive homomorphism were successively proposed. Particularly, the above algorithms belong to the category of homomorphic encryption algorithms.

By 2009, Gentry proposed the first fully homomorphic scheme based on the ideal lattice [8], which can conduct any number of addition and multiplication operations on the ciphertext. Since then, more fully homomorphic scheme acts have been proposed, such as the fully homomorphic scheme DGHV [9] based on integers, BGV scheme [10] based on the RLWE, GSW13 scheme [11] based on the approximate eigenvectors, the multiple keys fully homomorphic ciphertext scheme [12] based on NTRU, and so on.

The low encryption efficiency is a problem which is mutually faced by the somewhat homomorphic encryption (SHE) algorithm and the fully homomorphic encryption( FHE) algorithm. In order to elevate the encryption efficiency, various kinds of schemes have been proposed.For example, papers [13–16] introduce a scheme to elevate the efficiency of the RSA algorithm through different parallel methods, such as GPU, CPU or tree architecture. Wang et al. elaborated on the scheme of parallel technique on MapReduce so as to elevate the efficiency of Hill Cipher [17].

As for the fully homomorphic scheme, Gu proposed a kind of HE scheme which is based on the deal lattice together with SIMD technique [18]. Cheon improved the scheme of DGHV, and proposed an optimal method of batch processing plaintext [19]. Considering that the addition and multiplication calculations in the ciphertext homomorphism in the GSW scheme are only based on the addition and multiplication of the matrices, Hiromasa proposed a method to compress ciphertexts and optimize bootstrap [20].Moreover, the scheme was the first fully homomorphic method which can conduct encryptions of the matrices and support the homomorphic operations on the matrices.

Among all different kinds of the above mentioned HE algorithms, Hill Cipher has been proven to be lacking sufficient security. For the Paillier and RSA algorithms with the same length key, the Paillier algorithm has higher security. On the other hand, the Paillier algorithm is more suitable for parallel due to its property of additive homomorphism. More research has been done on the fully homomorphic encryption algorithm in recent years. However, due to the problem of encryption efficiency, most of them are still in the experimental stage and are not widely applied in practice.

With the goal of privacy protection, this paper realizes a kind of parallel encryption algorithm based on the MapReduce. Firstly, we use the additive homomorphism of the Paillier algorithm to divide the data that requires encryption into several approximately equal numbers according to the parity of each data packet. Then, using the parallelism in MapReduce, we realize the parallel encryption by grouping the plaintext. Experimental results show that the proposed scheme can achieve the speedup of 7.1 while maintaining security, thus solving the problem of low computational efficiency for a somewhat homomorphic encryption algorithm.

3 Background Knowledge

3.1 Paillier algorithm

In 1999, Paillier proposed a kind of probabilistic public key crypto system based on a high order residual class, i.e. the Paillier algorithm [6]. The concrete encryption scheme is defined as follows.

Generating key: Set n = p × q and λ = lcm(p − 1)(q − 1), where p and q are large primes, and then we randomly select a base g∈Zn2∗, this can be done efficiently by checking whether

gcd(L(gλmodn2),n)=1(1)

where the function L is defined as: L(u)=u−1n, Now, (n, g) is regarded as public keys while the pair (p, q) (or equivalently λ) remains private.

Encryption: Plaintext m ∈ Zn, a random number of r∈Zn∗ is selected, then the ciphertext is defined as follows:

c=E(m)=gmrnmodn2(2)

Decryption: Ciphertext c∈Zn2∗, Plaintext m is defined as follows:

m=D(c)=L(cλmodn2)L(gλmodn2)modn(3)

It can be observed that Paillier's public key encryption algorithm has additive homomorphism, and the proving process is listed as follows:

E(m1)×E(m2)=(gm1r1nmodn2)(gm2r2nmodn2)=gm1+m2(r1r2)nmodn2E(m1+m2)=gm1+m2rnmodn2(4)

where r is a random number. Set r = r1 × r2, then E(m1 + m2) = E(m1) × E(m2) are satisfied.

3.2 MapReduce Model

From the perspective of the software system, the hadoop system includes two parts: the distributed storage and the parallel computations. The Hadoop Distributed File System (denoted as HDFS) is mainly used for the distributed storage of massive-scale data, and among them, the master node controls and manages the whole system of distributed files which are named as NameNodes. Furthermore, each slave node which is responsible for data storage is defined as a DataNode.

In order to realize the parallel computation processing of the large data stored in the HDFS, Hadoop is used to propose a parallel computational framework (named MapReduce). The computational framework contains a master node (named JobTracker) and a multitude of slave nodes are defined as TaskTrackers. The JobTracker is mainly responsible for scheduling and managing the tasks in the operations, while the TaskTracker is responsible for executing the tasks distributed by the JobTracker.

The MapReduce parallel computing framework is a parallelized program execution system that provides a parallel processing model and a process comprising two stages of Map and Reduce. In the Map phase, the input tuples are partitioned by each Mapper, and tuples with the same partition value are passed to the same Reducer for correlation calculation.

4 An Encryption Scheme Based on the Additive Homomorphism

The encryption algorithm in this work mainly uses the additive homomorphism of the Paillier algorithm to encrypt, and is defined as follows.

E(m)=E(m1+m2)=E(m1)×E(m2)

To ensure the security of the encryption algorithm, the length of the public key is set to 256 bit, and the specific encryption scheme is listed as follows.

  1. According to the definition of Paillier encryption algorithm, public keys (n, g) and private keys (p, q) are generated.

