A Course in Number Theory and Cryptography

Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance

Vandersypen, L. M. K., Steffen, M., Breyta, G., Yannoni, C. S., Sherwood, M. H., & Chuang, I. L. (2001) · Nature · doi:10.1038/414883a · Cited by 1,738

The State of Elliptic Curve Cryptography

Koblitz, N., Menezes, A., & Vanstone, S. A. (2000) · Designs Codes and Cryptography · doi:10.1023/a:1008354106356 · Cited by 687

A verifiable secret shuffle and its application to e-voting

Neff, C. A. (2001) · ACM SIGSAC Conference on Computer and Communications Security (CCS) · doi:10.1145/501983.502000 · Cited by 513

Transactions papers a routing-driven Elliptic Curve Cryptography based key management scheme for Heterogeneous Sensor Networks

Du, X., Guizani, M., Xiao, Y., & Chen, H. (2009) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2009.060598 · Cited by 380

Efficient Arithmetic on Koblitz Curves

Solinas, J. A. (2000) · Designs Codes and Cryptography · doi:10.1023/a:1008306223194 · Cited by 345

Algebraic-geometry codes

Blake, I. F., Heegard, C., Høholdt, T., & Wei, V. K. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.720550 · Cited by 268

Montgomery Multiplication in GF(2k)

Koç, Ç. K., & Acar, T. (1998) · Designs Codes and Cryptography · doi:10.1023/a:1008208521515 · Cited by 267

Another Look at "Provable Security"

Koblitz, N., & Menezes, A. (2005) · Journal of Cryptology · doi:10.1007/s00145-005-0432-z · Cited by 215

Quantum Factorization of 143 on a Dipolar-Coupling Nuclear Magnetic Resonance System

Xu, N., Zhu, J., Lu, D., Zhou, X., Peng, X., & Du, J. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.130501 · Cited by 187

Quantum Adiabatic Algorithm for Factorization and Its Experimental Implementation

Peng, X., Liao, Z., Xu, N., Qin, G., Zhou, X., Suter, D., & Du, J. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.220405 · Cited by 175

Radio Resource Management Optimization of Flexible Satellite Payloads for DVB-S2 Systems

Cocco, G., de Cola, T., Angelone, M., et al. (2017) · IEEE Transactions on Broadcasting · doi:10.1109/tbc.2017.2755263 · Cited by 163

Popularization: Myths, Massmedia and Modernism

Ernest, P. (1996) · Springer eBooks · doi:10.1007/978-94-009-1465-0_24 · Cited by 163

Quantum cryptography

Hughes, R., Alde, D. M., Dyer, P. L., Luther, G. G., Morgan, G. L., & Schauer, M. M. (1995) · Contemporary Physics · doi:10.1080/00107519508222149 · Cited by 153

IEEE Standard Specifications for Public-Key Cryptography

Cryptography, P.-K. (2000) · IEEE Standards · doi:10.1109/ieeestd.2000.92292 · Cited by 149

SecureDAV: a secure data aggregation and verification protocol for sensor networks

Mahimkar, A. A., & Rappaport, T. S. (2005) · IEEE Global Telecommunications Conference (GLOBECOM) · doi:10.1109/glocom.2004.1378395 · Cited by 130

The State of Elliptic Curve Cryptography

Koblitz, N., Menezes, A., & Vanstone, S. A. (2000) · Springer eBooks · doi:10.1007/978-1-4757-6856-5_5 · Cited by 126

Elliptic curve ElGamal based homomorphic image encryption scheme for sharing secret images

Li, L., El‐Latif, A. A. A., & Niu, X. (2011) · Signal Processing · doi:10.1016/j.sigpro.2011.10.020 · Cited by 126

Security and Privacy in Biometrics

Campisi, P. (2013) · Springer eBooks · doi:10.1007/978-1-4471-5230-9 · Cited by 124

Hardware architectures for public key cryptography

Batina, L., Örs, B., Preneel, B., & Vandewalle, J. P. L. (2003) · Integration · doi:10.1016/s0167-9260(02)00053-6 · Cited by 108

Hardware implementation of an elliptic curve processor over GF(p)

Örs, B., Batina, L., Preneel, B., & Vandewalle, J. P. L. (2004) · IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP) · doi:10.1109/asap.2003.1212866 · Cited by 99

An elliptic curve implementation of the finite field digital signature algorithm

Koblitz, N. (1998) · Lecture notes in computer science · doi:10.1007/bfb0055739 · Cited by 85

Factorization of Numbers with the Temporal Talbot Effect: Optical Implementation by a Sequence of Shaped Ultrashort Pulses

