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Volumn 77, Issue 4, 2014, Pages 1547-1559

Synchronization of a novel fractional order stretch-twist-fold (STF) flow chaotic system and its application to a new authenticated encryption scheme (AES)

Author keywords

Cryptography; Encryption scheme; Fractional order system; Stretch twist fold flow; Synchronization

Indexed keywords

AUTHENTICATION; CHAOS THEORY; CHAOTIC SYSTEMS; DYNAMICAL SYSTEMS; SYNCHRONIZATION;

EID: 84901571816     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-014-1398-x     Document Type: Article
Times cited : (70)

References (50)
  • 2
    • 84927904552 scopus 로고
    • Origin of magnetic fields in astrophysics (Turbulent "dynamo" Mechanisms)
    • Vainshtein, S.I.; Zel'dovich, Y.A.B.: Origin of magnetic fields in astrophysics (Turbulent "Dynamo" Mechanisms). Physics-Uspekhi 15, 159-172 (1972)
    • (1972) Physics-Uspekhi , vol.15 , pp. 159-172
    • Vainshtein, S.I.1    Zel'Dovich, Y.A.B.2
  • 3
    • 0022061682 scopus 로고
    • Topological constraints associated with fast dynamo action
    • 10.1017/S002211208500163X 0604.76092
    • Moffatt, H.K.; Proctor, M.R.E.: Topological constraints associated with fast dynamo action. J. Fluid Mech. 154, 493-507 (1985)
    • (1985) J. Fluid Mech. , vol.154 , pp. 493-507
    • Moffatt, H.K.1    Proctor, M.R.E.2
  • 4
    • 0025573427 scopus 로고
    • On a class of steady confined Stokes flows with chaotic streamlines
    • 10.1017/S0022112090001999 0692.76028 1051334
    • Bajer, K.; Moffatt, H.K.: On a class of steady confined Stokes flows with chaotic streamlines. J. Fluid Mech. 212, 337-363 (1990)
    • (1990) J. Fluid Mech. , vol.212 , pp. 337-363
    • Bajer, K.1    Moffatt, H.K.2
  • 6
    • 0028444249 scopus 로고
    • Hamiltonian formulation of the equations of streamlines in three-dimensional steady flows
    • 10.1016/0960-0779(94)90130-9 0823.76066
    • Bajer, K.: Hamiltonian formulation of the equations of streamlines in three-dimensional steady flows. Chaos Solitons Fractals 4, 895-911 (1994)
    • (1994) Chaos Solitons Fractals , vol.4 , pp. 895-911
    • Bajer, K.1
  • 7
    • 30744479260 scopus 로고
    • Steady confined stokes flows with chaotic streamlines
    • Moffatt, H.K.; Tsinober, A. (eds.) Technical University of Denmark Cambridge University Press, Cambridge
    • Bajer, K.; Moffatt, H.N.; Nex, F.H.: Steady confined stokes flows with chaotic streamlines. In: Moffatt, H.K.; Tsinober, A. (eds.) Topological Fluid Mechanics. Proccedings of the IUTAM Symposium, Technical University of Denmark, pp. 459-466. Cambridge University Press, Cambridge (1990)
    • (1990) Topological Fluid Mechanics. Proccedings of the IUTAM Symposium , pp. 459-466
    • Bajer, K.1    Moffatt, H.N.2    Nex, F.H.3
  • 8
    • 0010704192 scopus 로고    scopus 로고
    • Fractal properties of the stretch-twist-flod magnetic dynamo
    • 10.1103/PhysRevE.53.4729
    • Vainshtein, S.I.; Sagdeev, R.Z.; Rosner, R.; et al.: Fractal properties of the stretch-twist-flod magnetic dynamo. Phys. Rev. E 53, 4729 (1996)
    • (1996) Phys. Rev. e , vol.53 , pp. 4729
    • Vainshtein, S.I.1    Sagdeev, R.Z.2    Rosner, R.3
  • 9
    • 21344443254 scopus 로고    scopus 로고
    • Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow
    • 10.1063/1.166151 1055.76523 1376896