  2. Assume that the length of the plaintext (L MB) can be divided into x groups of 256 bits in length, and the number of packets x is computed as follows

    x=⌈L×8×220256⌉=⌈L×22032⌉(5)

  3. For each packet, the plaintext is firstly converted to BigInteger type, the value of which is represented as m, and m = m1 + m2 is satisfied. Afterwards, the values of m1 and m2 are computed. If m is an even number (m mod 2 = 0), then m1=m2=m2, else the values of m1 and m2 are given as follows.

    m1=(m−1)/2m2=(m+1)/2(m mod2)=1(6)

  4. E(m1) and E(m2) are calculated respectively, and the specific formula is given as follows.

    E(m1)=gm1r1n mod n2E(m2)=gm2r2n mod n2(7)

The ciphertexts are E(m1) and E(m2). We let r1 = r2 while m1 = m2, hence, we just need to calculate E(m1) for E(m1) = E(m2).

During the decryption process, according to the additive homomorphism of Paillier, the algorithm can be figured out as follows.

E(m)=E(m1)×E(m2)mod n2(8)

Then, using the decryption formula (Eq. 3), the plaintext can be established.

5 Parallel Encryption Scheme based on the MapReduce

As is illustrated in this paper, the parallel encryption scheme based on the MapReduce combines the cloud environment and additive homomorphism of the Paillier algorithm, and realizes parallel encryptions by conducting blocking on the plaintexts. Thus, the encryption efficiency can be greatly enhanced.

5.1 Algorithm Flow

In the programming model of MapReduce, Split function is used to divide the input data into splints with fixed sizes based on the user's needs. Afterwards, the master node distributes them to different processors based on the relevant scheduling mechanism. The Map function conducts relevant operations on each splint after splinting blocks based on an algorithm self-defined by the user, with each Map accomplishing one part of the results. The Reduce function is responsible for integrating the results of all the Maps. The encryption calculation of each splint of the parallel scheme is independent. Therefore, it can be distributed to multiple Maps for encryption at the same time, and it can be defined as a tuple of polynomial time algorithms

∏=(Split,Map,Reduce)(9)

The specific process is as shown in Fig. 1.

Figure 1 Parallel encryption process of Paillier
Figure 1

Parallel encryption process of Paillier

5.2 Split Algorithm

We assume that p is the number of the cores for set processing, and the primary file is divided into n blocks (n > 1), and blocksizei indicates the size of the i-th block (i ≤ n). As the length of the encryption key is 256 bits, the size of the plaintext splint is an integral multiple of 32 bits, and specifically the size of each data block can be calculated with Eq. 10.

Bsizei(B)=⌈L×22032×n⌉×32i<nL×220−(n−1)⌈L×22032×n⌉×32i=n(10)

Fig. 2 shows the specific block algorithm. The content of the i-th splint is stored using the file buffer, and Key indicates the offset of the initial part of i-th splint in the file. Moreover, the value is stored in each file buffer.

Figure 2 shows the specific block algorithm
Figure 2

shows the specific block algorithm

5.3 Map Functions and Reduce Functions

Map ( ) is a single task, and the Mapper class refers to the one for realizing the Map tasks. Hadoop provides an abstract Mapper base class. We inherit this base class, and realize the functions of the relevant interfaces among them. The detailed interface of the Map ( ) method is defined as follows: public void map (Object key, Text value, Context context) throws IOException Interrupted Exception. The parameter key is the key value transmitted into the map, and the values is the corresponding key value, the context is parameter of the environment subject that an environmental subject for the access of Hadoop by the programs. Map functions repeatedly on each group of data in each block data. Fig. 3 shows the encryption algorithm implemented in each Map ( ).

Figure 3 Map function
Figure 3

Map function

The detailed interface of Reduce ( ) is defined as follows: protected void reduce (KEYIN key, Iterable<VALUEIN>values, Context context) throws IOException, Interrupted Exception { }. The input parameter key is the key value that is input to reduce, and the values are the lists of the corresponding key value, the context is the parameter of the environment subjects, which were the environment subjects for the accesses of Hadoop by the programs.

The <key, value> are merged using the key values of the Map functions outputs, and the different values under the same keys are merged into the same list, they are sequenced based on the key values. When the files are written, only the value portion is output without recording the key values. As the key values are the offsets of the texts, the local ciphertext can be spliced into the complete ciphertext output in order.

5.4 Performance Analysis

We assume that the entire encryption time of the Paillier algorithm, key generation and the encryption times are Tseq, Tkey and TEnc respectively. Then Tseq can be expressed as Tseq = Tkey + TEnc. We can know that the main computation overhead in the encryption scheme is the modular exponentiation computation.

Assuming that the time cost for a single modular exponentiation operation is Tpd, then the time cost for conducting one encryption computation is represented as 2Tpd. Based on the above assumption, the plaintext with a length of L(MB) is divided into χ groups. Hence, the time needed to encrypt the plaintext of length L(MB) is defined as TEnc = 2 × χ × Tpd, the entire encryption time is Tseq = Tkey + 2 × χ × Tpd. Based on Eq. 5, the following equation can be obtained

Tseq=Tkey+2×⌈L×22032⌉×Tpd(11)

When the value of L is bigger, Tkey can be ignored, and it can be seen that with the increase of L value, the encryption time Tseq basically presents a trend of linear rise.