Bigourd, D., Chatel, B., Schleich, W. P., & Girard, B. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.030202 · Cited by 84

Elementary Number Theory

Yan, S. Y. (2002) · Springer eBooks · doi:10.1007/978-3-662-04773-6_1 · Cited by 87

A Routing-Driven Key Management Scheme for Heterogeneous Sensor Networks

Du, X., Xiao, Y., Ci, S., et al. (2007) · International Conference on Communications · doi:10.1109/icc.2007.564 · Cited by 82

A Generalized Wiener Attack on RSA

Blömer, J., & May, A. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-24632-9_1 · Cited by 82

Gauss Sum Factorization with Cold Atoms

Gilowski, M., Wendrich, T., Müller, T., Jentsch, C., Ertmer, W. A., Rasel, E. M., & Schleich, W. P. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.030201 · Cited by 80

Maximum Likelihood Estimation Based Robust Chinese Remainder Theorem for Real Numbers and Its Fast Algorithm

Wang, W., Li, X., Wang, W., et al. (2015) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2015.2413378 · Cited by 75

Speeding up Exponentiation using an Untrusted Computational Resource

van Dijk, M., Clarke, D., Gassend, B., et al. (2006) · Designs Codes and Cryptography · doi:10.1007/s10623-005-3710-8 · Cited by 71

Scalable multicast security in dynamic groups

Molva, R. A., & Pannetrat, A. (1999) · Proceedings of the ACM Conference on Computer and Communications Security · doi:10.1145/319709.319723 · Cited by 62

Distributed Cardinality Estimation in Anonymous Networks

Varagnolo, D., Pillonetto, G., & Schenato, L. (2013) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2013.2287113 · Cited by 55

Neural Cryptography Based on Generalized Tree Parity Machine for Real-Life Systems

Jeong, S., Park, C.-H., Hong, D., et al. (2021) · Security and Communication Networks · doi:10.1155/2021/6680782 · Cited by 55

Private key agreement and secure communication for heterogeneous sensor networks

Rahman, S. M. M., & El‐Khatib, K. (2010) · Journal of Parallel and Distributed Computing · doi:10.1016/j.jpdc.2010.03.009 · Cited by 54

Securing the wireless internet

Gupta, V., & Gupta, S. (2001) · IEEE Communications Magazine · doi:10.1109/35.968814 · Cited by 49

On Graph-Based Cryptography and Symbolic Computations

Ustimenko, V. A. (2007) · Serdica Journal of Computing · doi:10.55630/sjc.2007.1.131-156 · Cited by 47

Cryptanalysis of the Chor—Rivest Cryptosystem

Vaudenay, S. (2000) · Journal of Cryptology · doi:10.1007/s001450010005 · Cited by 47

On linguistic dynamical systems, families of graphs of large girth, and cryptography

Ustimenko, V. (2006) · Journal of Mathematical Sciences · doi:10.1007/s10958-007-0453-2 · Cited by 45

A Robust Generalized Chinese Remainder Theorem for Two Integers

Li, X., Xia, X., Wang, W., et al. (2016) · IEEE Transactions on Information Theory · doi:10.1109/tit.2016.2614322 · Cited by 43

Some Parallel Algorithms for Integer Factorisation

Brent, R. P. (1999) · Lecture notes in computer science · doi:10.1007/3-540-48311-x_1 · Cited by 42

Factorizing numbers with the Gauss sum technique: NMR implementations

Mahesh, T. S., Rajendran, N., Peng, X., & Suter, D. (2007) · Physical Review A · doi:10.1103/physreva.75.062303 · Cited by 43

The Chinese Remainder Theorem and its application in a high-speed RSA crypto chip

Großschädl, J. (2002) · Annual Computer Security Applications Conference · doi:10.1109/acsac.2000.898893 · Cited by 41

Hardware and software symbiosis helps smart card evolution

Dhem, J.-F., & Feyt, N. (2001) · IEEE Micro · doi:10.1109/40.977754 · Cited by 40

On the Computation of Square Roots in Finite Fields

Müller, S. (2004) · Designs Codes and Cryptography · doi:10.1023/b:desi.0000015890.44831.e2 · Cited by 39

A hybrid network security algorithm based on Diffie Hellman and Text-to-Image Encryption algorithm

Abusukhon, A., Anwar, M. N., Mohammad, Z., et al. (2019) · Journal of Discrete Mathematical Sciences and Cryptography · doi:10.1080/09720529.2019.1569821 · Cited by 38