    • Vainshtein, D.L.; Vasiliev, A.A.; Neishtadt, A.I.: Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow. Chaos 6, 67-77 (1996)
    • (1996) Chaos , vol.6 , pp. 67-77
    • Vainshtein, D.L.1    Vasiliev, A.A.2    Neishtadt, A.I.3
  • 10
    • 0001067643 scopus 로고    scopus 로고
    • Stretch-twist-fold and ABC nonlinear dynamos: Restricted chaos
    • 10.1103/PhysRevE.56.1605 1464161
    • Vainshtein, S.I.; Sagdeev, R.Z.; Rosner, R.: Stretch-twist-fold and ABC nonlinear dynamos: restricted chaos. Phys. Rev. E 56, 1605 (1997)
    • (1997) Phys. Rev. e , vol.56 , pp. 1605
    • Vainshtein, S.I.1    Sagdeev, R.Z.2    Rosner, R.3
  • 11
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
    • Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141 (1963)
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 12
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • 10.1016/0375-9601(76)90101-8
    • Rossler, O.E.: An equation for continuous chaos. Phys. Lett. A 57, 397-398 (1976)
    • (1976) Phys. Lett. A , vol.57 , pp. 397-398
    • Rossler, O.E.1
  • 13
    • 10444267277 scopus 로고    scopus 로고
    • Chen's attractor exists
    • 10.1142/S0218127404011296 2099166
    • Zhou, T.; Tang, Y.; Chen, G.: Chen's attractor exists. Int. J. Bifurc. Chaos 9, 3167-3177 (2004)
    • (2004) Int. J. Bifurc. Chaos , vol.9 , pp. 3167-3177
    • Zhou, T.1    Tang, Y.2    Chen, G.3
  • 14
    • 41549111454 scopus 로고    scopus 로고
    • Sil'nikov chaos of the Liu system
    • 10.1063/1.2839909 2404655
    • Zhou, L.; Chen, F.: Sil'nikov chaos of the Liu system. Chaos 18, 013113 (2008)
    • (2008) Chaos , vol.18 , pp. 013113
    • Zhou, L.1    Chen, F.2
  • 15
    • 0036011505 scopus 로고    scopus 로고
    • A new chaotic attractor coined
    • 1063.34510
    • Lü, J.; Chen, G.: A new chaotic attractor coined. Int. J. Bifurc. Chaos 12, 659-661 (2002)
    • (2002) Int. J. Bifurc. Chaos , vol.12 , pp. 659-661
    • Lü, J.1    Chen, G.2
  • 16
    • 0037246536 scopus 로고    scopus 로고
    • A new chaotic system and its generation
    • 1078.37504
    • Liu, W.; Chen, G.: A new chaotic system and its generation. Int. J. Bifurc. Chaos 13, 261-267 (2003)
    • (2003) Int. J. Bifurc. Chaos , vol.13 , pp. 261-267
    • Liu, W.1    Chen, G.2
  • 17
    • 18144402417 scopus 로고    scopus 로고
    • Analysis of a new chaotic system
    • Qi, G.; Chen, G.; Du, S.; Chen, Z.; Yuan, Z.: Analysis of a new chaotic system. Phys. A 352, 295-308 (2005)
    • (2005) Phys. A , vol.352 , pp. 295-308
    • Qi, G.1    Chen, G.2    Du, S.3    Chen, Z.4    Yuan, Z.5
  • 18
    • 82255193996 scopus 로고    scopus 로고
    • A new chaotic attractor from hybrid optical bistable system
    • 1245.34053 2869213
    • Abdelouahab, M.S.; Hamri, N.E.: A new chaotic attractor from hybrid optical bistable system. Nonlinear Dyn. 67, 457-463 (2012)
    • (2012) Nonlinear Dyn. , vol.67 , pp. 457-463
    • Abdelouahab, M.S.1    Hamri, N.E.2
  • 19
    • 84870874704 scopus 로고    scopus 로고
    • A novel strange attractor with a stretched loop
    • 2998169
    • Bouali, S.: A novel strange attractor with a stretched loop. Nonlinear Dyn. 70, 2375-2381 (2012)
    • (2012) Nonlinear Dyn. , vol.70 , pp. 2375-2381
    • Bouali, S.1
  • 20
    • 77955508843 scopus 로고    scopus 로고
    • Chaos synchronization of an energy resource system based on linear control