During the process of the parallel encryptions, we assume that the operational process has no overlapping, the execution time Tn of the parallel encryption algorithm is composed of four parts, that is

Tn=Tcomm+Tkey+TMap+Treduce(12)

where Tcomm is the communication time, TMap is the parallel encryption time of Map, and Treduce is the time for conducting merging of the ciphertext based on the key values after encrypting.

Assume that the CPU has p cores, the plaintext with a length of L(MB) is divided into n blocks, and the processing time of the i-th block on the CPU core by a map is Ti, then

Tn=Tcomm+Tkey+Max(Ti)×⌈np⌉+Treduce(13)

Based on the size of each splint given by Eq. 10, it can be inferred that each block of plaintext contains the number of packets Bxi=⌈L×22032×n⌉, then

Ti=2×⌈L×22032×n⌉×Tpd(14)

Assuming the same size of plaintext data, the size of the generated ciphertext is the same, and the Reduce time needed by each group of data for the generation of the ciphertext is Tric. Afterwards, the Reduce time Treduce needed by the entire ciphertexts is listed as follows

Treduce=x×Tric=⌈L×22032⌉×Tric(15)

It can be learned that Treduce presents a proportional relation with the size of the generated ciphertext, and it can be derived as follows.

Tn=Tcomm+Tkey+2×⌈L×22032×n⌉×Tpd×⌈np⌉+⌈L×22032⌉×Tric(16)

If the value of L is bigger, Tkey and Tcomm can be ignored. According to the Eq. 16, we can conclude that with the value increasing, the main overhead of the encryption time Tn is shifted from being dominated by Map to Reduce.

The integral speed-up ratio Sp can be expressed as follows

Sp=TseqTn=Tkey+TEncTcomm+Tkey+TMap+Treduce(17)

As Tcomm and Tkey can be ignored, then the following equation can be obtained.

Sp≈2×⌈L×22032⌉×Tpd2×⌈L×22032×n⌉×Tpd×⌈np⌉+⌈L×22032⌉×Tric≈11n×⌈np⌉+Tric2×Tpd(18)

We can know that when the total core number p is fixed and n ∈ (kp, kp + p], the speed-up ratio ηT presents an increasing trend, and the maximum will not exceed p with k a natural number.

5.5 Security Analysis

This scheme is homomorphic, and under the selection of the plaintext attacks, it is semantically secure. In paper [6], the encryption scheme proposed by Paillier is designed based on the calculations among the ZN2∗ group, of which N is a module of RSA. As < N, g > ∈ Pn is satisfied, the following equation can be satisfied PN,g:Z×ZN∗→ZN2∗.

Paillier has proved that PN,g is a one-way trapdoor permutation. As Pn is a bijection, it is known as < N, g > ∈ Pn. For an element c∈ZN2∗, there exists a sole (m,r)∈ZN×ZN∗, which satisfies c = gmrN modN2, m is known as a class that c relates to N and g, and is recorded as ClassN, g(c). In case the decomposition of N is known, it is easy to calculate ClassN, g(c). On the other hand, if the decomposition of N is not known, up till now, no polynomial time algorithm for calculating ClassN, g(c) has been found. We represent the unidirectional polarity of PN,g as Pailier1[N, g]. This is where the hardness in the calculations of composite residuosity class, i.e. Pailier1[N, g] = Class[N, g].

The safety of the MapReduce operation mainly derives from Job Submission and Task shuffle. In the Submission Job phase all of the work submitted or the operation of the track are using RPC (Remote Procedure Call Protocol) with the Kerberos implementation of the certification. In the stage of Task, each task submitted by a user is initiated by the user's identity, so that a user's task will not be sent the operating system of signal to Task Tracker or other user's task. In the shuffle stage, when the end of a map task is running, it may provide the results to management Task Tracker. Afterwards, each reduce task will request the data processed by itself from the Task Tracker by HTTP, and then Hadoop should ensure that other users can't obtain the intermediate results of map task. Based on the above definitions, the safety of data in the MapReduce process can be guaranteed.

6 Experiment Testing and Analysis

6.1 Experiment settings

The hardware platform used in this experiment includes a Master node and three slave nodes. Particularly, the Master node is responsible for the monitoring and scheduling of jobs, while the slave node is in charge of storage file distribution and calculation. The specific hardware configurations and software environment of each node are listed in the node configurations of experiment cluster in Table 1.

Table 1

Software and hardware configuration

Product nameThe parameter and model
CPUIntel Xeon E3-1225v3
Cash3.2 GHz/8M
Memory bank16 GB(2×8 GB)1333 MHzDual Ranked RDIM
Hard disk1 TB 3.5-inch 7200 RPM SATA II
Operating SystemCent OS Linux Server 6.6
JAVA VMJAVA 1.7.0
HadoopHadoop-2.5.2

6.2 Experiment Results Analysis

In this experiment, encryption tests are conducted on the plaintexts with respective sizes of 256MB, 512MB, 768MB, 1024 MB,1280 MB,1536 MB,1792 MB and 2048 MB. The experiment involves two kinds of serial and the parallel test. In the serial environment, direct encryption is conducted on the plaintexts without the need of splinting. In contrast, the data needs to be splinted into lots of blocks in the parallel environment. The block size used in this experimental environment is set to 64MB, therefore, these files are divided into different data blocks, with the number of data blocks being 4, 8, 12, 16, 20, 24,28 and 32 respectively.