The Diffie-Hellman key exchange protocol and non-abelian nilpotent groups

Mahalanobis, A. (2008) · Israel Journal of Mathematics · doi:10.1007/s11856-008-1008-z · Cited by 37

An FPGA implementation of an elliptic curve processor GF(2 m )

Mentens, N., Ors, S. B., & Preneel, B. (2004) · ACM Great Lakes Symposium on VLSI (GLSVLSI) · doi:10.1145/988952.989062 · Cited by 37

Comments on "A practical (t, n) threshold proxy signature scheme based on the RSA cryptosystem"

Wang, G., Bao, F., Zhou, J., et al. (2004) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2004.52 · Cited by 36

ECC Based Threshold Cryptography for Secure Data Forwarding and Secure Key Exchange in MANET (I)

Ertaul, L., & Lu, W. (2005) · Lecture notes in computer science · doi:10.1007/11422778_9 · Cited by 34

Efficient Arithmetic on Koblitz Curves

Solinas, J. A. (2000) · Springer eBooks · doi:10.1007/978-1-4757-6856-5_6 · Cited by 34

The RSA Public Key Cryptosystem

Wardlaw, W. P. (2000) · Springer eBooks · doi:10.1007/978-3-642-59663-6_6 · Cited by 33

Exploring the Design Space of Prime Field vs. Binary Field ECC-Hardware Implementations

Wenger, E., & Hutter, M. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-29615-4_18 · Cited by 33

On Nesterov's Approach to Semi-infinite Programming

Faybusovich, L. E. (2002) · Acta Applicandae Mathematicae · doi:10.1023/a:1020643711475 · Cited by 33

Enhancing the security in RSA and elliptic curve cryptography based on addition chain using simplified Swarm Optimization and Particle Swarm Optimization for mobile devices

Mullai, A., & Mani, K. (2020) · International Journal of Information Technology · doi:10.1007/s41870-019-00413-8 · Cited by 32

Comparison of ECC and RSA Algorithm with DNA Encoding for IoT Security

Bansal, M., Gupta, S., & Mathur, S. (2021) · International Conference on Inventive Computation Technologies (ICICT) · doi:10.1109/icict50816.2021.9358591 · Cited by 32

Cryptanalysis of the Chor-Rivest cryptosystem

Vaudenay, S. (1998) · Lecture notes in computer science · doi:10.1007/bfb0055732 · Cited by 32

Low complexity multiplication in a finite field using ring representation

Katti, R., & Brennan, J. P. (2003) · IEEE Transactions on Computers · doi:10.1109/tc.2003.1190583 · Cited by 28

Data Encryption and Authetication Using Public Key Approach

Nagaraj, S., Raju, G. S. V. P., & Srinadth, V. (2015) · Procedia Computer Science · doi:10.1016/j.procs.2015.04.161 · Cited by 28

A novel network security algorithm based on private key encryption

Abusukhon, A., & Talib, M. (2012) · doi:10.1109/cybersec.2012.6246080 · Cited by 27

The Largest Dynamic Range of a Generalized Chinese Remainder Theorem for Two Integers

Wang, W., Li, X., Xia, X., et al. (2014) · IEEE Signal Processing Letters · doi:10.1109/lsp.2014.2322200 · Cited by 27

Graphstega: Graph Steganography Methodology

Desoky, A., & Younis, M. (2008) · Journal of Digital Forensic Practice · doi:10.1080/15567280701797087 · Cited by 26

Reconfigurable modular arithmetic logic unit supporting high-performance RSA and ECC over GF(p)

Sakiyama, K., Mentens, N., Batina, L., et al. (2007) · International Journal of Electronics · doi:10.1080/00207210701293264 · Cited by 26

Trapdoor Hard-to-Invert Group Isomorphisms and Their Application to Password-Based Authentication

Catalano, D., Pointcheval, D., & Pornin, T. (2006) · Journal of Cryptology · doi:10.1007/s00145-006-0431-8 · Cited by 25

On the implementation of cryptoalgorithms based on algebraic graphs over some commutative rings

Kotorowicz, & Ustimenko (2008) · Condensed Matter Physics · doi:10.5488/cmp.11.2.347 · Cited by 24

Lower bounds on the linear complexity of the discrete logarithm in finite fields

Meidl, W., & Winterhof, A. (2001) · IEEE Transactions on Information Theory · doi:10.1109/18.959261 · Cited by 24

Evaluation codes and their basic parameters

Jaramillo-Velez, D., Pinto, M. V., & Villarreal, R. H. (2020) · Designs Codes and Cryptography · doi:10.1007/s10623-020-00818-8 · Cited by 23

