Đang tải... (xem toàn văn)
V§n đ• v• qu£n lý và đ£m b£o an toàn thông tin đi»n tß đang là mºt th¡ch thøc lớn đŁi với c¡c nhà nghi¶n cøu v• b£o m“t v… b£o m“t là mºt kỹ thu“t thi‚t y‚u trong h» thŁng thông tin. Xu hướng ph¡t tri”n công ngh» thông tin là người dùng có th” chia s· và sß dụng chung tài nguy¶n m⁄ng tł nhœng vị tr‰ địa lý kh¡c nhau trong c¡c thời đi”m kh¡c nhau, d¤n đ‚n sự ph¥n t¡n tài nguy¶n và t«ng nguy cơ m§t m¡t dœ li»u hoặc rÆ r¿ c¡c thông tin có gi¡ trị. Mở rºng c¡c k‚t nŁi làm xu§t hi»n nhi•u lØ hŒng b£o m“t, do đó tài nguy¶n m⁄ng có nguy cơ bị t§n công và x¥m ph⁄m 104. V… v“y, mục ti¶u cıa b£o m“t không ch¿ n‹m trong lĩnh vực b£o v» dœ li»u mà cÆn nhi•u ph⁄m trù kh¡c như ki”m duy»t web, b£o m“t internet, b£o m“t http, b£o m“t tr¶n c¡c h» thŁng thanh to¡n đi»n tß hoặc giao dịch trực tuy‚n. Ph⁄m vi b£o m“t không ch¿ gói gọn trong mºt m¡y t‰nh mà cÆn b£o m“t c¡c k‚t nŁi m¡y t‰nh tr¶n ph⁄m vi toàn cƒu, trong nhi•u ph¥n lo⁄i m⁄ng và đường truy•n kh¡c nhau như m⁄ng internet, m⁄ng di đºng, m⁄ng thông tin v» tinh 38, 56, 97.
B GIO DC V O TO TRNG I HC BCH KHOA H NI T TH KIM HU NGHIấN CU H MT M KHI DA TRấN HN LON RI RC LUN N TIN S K THUT VIN THễNG H NI - 2017 B GIO DC V O TO TRNG I HC BCH KHOA H NI T TH KIM HU NGHIấN CU H MT M KHI DA TRấN HN LON RI RC LUN N TIN S K THUT VIN THễNG Chuyờn ngnh: K THUT VIN THễNG Mó ngnh: 62520208 GING VIấN HNG DN KHOA HC: PGS.TS HONG MNH THNG H NI - 2017 LI CAM OAN Tụi xin cam oan cỏc kt qu trỡnh by lun ỏn l cụng trỡnh nghiờn cu ca tụi di s hng dn ca cỏn b hng dn Cỏc s liu, kt qu trỡnh by lun ỏn l hon ton trung thc v cha c cụng b bt k cụng trỡnh no trc õy Cỏc kt qu s dng tham kho u ó c trớch dn y v theo ỳng quy nh H Ni, ngy 27 thỏng 03 nm 2017 Tỏc gi T Th Kim Hu Ging viờn hng dn PGS.TS Hong Mnh Thng LI CM N hon thnh c lun ỏn ny, tụi xin gi li bit n sõu sc n cỏc thy cụ, cỏc ng nghip b mụn in t v K thut mỏy tớnh, Vin in t Vin thụng ó h tr v giỳp tụi sut quỏ trỡnh lm Lun ỏn Tin s ti trng i hc Bỏch Khoa H Ni Tụi xin cm n n Thy giỏo hng dn PGS.TS Hong Mnh Thng ó hng dn v ch bo sut quỏ trỡnh lm Lun ỏn Tụi cng xin gi li cm n n GS Kris Steenhaus v GS An Braeken v nhng gúp ý quan trng i vi Lun ỏn v giỳp tụi sut thi gian nghiờn cu ti trng i hc T Brussel, Vng Quc B Tụi cng xin gi li cm n n TS Nguyn Tin Hũa ó h tr vic trỡnh by lun ỏn Cui cựng tụi xin gi li cm n n gia ỡnh ó ng viờn tụi vt qua khú khn hon thnh Lun ỏn ny Tụi xin chõn thnh cm n! Mc lc MC LC DANH MC CC T VIT TT iv DANH MC HèNH V vi DANH MC BNG ix DANH