In the experiments, four computational nodes are used, with the core number of the CPU being 4, and the total core number for the CPU is 16. Table 2 respectively records the sizes of the different files, the encryption time of the files and the total speed-up ratio under the serial and the parallel environment. FS, SET, PET, MMT and RT respectively mean File size, Serial encryption time, Parallel encryption time, Max Map time and Reduce time. Fig. 4 indicates the encryption time of files of different sizes under the serial and the parallel environments, Fig. 5 indicates the integral speed-up ratio of files of different sizes under the serial and the parallel environments.

Figure 4 The contrast diagram of encryption time
Figure 4

The contrast diagram of encryption time

Figure 5 The speed-up rate of the different size file
Figure 5

The speed-up rate of the different size file

Table 2

The test results of different files

FS(MB)SET(s)PET(s)MMT(s)RT(s)SP
2561473478382873.1
51230135874011785.1
76845287284312866.2
102460458644413897.0
1280773412314645436.2
1536891613824456646.5
17921060715244617876.9
20481266617884539027.1

From the above experimental results (shown in Table 2, Fig. 4 and Fig. 5), the following conclusions can be drawn.

  1. Under the circumstance of fixed node numbers, the time needed by the serial encryption presents a proportional relation with the plaintext size.

  2. The time needed by the parallel encryption increases along with the increase of the plaintext.

  3. When n < p, the time consumption of the map functions is the main time consumption of the encryption process, and when n is increasingly approaching p, the difference between the time consumed by the reduce functions and the map functions gradually decreases.

  4. When n > p, and along with the increase of n, the time consumption of reduce functions becomes the main time consumption during the encryption process. The main reason being that only one node is responsible for Reduce, and this also constrains the speed-up ratio.

  5. When n < p, the speed-up ratio Sp increases faster, and when n = p, the maximum value of Sp is reached. When n > p, at each n ∈ (kp, kp + P), the speed-up ratio presents a trend of slow increase, and when n = (k + 1) × p, the maximum value is reached.

7 Conclusion

In this paper, we propose a novel privacy-preserving PHE scheme based on MapReduce, which uses the additive homomorphism of the Paillier algorithm. The proposed scheme is suitable for cloud computing environments due to its parallelism. Experimental results indicate that the scheme enabled the speed-up ratio to reach 7.1 through the parallelism of clusters.

In the future, we will extend this work in the following aspects: (1) To conduct the optimization of the Reduce functions and then adopt two or more Reducers. (2) To study the parallelism of other HE algorithms, and then compare them with the efficiency of this algorithm so as to find out the optimal HE algorithm.

Acknowledgement

This research is supported by the National Natural Science Foundation of China under the Grants nos. 61572263, 61502251 and 61502243, Natural Science Foundation of Jiangsu Province under the Grants nos. BK20151511, BK20141429 and BK20161516, Colleges and Universities in Jiangsu Province plans to graduate research and innovation under Grant no. KYLX_0816, Natural Science Research Project of Jiangsu University under the Grants nos.(14KJB520031 and 15KJB520027),the Nature Science Project of Nanjing University of Posts and Telecommunications under the Grants nos.(NY215097 and NY214127).

References

[1] Huang R.W., Gui X.L., Yu S., et al., Privacy-preserving computable encryption scheme of cloud computing, CJC., 2011, 34, 2391-2402.10.3724/SP.J.1016.2011.02391Suche in Google Scholar

[2] Gao W., Zali M.R., Degree-based indices computation for special chemical molecular structures using edge dividing method, AMNS., 2016, 1, 94-117.10.21042/AMNS.2016.1.00009Suche in Google Scholar

[3] Rivest R.L., Adleman L., Dertouzos M.L., On data banks and privacy homomorphisms, J. FDN SECURE COMPUTATI., 1978, 169-179.Suche in Google Scholar

[4] Rivest R., Shamir A., Adleman L., A method for obtaining digital signatures and public-key cryptosystems, COMMUM ACM., 1978, 21, 120-126.10.21236/ADA606588Suche in Google Scholar

[5] Elgamal T., A public key cryptosystem and a signature scheme based on discrete logarithms, IEEE Trans. Inf. Theory., 1985, 31, 469-472.10.1007/3-540-39568-7_2Suche in Google Scholar

[6] Paillier P., Public-key cryptosystems based on composite degree residuosity classes, EUROCRYPT'99 (2-6 May 1999,Prague, Czech republic), Springer, Berlin, Heidelberg, 1999, 223-238.10.1007/3-540-48910-X_16Suche in Google Scholar

[7] Boneh D., Goh E.J., Nissim K., Evaluating 2-DNF formulas on ciphertexts, Second Theory of Cryptography Conference (10-12, February 2005, Cambridge, MA, United states), Springer, Berlin, Heidelberg, 2005, 325-341.10.1007/978-3-540-30576-7_18Suche in Google Scholar

[8] Gentry C., Fully homomorphic encryption using ideal lattices, ACM symposium on Theory of Computing (May 31-June 2, 2009, Bethesda, MD, United states), Association for Computing Machinery, New York, 2009, 169-178.10.1145/1536414.1536440Suche in Google Scholar

[9] Dijk M., Gentry C., Halevi S., et al., Full homomorphic encryption over the integers, Advances in Cryptology EUROCRYPT 2010, Springer, Berlin Heidelberg, 2009, 24-43.10.1007/978-3-642-13190-5_2Suche in Google Scholar

[10] Brakerski Z., Gentry C., Vaikuntanathan V., (Leveled) Full homomorphic encryption without bootstrapping, the 3th Innovations in Theoretical Computer Science Conference (8-10, January, 2012, Cambridge, Massachusetts, UK), ACM, New York, 2012, 309-325.10.1145/2090236.2090262Suche in Google Scholar