    • 1216.34061 2683793
    • Wang, Z.: Chaos synchronization of an energy resource system based on linear control. Nonlinear Anal. Real World Appl. 11, 3336-3343 (2010)
    • (2010) Nonlinear Anal. Real World Appl. , vol.11 , pp. 3336-3343
    • Wang, Z.1
  • 21
    • 31144433846 scopus 로고    scopus 로고
    • Adaptive synchronization between two different chaotic systems wih unknown parameters
    • 1195.93121
    • Zhang, H.; Huang, W.; Wang, Z.; Chai, T.: Adaptive synchronization between two different chaotic systems wih unknown parameters. Phys. Lett. A 350, 363-366 (2006)
    • (2006) Phys. Lett. A , vol.350 , pp. 363-366
    • Zhang, H.1    Huang, W.2    Wang, Z.3    Chai, T.4
  • 22
    • 79955111919 scopus 로고    scopus 로고
    • Hybrid control for synchronizing a chaotic system
    • 1221.93159 2793661
    • Shieh, C.S.; Hung, R.T.: Hybrid control for synchronizing a chaotic system. Appl. Math. Model. 35, 3751-3758 (2011)
    • (2011) Appl. Math. Model. , vol.35 , pp. 3751-3758
    • Shieh, C.S.1    Hung, R.T.2
  • 23
    • 84866095947 scopus 로고    scopus 로고
    • Dynamics analysis and hybrid function projective synchronization of a new chaotic system
    • 1263.34071
    • Wu, X.; Li, S.: Dynamics analysis and hybrid function projective synchronization of a new chaotic system. Nonlinear Dyn. 69, 1979-1994 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , pp. 1979-1994
    • Wu, X.1    Li, S.2
  • 24
    • 84863988396 scopus 로고    scopus 로고
    • Adaptive synchronization of the energy resource systems with mismatched parameters via linear feedback control
    • 1253.93068
    • Shi, X.; Wang, Z.: Adaptive synchronization of the energy resource systems with mismatched parameters via linear feedback control. Nonlinear Dyn. 69, 993-997 (2012)
    • (2012) Nonlinear Dyn. , vol.69 , pp. 993-997
    • Shi, X.1    Wang, Z.2
  • 25
    • 84880920985 scopus 로고    scopus 로고
    • A new chaotic attractor and its robust function projective synchronization
    • 1281.34103 3083828
    • Kim, D.; Chang, P.H.; Kim, S.H.: A new chaotic attractor and its robust function projective synchronization. Nonlinear Dyn. 73, 1883-1893 (2013)
    • (2013) Nonlinear Dyn. , vol.73 , pp. 1883-1893
    • Kim, D.1    Chang, P.H.2    Kim, S.H.3
  • 26
    • 84882454634 scopus 로고    scopus 로고
    • Hybrid phase synchronization between identical and nonidentical three-dimensional chaotic systems using the active control method
    • 1281.34064 3094792
    • Das, S.; Srivastava, M.; Leung, A.Y.T.: Hybrid phase synchronization between identical and nonidentical three-dimensional chaotic systems using the active control method. Nonlinear Dyn. 73, 2261-2272 (2013)
    • (2013) Nonlinear Dyn. , vol.73 , pp. 2261-2272
    • Das, S.1    Srivastava, M.2    Leung, A.Y.T.3
  • 27
    • 84962668447 scopus 로고    scopus 로고
    • Synchronization of chaotic systems using feedback controller: An application to Diffie-Hellman key exchange protocol and ElGamal public key cryptosystem
    • doi: 10.1016/j.joems.2013.10.003
    • Balasubramaniam, P.; Muthukumar, P.: Synchronization of chaotic systems using feedback controller: an application to Diffie-Hellman key exchange protocol and ElGamal public key cryptosystem. J. Egypt. Math. Soc. (2013). doi: 10.1016/j.joems.2013.10.003
    • (2013) J. Egypt. Math. Soc.