MC Kí HIU TON HC xi M U xii Chng MT M KHI HN LON 1.1 Gii thiu 1.2 Nguyờn lý thit k mt mó hn lon 1.3 Cỏc cũn tn ti h mt mó hn lon 1.4 xut h mt mó hn lon ri rc da trờn cu trỳc mng thay th hoỏn v (SPN) 11 1.5 ng dng mt mó nh RGB 13 1.5.1 Thut toỏn lp mó 16 1.5.2 Thut toỏn gii mó 17 1.5.3 B to khúa hn lon 18 1.5.4 Phõn tớch bo mt 21 1.5.5 Ti nguyờn thc thi 24 1.6 Kt lun chng 24 Chng XUT H MT KHI HNG NH DA VO CC C TNH HN LON CA HM SKEW TENT V STANDARD RI RC 26 2.1 Gii thiu 26 2.2 Hm hn lon ri rc mt chiu ri rc 27 2.2.1 S m Lyapunov ri rc 27 i ii 2.2.2 Thit k cỏc lp S-box ì da trờn tớnh cht hm Skew Tent ri rc 30 2.2.3 Phõn tớch bo mt 36 2.3 Tớnh cht trn v c trng thng kờ ca hm hn lon ri rc hai chiu 38 2.3.1 Cỏc dng thc toỏn hc ca hm hn lon ri rc hai chiu 38 2.3.2 Tớnh cht ng hc ca hm hn lon hai chiu 41 2.3.3 Lp hoỏn v ph thuc tham s s dng hm Standard hai chiu 44 2.4 xut cỏc thit k h mt mó hn lon hng nh 47 2.4.1 c trng ca h mt mó hng nh 47 2.4.2 Thit k lp thay th S-box da trờn hn lon 49 2.4.3 Thit k lp khuch tỏn da trờn hn lon 51 2.5 Kt lun chng 58 Chng M RNG HM ARNOLD CAT V CC NG DNG 60 3.1 Gii thiu 60 3.2 M rng hm Arnol Cat hai chiu da trờn bin i gi Hadamard nhanh 62 3.2.1 Hai dng thc m rng hm Cat theo phng phỏp tng hp a chiu v m rng khụng gian 63 3.2.2 xut hm nhiu chiu Cat-Hadamard 65 3.3 Phõn b chu k ca hm Cat-Hadamard 70 3.4 Tớnh ng hc ca hm Cat-Hadamard 74 3.4.1 Tớnh hn lon 74 3.4.2 Phõn phi thng kờ 76 3.4.3 Entropy 79 3.5 B to a ma trn MDS 80 3.5.1 xut thut toỏn tỡm kim a ma trn MDS kớch thc ì da trờn cỏc ma trn Cat m rng 85 3.5.2 Khụng gian tham s iu khin 87 3.5.3 Cỏc ma trn MDS hiu qu 89 iii 3.6 B to chui s gi ngu nhiờn 90 3.7 Kt lun chng 94 KT LUN 96 DANH MC CC CễNG TRèNH CễNG B CA LUN N 98 DANH MC CC T VIT TT Vit tt Tờn ting Anh AES Advanced Encryption Standard Chun mó húa tiờn tin ADC Average Distance Change Khong cỏch thay i trung Among Adjacent Bits bỡnh ca cỏc bit lõn cn Output bit Tiờu chun bit independence criterion u c lp BIC Tờn ting Vit Ciphertext Cipher text Vn bn c mó húa CBC Chaining Block Cipher Mt mó múc xớch CDR Cipher Difference Rate T l sai khỏc bn mó COT Ciphertext Only Attack Tn cụng ch bit bn mó CPA Chosen Plaintext Attack Tn cụng bn rừ chn sn CCA Chosen ciphertext Attack Tn cụng bn mó chn sn CNN Cellular Neural Network Mng N ron t bo DES Data Encryption Standard Chun mó húa d liu ECB Electronic Code Book Ch bng tra mó in t ECRYPT European Network of Mng li nghiờn cu Excellence for Cryptology v mt mó ti chõu u Fast Pseudo