[11] Gentry C., Sahai A., Waters B., Homomorphic encryption from learning with errors: Conceptually-simpler, asymptotically-faster, attribute-based, 33rd Annual International Cryptology Conference (18-22, August, 2013, Santa Barbara, CA, United states), Springer, Heidelberg, 2013, 75-92.10.1007/978-3-642-40041-4_5Suche in Google Scholar

[12] López-Alt A., Tromer E., On-the-fly multiparty computation on the cloud via multikey full homomorphic encryption, 44rd annual ACM symposium on Theory of computing (19-22, May, 2012, New York, NY, United states), ACM, New York, 2012, 1219-1234.10.1145/2213977.2214086Suche in Google Scholar

[13] Tembhurne J.V., Sathe S.R., RSA Public Key Acceleration on CUDA GPU, Proceedings of ICAIECES 2015 (22-23, April, 2015, Chennai, India), Springer Verlag, 2016, 365-375.10.1007/978-81-322-2656-7_33Suche in Google Scholar

[14] Victor M., Pérez G., Susan F., et al., Applied mathematics and nonlinear sciences in the war on cancer, AMNS., 2016, 1, 423-436.10.21042/AMNS.2016.2.00036Suche in Google Scholar

[15] Lin C.H., Liu J.C.,Li C.C., Parallel modulus operations in RSA encryption by CPU/GPU hybrid computation, 9th Asia Joint Conference on Information Security (January 26, 2014, Wuchang, Wuhan, China), Institute of Electrical and Electronics Engineers Inc, 2014, 71-75.10.1109/AsiaJCIS.2014.25Suche in Google Scholar

[16] Ithnin M.D.N., Parallel RSA encryption based on tree architecture, J. CHIN INST ENG., 2013, 36, 658-666.10.1080/02533839.2012.737113Suche in Google Scholar

[17] Wang X.Y., Min Z., Parallel algorithm for Hill Cipher on MapReduce, 2nd IEEE International Conference on Progress in Informatics and Computing (16-18, May, 2014, Shanghai, China), Institute of Electrical and Electronics Engineers Inc, 2014, 493-497.10.1109/PIC.2014.6972384Suche in Google Scholar

[18] Gu C.S., Fully homomorphic encryption from approximate ideal lattices, JSW, 2015, 26, 2696-2719.Suche in Google Scholar

[19] Cheon J.H., Coron J.S., Kim J., et al., Batch full homomorphic encryption over the integer, INFORM SCIENCES, 2015, 310, 315-335.10.1016/j.ins.2015.03.019Suche in Google Scholar

[20] Hiromasa R., Abe M., Okamoto T., Packing messages and optimizing bootstrapping in GSW-FHE, IEICE Trans Fund Electron Commun Comput Sci, 2016, E99A, 73-82.10.1007/978-3-662-46447-2_31Suche in Google Scholar

Received: 2016-12-2
Accepted: 2016-12-16
Published Online: 2017-4-6

© 2017 Zhaoe Min et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Artikel in diesem Heft