    • Balasubramaniam, P.1    Muthukumar, P.2
  • 28
    • 77956575738 scopus 로고    scopus 로고
    • Complex dynamics in the stretch-twist-fold flow
    • 1204.37083 2718359
    • Bao, J.; Yang, Q.: Complex dynamics in the stretch-twist-fold flow. Nonlinear Dyn. 61, 773-781 (2010)
    • (2010) Nonlinear Dyn. , vol.61 , pp. 773-781
    • Bao, J.1    Yang, Q.2
  • 29
    • 84880701018 scopus 로고    scopus 로고
    • Nonlinear analysis of stretch-twist-fold (STF) flow
    • 3046914
    • Aqeel, M.; Yue, Z.: Nonlinear analysis of stretch-twist-fold (STF) flow. Nonlinear Dyn. 72, 581-590 (2013)
    • (2013) Nonlinear Dyn. , vol.72 , pp. 581-590
    • Aqeel, M.1    Yue, Z.2
  • 30
    • 84877608975 scopus 로고    scopus 로고
    • Chaotification in the stretch-twist-fold (STF) flow
    • Yue, B.Z.; Aqeel, M.: Chaotification in the stretch-twist-fold (STF) flow. Chin. Sci. Bull. 58, 1655-1662 (2013)
    • (2013) Chin. Sci. Bull. , vol.58 , pp. 1655-1662
    • Yue, B.Z.1    Aqeel, M.2
  • 31
    • 0000378977 scopus 로고    scopus 로고
    • Quantum Levy processes and fractional kinetics
    • Kusnezov, D.; Bulgac, A.; Dang, D.G.: Quantum Levy processes and fractional kinetics. Phys. Rev. Lett. 82, 1136 (1999)
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 1136
    • Kusnezov, D.1    Bulgac, A.2    Dang, D.G.3
  • 32
    • 0034517069 scopus 로고    scopus 로고
    • Fractional market dynamics
    • 1802416
    • Laskin, N.: Fractional market dynamics. Phys. A 287, 482-492 (2000)
    • (2000) Phys. A , vol.287 , pp. 482-492
    • Laskin, N.1
  • 33
    • 0030531939 scopus 로고    scopus 로고
    • Fractional-order diffusion-wave equation
    • 0846.35001 1372176
    • El-Sayed, A.M.A.: Fractional-order diffusion-wave equation. Int. J. Theor. Phys. 35, 311-322 (1996)
    • (1996) Int. J. Theor. Phys. , vol.35 , pp. 311-322
    • El-Sayed, A.M.A.1
  • 34
    • 77956595176 scopus 로고    scopus 로고
    • A new chaotic system with fractional order and its projective synchronization
    • 1204.37035
    • Wu, X.; Wang, H.: A new chaotic system with fractional order and its projective synchronization. Nonlinear Dyn. 61, 407-417 (2010)
    • (2010) Nonlinear Dyn. , vol.61 , pp. 407-417
    • Wu, X.1    Wang, H.2
  • 35
    • 77955654277 scopus 로고    scopus 로고
    • Adaptive feedback control and synchronization of non-identical chaotic fractional order systems
    • 1194.93105 2658527
    • Odibat, Z.M.: Adaptive feedback control and synchronization of non-identical chaotic fractional order systems. Nonlinear Dyn. 60, 479-487 (2010)
    • (2010) Nonlinear Dyn. , vol.60 , pp. 479-487
    • Odibat, Z.M.1
  • 36
    • 84867977717 scopus 로고    scopus 로고
    • Chaos in the fractional-order complex Lorenz system and its synchronization
    • 1268.34022 3010577
    • Luo, C.; Wang, X.: Chaos in the fractional-order complex Lorenz system and its synchronization. Nonlinear Dyn. 71, 241-257 (2013)
    • (2013) Nonlinear Dyn. , vol.71 , pp. 241-257
    • Luo, C.1    Wang, X.2
  • 37
    • 84867897789 scopus 로고    scopus 로고
    • Studying on the stability of fractional-order nonlinear system
    • 1267.34013 2991287
    • Zhao, L.D.; Hu, J.B.; Fang, J.A.; Zhang, W.B.: Studying on the stability of fractional-order nonlinear system. Nonlinear Dyn. 70, 475-479 (2012)
    • (2012) Nonlinear Dyn. , vol.70 , pp. 475-479
    • Zhao, L.D.1    Hu, J.B.2    Fang, J.A.3    Zhang, W.B.4
  • 38
    • 84888605479 scopus 로고    scopus 로고
    • Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography
    • 1284.34065 3127122
    • Muthukumar, P.; Balasubramaniam, P.: Feedback synchronization of the fractional order reverse butterfly-shaped chaotic system and its application to digital cryptography. Nonlinear Dyn. 74, 1169-1181 (2013)
    • (2013) Nonlinear Dyn. , vol.74 , pp. 1169-1181
    • Muthukumar, P.1    Balasubramaniam, P.2
  • 39
    • 57649105528 scopus 로고    scopus 로고
    • A note on the stability of fractional order systems
    • 1168.34036 2488105