Factoring numbers with interfering random waves

Weber, S. J., Chatel, B., & Girard, B. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/83/34008 · Cited by 22

A high-speed ECC-based wireless authentication on an ARM microprocessor

Aydos, M., Yantk, T., & Koç, Ç. K. (2002) · Annual Computer Security Applications Conference · doi:10.1109/acsac.2000.898895 · Cited by 21

Cryptography, trusted third parties and escrow

Phoenix, S. J. D. (1997) · BT Technology Journal · doi:10.1023/a:1018680606917 · Cited by 21

Enhancing Big Data Security using Elliptic Curve Cryptography

Gupta, S., Vashisht, S., Singh, D. P., et al. (2019) · International Conference on Automation, Computational and Technology Management (ICACTM) · doi:10.1109/icactm.2019.8776764 · Cited by 20

Securing air-ground communications

McParland, T., Patel, V., & Hughes, W. J. (2002) · AIAA/IEEE Digital Avionics Systems Conference (DASC) · doi:10.1109/dasc.2001.964187 · Cited by 20

Exploring Advanced Encryption and Steganography Techniques for Image Security

Kataria, M., Jain, K., & Subramanian, N. (2023) · International Symposium on Digital Forensics and Security (ISDFS) · doi:10.1109/isdfs58141.2023.10131890 · Cited by 21

An Enhanced Symmetric Key Cryptography Algorithm to Improve Data Security

KumarPandey, K., Rangari, V., & Sinha, S. K. (2013) · International Journal of Computer Applications · doi:10.5120/13028-0215 · Cited by 19

Twisted Edwards Elliptic Curves for Zero-Knowledge Circuits

Bellés-Muñoz, M., Whitehat, B., Baylina, J., et al. (2021) · Mathematics · doi:10.3390/math9233022 · Cited by 19

A Cryptographic Method for Secure Watermark Detection

Malkin, M., & Kalker, T. (2007) · Lecture notes in computer science · doi:10.1007/978-3-540-74124-4_3 · Cited by 19

On Small World Semiplanes with Generalised Schubert Cells

Futorny, V., & Ustimenko, V. (2007) · Acta Applicandae Mathematicae · doi:10.1007/s10440-007-9144-8 · Cited by 19

Group ring based public key cryptosystems

Mittal, G., Kumar, S., Narain, S., et al. (2021) · Journal of Discrete Mathematical Sciences and Cryptography · doi:10.1080/09720529.2020.1796868 · Cited by 18

A Hardware Processor Supporting Elliptic Curve Cryptography for Less than 9 kGEs

Wenger, E., & Hutter, M. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-27257-8_12 · Cited by 18

Spectral Modular Exponentiation

Saldamlı, G., & Koç, Ç. K. (2007) · IEEE Symposium on Computer Arithmetic (ARITH) · doi:10.1109/arith.2007.34 · Cited by 18

Efficient proxy multisignature schemes based on the elliptic curve cryptosystem

Chen, T., Chung, Y., & Huang, G.-S. (2003) · Computers & Security · doi:10.1016/s0167-4048(03)00614-x · Cited by 17

Symmetric Key Encryption using Iterated Fractal Functions

Roseville, 9., & Agarwal, S. (2017) · International Journal of Computer Network and Information Security · doi:10.5815/ijcnis.2017.04.01 · Cited by 17

A proxy-protected proxy signature scheme based on elliptic curve cryptosystem

Chen, T., Liu, T.-P., & Chung, Y. (2004) · doi:10.1109/tencon.2002.1181245 · Cited by 17

A Structural Comparison of the Computational Difficulty of Breaking Discrete Log Cryptosystems

Sakurai, K., & Shizuya, H. (1998) · Journal of Cryptology · doi:10.1007/s001459900033 · Cited by 17

Analysis of Neural Synchronization Using Genetic Approach for Secure Key Generation

Santhanalakshmi, S., Sangeeta, K., & Patra, G. K. (2015) · Communications in computer and information science · doi:10.1007/978-3-319-22915-7_20 · Cited by 16

A Secure Network Communication Protocol Based on Text to Barcode Encryption Algorithm

Abusukhon, A., & Hawashin, B. (2015) · International Journal of Advanced Computer Science and Applications · doi:10.14569/ijacsa.2015.061209 · Cited by 16

Securing Data Exchange with Elliptic Curve Cryptography: A Novel Hash-Based Method for Message Mapping and Integrity Assurance

Lahraoui, Y., Lazaar, S., Amal, Y., & Nitaj, A. (2024) · Cryptography · doi:10.3390/cryptography8020023 · Cited by 18