  1. Regular Articles
  2. Analysis of a New Fractional Model for Damped Bergers’ Equation
  3. Regular Articles
  4. Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem
  5. Regular Articles
  6. Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients
  7. Regular Articles
  8. Investigation of a curve using Frenet frame in the lightlike cone
  9. Regular Articles
  10. Construction of complex networks from time series based on the cross correlation interval
  11. Regular Articles
  12. Nonlinear Schrödinger approach to European option pricing
  13. Regular Articles
  14. A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations
  15. Regular Articles
  16. A new miniaturized negative-index meta-atom for tri-band applications
  17. Regular Articles
  18. Seismic stability of the survey areas of potential sites for the deep geological repository of the spent nuclear fuel
  19. Regular Articles
  20. Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays
  21. Regular Articles
  22. Sensitivity analysis and economic optimization studies of inverted five-spot gas cycling in gas condensate reservoir
  23. Regular Articles
  24. Quantum mechanics with geometric constraints of Friedmann type
  25. Regular Articles
  26. Modeling and Simulation for an 8 kW Three-Phase Grid-Connected Photo-Voltaic Power System
  27. Regular Articles
  28. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
  29. Regular Articles
  30. Analysis of Drude model using fractional derivatives without singular kernels
  31. Regular Articles
  32. An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method
  33. Regular Articles
  34. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method
  35. Regular Articles
  36. Quantum mechanical calculation of electron spin
  37. Regular Articles
  38. CO2 capture by polymeric membranes composed of hyper-branched polymers with dense poly(oxyethylene) comb and poly(amidoamine)
  39. Regular Articles
  40. Chain on a cone
  41. Regular Articles
  42. Multi-task feature learning by using trace norm regularization
  43. Regular Articles
  44. Superluminal tunneling of a relativistic half-integer spin particle through a potential barrier
  45. Regular Articles
  46. Neutrosophic triplet normed space
  47. Regular Articles
  48. Lie algebraic discussion for affinity based information diffusion in social networks
  49. Regular Articles
  50. Radiation dose and cancer risk estimates in helical CT for pulmonary tuberculosis infections
  51. Regular Articles
  52. A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives
  53. Regular Articles
  54. Some new remarks on MHD Jeffery-Hamel fluid flow problem
  55. Regular Articles
  56. Numerical investigation of magnetohydrodynamic slip flow of power-law nanofluid with temperature dependent viscosity and thermal conductivity over a permeable surface
  57. Regular Articles
  58. Charge conservation in a gravitational field in the scalar ether theory
  59. Regular Articles
  60. Measurement problem and local hidden variables with entangled photons
  61. Regular Articles
  62. Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition
  63. Regular Articles
  64. Fabrication and application of coaxial polyvinyl alcohol/chitosan nanofiber membranes
  65. Regular Articles
  66. Calculating degree-based topological indices of dominating David derived networks
  67. Regular Articles
  68. The structure and conductivity of polyelectrolyte based on MEH-PPV and potassium iodide (KI) for dye-sensitized solar cells
  69. Regular Articles
  70. Chiral symmetry restoration and the critical end point in QCD
  71. Regular Articles
  72. Numerical solution for fractional Bratu’s initial value problem
  73. Regular Articles
  74. Structure and optical properties of TiO2 thin films deposited by ALD method
  75. Regular Articles
  76. Quadruple multi-wavelength conversion for access network scalability based on cross-phase modulation in an SOA-MZI
  77. Regular Articles
  78. Application of ANNs approach for wave-like and heat-like equations
  79. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  80. Study on node importance evaluation of the high-speed passenger traffic complex network based on the Structural Hole Theory
  81. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  82. A mathematical/physics model to measure the role of information and communication technology in some economies: the Chinese case
  83. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  84. Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps
  85. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  86. On the libration collinear points in the restricted three – body problem
  87. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  88. Research on Critical Nodes Algorithm in Social Complex Networks
  89. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  90. A simulation based research on chance constrained programming in robust facility location problem
  91. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  92. A mathematical/physics carbon emission reduction strategy for building supply chain network based on carbon tax policy
  93. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  94. Mathematical analysis of the impact mechanism of information platform on agro-product supply chain and agro-product competitiveness
  95. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  96. A real negative selection algorithm with evolutionary preference for anomaly detection
  97. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  98. A privacy-preserving parallel and homomorphic encryption scheme
  99. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  100. Random walk-based similarity measure method for patterns in complex object
  101. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  102. A Mathematical Study of Accessibility and Cohesion Degree in a High-Speed Rail Station Connected to an Urban Bus Transport Network
  103. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  104. Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter
  105. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  106. Oil exploration oriented multi-sensor image fusion algorithm
  107. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  108. Analysis of Product Distribution Strategy in Digital Publishing Industry Based on Game-Theory
  109. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  110. Expanded Study on the accumulation effect of tourism under the constraint of structure
  111. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  112. Unstructured P2P Network Load Balance Strategy Based on Multilevel Partitioning of Hypergraph
  113. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  114. Research on the method of information system risk state estimation based on clustering particle filter
  115. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  116. Demand forecasting and information platform in tourism
  117. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  118. Physical-chemical properties studying of molecular structures via topological index calculating
  119. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  120. Local kernel nonparametric discriminant analysis for adaptive extraction of complex structures