    • Tavazoei, M.S.; Haeri, M.: A note on the stability of fractional order systems. Math. Comput. Simulat. 79, 1566-1576 (2009)
    • (2009) Math. Comput. Simulat. , vol.79 , pp. 1566-1576
    • Tavazoei, M.S.1    Haeri, M.2
  • 40
    • 84948973239 scopus 로고
    • Message recovery for signature schemes based on the discrete logarithm problem
    • Nyberg, K.; Rueppel, R.A.: Message recovery for signature schemes based on the discrete logarithm problem. Lect. Notes Comput. Sci. 950, 182-193 (1995)
    • (1995) Lect. Notes Comput. Sci. , vol.950 , pp. 182-193
    • Nyberg, K.1    Rueppel, R.A.2
  • 41
    • 84977255207 scopus 로고
    • Linear models of dissipation whose Q is almost frequency independent
    • Caputo, M.: Linear models of dissipation whose Q is almost frequency independent. Part II. J. R. Astron. Soc. 13, 529-539 (1967)
    • (1967) Part II. J. R. Astron. Soc. , vol.13 , pp. 529-539
    • Caputo, M.1
  • 42
    • 34347330038 scopus 로고    scopus 로고
    • A necessary condition for double scroll attractor existence in fractional-order systems
    • 1209.37037
    • Tavazoei, M.S.; Haeri, M.: A necessary condition for double scroll attractor existence in fractional-order systems. Phys. Lett. A 367, 102-113 (2007)
    • (2007) Phys. Lett. A , vol.367 , pp. 102-113
    • Tavazoei, M.S.1    Haeri, M.2
  • 43
    • 0002731965 scopus 로고    scopus 로고
    • Stability results for fractional differential equations with applications to control processing
    • Lille, France
    • Matignon, D.: Stability results for fractional differential equations with applications to control processing. In: Proceedings of IMACS-SMC, pp. 963-968. Lille, France (1996)
    • (1996) Proceedings of IMACS-SMC , pp. 963-968
    • Matignon, D.1
  • 44
    • 85032883059 scopus 로고
    • A public key cryptosystem and a signature scheme based on discrete logarithms
    • Springer, Berlin
    • ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Proceedings of CRYPTO 84, pp. 10-18. Springer, Berlin (1985)
    • (1985) Proceedings of CRYPTO , vol.84 , pp. 10-18
    • Elgamal, T.1
  • 45
    • 0029375592 scopus 로고
    • Authenticated encryption scheme without using a one way function
    • Lee, W.B.; Chang, C.C.: Authenticated encryption scheme without using a one way function. Electron. Lett. 31, 1656 (1995)
    • (1995) Electron. Lett. , vol.31 , pp. 1656
    • Lee, W.B.1    Chang, C.C.2
  • 46
    • 0037097054 scopus 로고    scopus 로고
    • Convertible authenticated encryption scheme
    • Wu, T.S.; Hsu, C.L.: Convertible authenticated encryption scheme. J. Syst. Softw. 62, 205-209 (2002)
    • (2002) J. Syst. Softw. , vol.62 , pp. 205-209
    • Wu, T.S.1    Hsu, C.L.2
  • 47
    • 0037421773 scopus 로고    scopus 로고
    • Publicly verifiable authenticated encryption
    • Ma, C.; Chen, K.: Publicly verifiable authenticated encryption. Electron. Lett. 39, 281-282 (2003)
    • (2003) Electron. Lett. , vol.39 , pp. 281-282
    • Ma, C.1    Chen, K.2
  • 48
    • 54949116025 scopus 로고    scopus 로고
    • Method for simulation of the fractional order chaotic systems
    • Petras, I.: Method for simulation of the fractional order chaotic systems. Acta Mont. Slovaca 11, 273-277 (2006)
    • (2006) Acta Mont. Slovaca , vol.11 , pp. 273-277
    • Petras, I.1
  • 49
    • 34250012626 scopus 로고    scopus 로고
    • Realization of fractional-order Liu chaotic system by circuit
    • Jun-Jie, L.; Chong-Xin, L.: Realization of fractional-order Liu chaotic system by circuit. Chin. Phys. 16, 1586 (2007)
    • (2007) Chin. Phys. , vol.16 , pp. 1586
    • Jun-Jie, L.1    Chong-Xin, L.2
  • 50
    • 84874339642 scopus 로고    scopus 로고
    • A fractional order hyperchaotic system derived from a Liu system and its circuit realization
    • Qiang, H.; Chong-Xin, L.; Lei, S.; Da-Rui, Z.: A fractional order hyperchaotic system derived from a Liu system and its circuit realization. Chin. Phys. B 22, 020502 (2013)
    • (2013) Chin. Phys. B , vol.22 , pp. 020502
    • Qiang, H.1    Chong-Xin, L.2    Lei, S.3    Da-Rui, Z.4


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