A public key cryptosystem using Affine Hill Cipher under modulation of prime number

Sundarayya, P., & Prasad, G. V. R. J. S. (2019) · Journal of Information and Optimization Sciences · doi:10.1080/02522667.2018.1470751 · Cited by 16

Comparing the MOV and FR Reductions in Elliptic Curve Cryptography

Harasawa, R., Shikata, J., Suzuki, J., et al. (1999) · Lecture notes in computer science · doi:10.1007/3-540-48910-x_14 · Cited by 16

Interpolation of the discrete logarithm in Fq by Boolean functions and by polynomials in several variables modulo a divisor of q−1

Lange, T., & Winterhof, A. (2003) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(02)00445-6 · Cited by 16

Relative generalized Hamming weights of q-ary Reed-Muller codes

Geil, O., & Martin, S. (2017) · Advances in Mathematics of Communications · doi:10.3934/amc.2017041 · Cited by 15

Quantization Error Spectra Structure of a DTC Synthesizer via the DFT Axis Scaling Property

Talwalkar, S. A. (2011) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2011.2173384 · Cited by 15

On the Security of the RSA-Based Multisignature Scheme for Various Group Structures

Doi, H., Mambo, M., & Okamoto, E. (2000) · Lecture notes in computer science · doi:10.1007/10718964_29 · Cited by 15

Hybrid scheme for factorisation: Factoring 551 using a 3-qubit NMR quantum adiabatic processor

Pal, S., Moitra, S., Anjusha, V. S., Kumar, A., & Mahesh, T. S. (2019) · Pramana · doi:10.1007/s12043-018-1684-0 · Cited by 18

Authenticated key distribution using given set of primes for secret sharing

Chandramowliswaran, N., Srinivasan, S., & Muralikrishna, P. (2014) · Systems Science & Control Engineering · doi:10.1080/21642583.2014.985803 · Cited by 14

Elliptic curve cryptosystem ElGamal encryption and transmission scheme

Minfeng, F., & Wei, C. (2010) · International Conference on Computer Application and System Modeling · doi:10.1109/iccasm.2010.5620105 · Cited by 14

Pseudorandom Bit Sequence Generator for Stream Cipher Based on Elliptic Curves

Jilna, P., & Deepthi, P. P. (2015) · Mathematical Problems in Engineering · doi:10.1155/2015/257904 · Cited by 14

Generating the Best Fit Key in Cryptography using Genetic Algorithm

Jawaid, S., & Jamal, A. (2014) · International Journal of Computer Applications · doi:10.5120/17301-7767 · Cited by 14

Identity and Pairing-Based Secure Key Management Scheme for Heterogeneous Sensor Networks

Rahman, S. M. M., Nasser, N., & Saleh, K. A. (2008) · IEEE International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob) · doi:10.1109/wimob.2008.79 · Cited by 14

Undeniable signature scheme based over group ring

Goel, N., Gupta, I., Dubey, M. K., et al. (2016) · Applicable Algebra in Engineering Communication and Computing · doi:10.1007/s00200-016-0293-8 · Cited by 14

Security in Wireless Sensor Networks

Nasser, N., Salti, T. E., & Rahman, S. M. M. (2009) · Wireless networks and mobile communications · doi:10.1201/9781420077780.ch15 · Cited by 14

Hardware Implementation of Finite-Field Division

Deschamps, J., & Sutter, G. D. (2006) · Acta Applicandae Mathematicae · doi:10.1007/s10440-006-9049-y · Cited by 14

Data encryption algorithms using one-dimensional chaotic maps

Jessa, M. (2000) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2000.857194 · Cited by 13

Course Organisers: Course Organisers: Course Organisers: Course Organisers

Chavatte‐Palmer, P. (2023) · HAL (Le Centre pour la Communication Scientifique Directe)

Revamping an English for Specific Academic Purposes Course for Problem-Based Learning: Reflections from Course DevelopersPreprint

Yung, K. W. H., & Fong, N. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4410387

The Views of the Undergraduate Students who are Taking the Course of Piano about the Course

UMUZDAŞ, M. S. (2014) · Procedia - Social and Behavioral Sciences · doi:10.1016/j.sbspro.2014.01.1004

Prerequisite Course Recommendation Based on Course Description and Students’ Grades

Zhou, H. (2020) · Journal of Purdue Undergraduate Research · doi:10.7771/2158-4052.1457

Reform and Practice of the Course Whole Assessment and Evaluation of Professional Course—Take a Course in Building Materials as Example

张, 国. (2021) · Advances in Education · doi:10.12677/ae.2021.111027