  121. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  122. City traffic flow breakdown prediction based on fuzzy rough set
  123. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  124. Conservation laws for a strongly damped wave equation
  125. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  126. Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution
  127. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  128. Computing the Ediz eccentric connectivity index of discrete dynamic structures
  129. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  130. A discrete epidemic model for bovine Babesiosis disease and tick populations
  131. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  132. Study on maintaining formations during satellite formation flying based on SDRE and LQR
  133. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  134. Relationship between solitary pulmonary nodule lung cancer and CT image features based on gradual clustering
  135. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  136. A novel fast target tracking method for UAV aerial image
  137. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  138. Fuzzy comprehensive evaluation model of interuniversity collaborative learning based on network
  139. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  140. Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation
  141. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  142. After notes on self-similarity exponent for fractal structures
  143. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  144. Excitation probability and effective temperature in the stationary regime of conductivity for Coulomb Glasses
  145. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  146. Comparisons of feature extraction algorithm based on unmanned aerial vehicle image
  147. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  148. Research on identification method of heavy vehicle rollover based on hidden Markov model
  149. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  150. Classifying BCI signals from novice users with extreme learning machine
  151. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  152. Topics on data transmission problem in software definition network
  153. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  154. Statistical inferences with jointly type-II censored samples from two Pareto distributions
  155. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  156. Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme
  157. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  158. Analysis on trust influencing factors and trust model from multiple perspectives of online Auction
  159. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  160. Coupling of two-phase flow in fractured-vuggy reservoir with filling medium
  161. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  162. Production decline type curves analysis of a finite conductivity fractured well in coalbed methane reservoirs
  163. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  164. Flow Characteristic and Heat Transfer for Non-Newtonian Nanofluid in Rectangular Microchannels with Teardrop Dimples/Protrusions
  165. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  166. The size prediction of potential inclusions embedded in the sub-surface of fused silica by damage morphology
  167. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  168. Research on carbonate reservoir interwell connectivity based on a modified diffusivity filter model
  169. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  170. The method of the spatial locating of macroscopic throats based-on the inversion of dynamic interwell connectivity
  171. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  172. Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method
  173. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  174. A volumetric ablation model of EPDM considering complex physicochemical process in porous structure of char layer
  175. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  176. Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
  177. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  178. Macroscopic lattice Boltzmann model for heat and moisture transfer process with phase transformation in unsaturated porous media during freezing process
  179. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  180. Modelling of intermittent microwave convective drying: parameter sensitivity
  181. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  182. Simulating gas-water relative permeabilities for nanoscale porous media with interfacial effects
  183. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  184. Simulation of counter-current imbibition in water-wet fractured reservoirs based on discrete-fracture model
  185. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  186. Investigation effect of wettability and heterogeneity in water flooding and on microscopic residual oil distribution in tight sandstone cores with NMR technique
  187. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  188. Analytical modeling of coupled flow and geomechanics for vertical fractured well in tight gas reservoirs
  189. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  190. Special Issue: Ever New "Loopholes" in Bell’s Argument and Experimental Tests
  191. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  192. The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  193. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  194. Erratum to: The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  195. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  196. Rhetoric, logic, and experiment in the quantum nonlocality debate
  197. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  198. What If Quantum Theory Violates All Mathematics?
  199. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  200. Relativity, anomalies and objectivity loophole in recent tests of local realism
  201. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  202. The photon identification loophole in EPRB experiments: computer models with single-wing selection
  203. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  204. Bohr against Bell: complementarity versus nonlocality
  205. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  206. Is Einsteinian no-signalling violated in Bell tests?
  207. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  208. Bell’s “Theorem”: loopholes vs. conceptual flaws
  209. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  210. Nonrecurrence and Bell-like inequalities
  211. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  212. Three-dimensional computer models of electrospinning systems
  213. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  214. Electric field computation and measurements in the electroporation of inhomogeneous samples
  215. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
https://doi.org/10.1515/phys-2017-0014
Schlagwörter für diesen Artikel
privacy protection; homomorphic encryption; parallel encryption; parallel homomorphic encryption; cloud computing; MapReduce
Creative Commons
BY-NC-ND 3.0

Artikel in diesem Heft

  1. Regular Articles
  2. Analysis of a New Fractional Model for Damped Bergers’ Equation
  3. Regular Articles
  4. Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem
  5. Regular Articles
  6. Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients
  7. Regular Articles
  8. Investigation of a curve using Frenet frame in the lightlike cone
  9. Regular Articles
  10. Construction of complex networks from time series based on the cross correlation interval
  11. Regular Articles
  12. Nonlinear Schrödinger approach to European option pricing
  13. Regular Articles
  14. A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations
  15. Regular Articles
  16. A new miniaturized negative-index meta-atom for tri-band applications
  17. Regular Articles
  18. Seismic stability of the survey areas of potential sites for the deep geological repository of the spent nuclear fuel
  19. Regular Articles
  20. Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays
  21. Regular Articles
  22. Sensitivity analysis and economic optimization studies of inverted five-spot gas cycling in gas condensate reservoir
  23. Regular Articles
  24. Quantum mechanics with geometric constraints of Friedmann type
  25. Regular Articles
  26. Modeling and Simulation for an 8 kW Three-Phase Grid-Connected Photo-Voltaic Power System
  27. Regular Articles
  28. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
  29. Regular Articles
  30. Analysis of Drude model using fractional derivatives without singular kernels
  31. Regular Articles
  32. An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method
  33. Regular Articles
  34. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method
  35. Regular Articles
  36. Quantum mechanical calculation of electron spin
  37. Regular Articles
  38. CO2 capture by polymeric membranes composed of hyper-branched polymers with dense poly(oxyethylene) comb and poly(amidoamine)
  39. Regular Articles
  40. Chain on a cone
  41. Regular Articles
  42. Multi-task feature learning by using trace norm regularization
  43. Regular Articles
  44. Superluminal tunneling of a relativistic half-integer spin particle through a potential barrier
  45. Regular Articles
  46. Neutrosophic triplet normed space
  47. Regular Articles
  48. Lie algebraic discussion for affinity based information diffusion in social networks
  49. Regular Articles
  50. Radiation dose and cancer risk estimates in helical CT for pulmonary tuberculosis infections
  51. Regular Articles
  52. A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives
  53. Regular Articles
  54. Some new remarks on MHD Jeffery-Hamel fluid flow problem
  55. Regular Articles
  56. Numerical investigation of magnetohydrodynamic slip flow of power-law nanofluid with temperature dependent viscosity and thermal conductivity over a permeable surface
  57. Regular Articles
  58. Charge conservation in a gravitational field in the scalar ether theory
  59. Regular Articles
  60. Measurement problem and local hidden variables with entangled photons
  61. Regular Articles
  62. Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition
  63. Regular Articles
  64. Fabrication and application of coaxial polyvinyl alcohol/chitosan nanofiber membranes
  65. Regular Articles
  66. Calculating degree-based topological indices of dominating David derived networks
  67. Regular Articles
  68. The structure and conductivity of polyelectrolyte based on MEH-PPV and potassium iodide (KI) for dye-sensitized solar cells
  69. Regular Articles
  70. Chiral symmetry restoration and the critical end point in QCD
  71. Regular Articles
  72. Numerical solution for fractional Bratu’s initial value problem
  73. Regular Articles
  74. Structure and optical properties of TiO2 thin films deposited by ALD method
  75. Regular Articles
  76. Quadruple multi-wavelength conversion for access network scalability based on cross-phase modulation in an SOA-MZI
  77. Regular Articles
  78. Application of ANNs approach for wave-like and heat-like equations
  79. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  80. Study on node importance evaluation of the high-speed passenger traffic complex network based on the Structural Hole Theory
  81. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  82. A mathematical/physics model to measure the role of information and communication technology in some economies: the Chinese case
  83. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  84. Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps
  85. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  86. On the libration collinear points in the restricted three – body problem
  87. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  88. Research on Critical Nodes Algorithm in Social Complex Networks
  89. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  90. A simulation based research on chance constrained programming in robust facility location problem
  91. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  92. A mathematical/physics carbon emission reduction strategy for building supply chain network based on carbon tax policy
  93. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  94. Mathematical analysis of the impact mechanism of information platform on agro-product supply chain and agro-product competitiveness
  95. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  96. A real negative selection algorithm with evolutionary preference for anomaly detection
  97. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  98. A privacy-preserving parallel and homomorphic encryption scheme
  99. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  100. Random walk-based similarity measure method for patterns in complex object
  101. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  102. A Mathematical Study of Accessibility and Cohesion Degree in a High-Speed Rail Station Connected to an Urban Bus Transport Network
  103. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  104. Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter
  105. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  106. Oil exploration oriented multi-sensor image fusion algorithm
  107. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  108. Analysis of Product Distribution Strategy in Digital Publishing Industry Based on Game-Theory
  109. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  110. Expanded Study on the accumulation effect of tourism under the constraint of structure
  111. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  112. Unstructured P2P Network Load Balance Strategy Based on Multilevel Partitioning of Hypergraph
  113. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  114. Research on the method of information system risk state estimation based on clustering particle filter
  115. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  116. Demand forecasting and information platform in tourism
  117. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  118. Physical-chemical properties studying of molecular structures via topological index calculating
  119. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  120. Local kernel nonparametric discriminant analysis for adaptive extraction of complex structures
  121. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  122. City traffic flow breakdown prediction based on fuzzy rough set
  123. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  124. Conservation laws for a strongly damped wave equation
  125. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  126. Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution
  127. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  128. Computing the Ediz eccentric connectivity index of discrete dynamic structures
  129. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  130. A discrete epidemic model for bovine Babesiosis disease and tick populations
  131. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  132. Study on maintaining formations during satellite formation flying based on SDRE and LQR
  133. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  134. Relationship between solitary pulmonary nodule lung cancer and CT image features based on gradual clustering
  135. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  136. A novel fast target tracking method for UAV aerial image
  137. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  138. Fuzzy comprehensive evaluation model of interuniversity collaborative learning based on network
  139. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  140. Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation
  141. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  142. After notes on self-similarity exponent for fractal structures
  143. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  144. Excitation probability and effective temperature in the stationary regime of conductivity for Coulomb Glasses
  145. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  146. Comparisons of feature extraction algorithm based on unmanned aerial vehicle image
  147. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  148. Research on identification method of heavy vehicle rollover based on hidden Markov model
  149. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  150. Classifying BCI signals from novice users with extreme learning machine
  151. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  152. Topics on data transmission problem in software definition network
  153. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  154. Statistical inferences with jointly type-II censored samples from two Pareto distributions
  155. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  156. Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme
  157. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  158. Analysis on trust influencing factors and trust model from multiple perspectives of online Auction
  159. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  160. Coupling of two-phase flow in fractured-vuggy reservoir with filling medium
  161. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  162. Production decline type curves analysis of a finite conductivity fractured well in coalbed methane reservoirs
  163. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  164. Flow Characteristic and Heat Transfer for Non-Newtonian Nanofluid in Rectangular Microchannels with Teardrop Dimples/Protrusions
  165. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  166. The size prediction of potential inclusions embedded in the sub-surface of fused silica by damage morphology
  167. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  168. Research on carbonate reservoir interwell connectivity based on a modified diffusivity filter model
  169. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  170. The method of the spatial locating of macroscopic throats based-on the inversion of dynamic interwell connectivity
  171. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  172. Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method
  173. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  174. A volumetric ablation model of EPDM considering complex physicochemical process in porous structure of char layer
  175. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  176. Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
  177. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  178. Macroscopic lattice Boltzmann model for heat and moisture transfer process with phase transformation in unsaturated porous media during freezing process
  179. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  180. Modelling of intermittent microwave convective drying: parameter sensitivity
  181. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  182. Simulating gas-water relative permeabilities for nanoscale porous media with interfacial effects
  183. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  184. Simulation of counter-current imbibition in water-wet fractured reservoirs based on discrete-fracture model
  185. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  186. Investigation effect of wettability and heterogeneity in water flooding and on microscopic residual oil distribution in tight sandstone cores with NMR technique
  187. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  188. Analytical modeling of coupled flow and geomechanics for vertical fractured well in tight gas reservoirs
  189. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  190. Special Issue: Ever New "Loopholes" in Bell’s Argument and Experimental Tests
  191. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  192. The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  193. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  194. Erratum to: The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  195. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  196. Rhetoric, logic, and experiment in the quantum nonlocality debate
  197. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  198. What If Quantum Theory Violates All Mathematics?
  199. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  200. Relativity, anomalies and objectivity loophole in recent tests of local realism
  201. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  202. The photon identification loophole in EPRB experiments: computer models with single-wing selection
  203. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  204. Bohr against Bell: complementarity versus nonlocality
  205. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  206. Is Einsteinian no-signalling violated in Bell tests?
  207. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  208. Bell’s “Theorem”: loopholes vs. conceptual flaws
  209. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  210. Nonrecurrence and Bell-like inequalities
  211. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  212. Three-dimensional computer models of electrospinning systems
  213. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  214. Electric field computation and measurements in the electroporation of inhomogeneous samples
  215. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 8.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/phys-2017-0014/html
Button zum nach oben scrollen