Hadamard Bin i gi Transform Hadamard nhanh IP Internet Protocol Giao thc liờn mng IoTs Internet of Things Mng li thit b FPHT kt ni Internet KPA Known Plaintext Attack iv Tn cụng bit v bn rừ LE Lyapunov Exponent S m Lyapunov LWC Lightweight Cryptography Mt mó hng nh MDS Maximum Distance Separable Ma trn phõn chia matrix khong cỏch ln nht MMDSG Multi-MDS matrix Generator B to a ma trn MDS NIST National Institute of Vin tiờu chun o lng Standards and Technology v cụng ngh quc gia Number of Changing T l thay i Pixel Rate s lng im nh Plaintext Plain text Bn rừ PRNG Pseudo Random Number B to chui s Generator gi ngu nhiờn S Sender Ngi gi SAC Strict avalanche criterion Tiờu chun thỏc cht SampEn Sample Entropy Giỏ tr Entropy mu SPN Substitution - Permutation Mng hoỏn v thay th NPCR Network SRAM Static random-access memory B nh tnh truy cp ngu nhiờn RFID Radio Frequency Identification Cụng ngh nhn dng bng súng vụ tuyn R Receiver Ngi nhn UACI Unified Averaged Mt thay i trung Changed Intensity bỡnh phõn b ng nht Danh sỏch hỡnh v Cỏc hỡnh thc tn cụng bo mt mng xiii Cỏc mc bo v mng thụng tin xiv Mụ hỡnh truyn tin mt xvi Bin i theo thi gian ri rc ca bin trng thỏi h Lorenz hn lon xxii Bin i theo thi gian ca bin xn vi hai iu kin to sai khỏc rt nh l x = 0.05 h Lorenz hn lon xxiii 1.1 Lc phõn nhỏnh ca hm Logistic 1.2 c tớnh ng hc phc ca hm Logistic tham s r tha iu kin hn lon r 3.828427 1.3 Mụ hỡnh thit k thut toỏn mt mó hn lon 12 1.4 S thit k phn cng 13 1.5 S h mt mó hn lon theo cu trỳc mng thay th - hoỏn v (SPN) 14 1.6 Thut toỏn mó húa nh RGB 15 1.7 B to khúa hn lon 19 1.8 u ca b to khúa hn lon sau 1000 ln ly mu 20 1.9 Hỡnh nh ca bn rừ v bn mó tng ng vi thut toỏn xut 21 1.10 So sỏnh lc phõn b mc xỏm ca cỏc cp nh rừ/mó 22 2.1 S m Lyapunov ca cỏc hm hn lon mt chiu ph thuc mt tham s c trng 30 2.2 th biờn v pha ca hm Skew Tent 31 2.3 phi tuyn ca cỏc S-box 35 2.4 Giỏ tr trung bỡnh ca ma trn ph thuc 36 2.5 Tiờu chun bit u c lp 37 2.6 Xỏc sut sai phõn ca cỏc S-box SK (X) c tớnh tng ng vi s ln lp khỏc 38 vi KT LUN Mt s kt qu t c ca Lun ỏn xut thut toỏn mt mó da trờn hn lon ri rc Trong ú, thay th cỏc chc nng h mt mó theo cu trỳc mng hoỏn v thay th bng h thng hn lon ri rc Da vo vic so sỏnh s ging v khỏc ca mt mó v mt mó hn lon, t ú xut cỏc h hn lon phự hp vi tiờu thit k v m rng h mt mó Nh l thay th khúa ti mi vũng lp l cỏc tham s iu khin ca h hn lon, cỏc bc lp ca h hn lon thay th quỏ trỡnh lp li ton b thut toỏn mt mó tng tớnh Confusion (ln xn, hn n) v tớnh Diffusion (khuch tỏn) nhm to cỏc s phc hoc che du gia bn rừ v bn mó, bn mó v khúa Lun ỏn cng xut mụ hỡnh thit k phn cng phự hp vi h mt mó hn lon Da trờn mụ hỡnh ny, cú th iu khin s vũng lp cõn bng thi gian thc thi vi hiu qu bo mt xut dựng hm hn lon cho mt mó hng nh ci thin cỏc nhc im v bo mt ca mt mó hng nh Bi toỏn thit k mt mó hng nh s dng hm hn lon ri rc nh l mt hng i mi ci thin thi gian thc thi v kh nng bo mt cho mt mó hng nh T cỏc phõn tớch chi tit v tớnh cht ca cỏc h hn lon mt chiu v hai chiu, Lun ỏn ó la chn h hn lon ri rc phự hp vi thit k mt mó hng nh xut hai thit k quan trng l thit k lp thay th S-box ì v thit k lp hoỏn v da trờn hai hm hn lon c bn l hm SKEW TENT v STANDARD, Lun ỏn ó chng minh hai thit k trờn l kh thi v mt thc thi v bo mt ỏp dng vo mụ hỡnh mt mó hng nh xut phng phỏp m rng hm Arnold Cat ri rc da trờn bin i gi Hadamard nhanh gi l hm Cat-Hadamard Phõn tớch cỏc c trng hn lon ca hm Cat-Hadamard nh s m Lyapunov ln nht, ỏnh giỏ ngu nhiờn tớn hiu u bng KS entropy hoc kim tra tớnh cht phõn 96 97 b u qua hm thng kờ Chi-bỡnh phng Kt qu t c l hm CatHadamard k tha hon ton cỏc c tớnh hn lon ca hm Cat hai chiu, ú cú th thay th hm Cat bi Cat-Hadamard cỏc ng dng mt mó Ngoi ra, phõn b chu k ca hm Cat-Hadamard 4-chiu c tớnh toỏn chi tit, kt qu thu c chu k nh nht ca hm Cat-Hadamard hu hn cú tham s iu khin bin thiờn, ln hn chu k ca hm Cat hai chiu Trong xut m rng hm Cat, mi quan h gia chu k chui Fibonacci gii hn bi phộp chia modulo bi mt s nguyờn t v chu k ca hm Cat-Hadamard ó c tỡm T ú, gim c phc ca thut toỏn tỡm chu k tng quỏt cho hm Cat m rng nhiu chiu Hm Cat m rng c s dng xut b to a ma trn MDS v b to chui s gi ngu nhiờn Lun ỏn xut cỏc hng phỏt trin tip theo nh sau Thut toỏn mt mó hn lon da trờn cu trỳc mng thay th-hoỏn v cú th iu khin tng gim s vũng lp cho tng hoc cho ton b thut toỏn lm tng gim phc thut toỏn, tỡm im iu khin ti u cú th tha hip gia phc tớnh toỏn, thi gian x lý v thc thi v bo mt ca h mt mó Ngoi xut hm mt chiu cho cỏc quỏ trỡnh thay th cú th ng dng cu trỳc mng Feistel Da vo ú a so sỏnh cỏc c tớnh bo mt ca hai mụ hỡnh ca mt mó l SPN v Feistel v ỏp dng vo cỏc mụ hỡnh bo mt trao i hoc lu tr thụng tin Mt m rng khỏc ca thut toỏn mt mó hn lon l nghiờn cu cỏc phng phỏp sinh khúa gi ngu nhiờn, to khụng gian khúa vụ hn cho cỏc hm hn lon tng khõu x lý ca thut toỏn Ngoi ra, ỏnh giỏ nng lc ca h mt mó hn lon thụng qua cỏc phng phỏp phõn tớch mó chun cng l mt hng nghiờn cu mi Nghiờn cu lp S-box múc xớch theo mụ hỡnh x lý song song ti u húa v mt thc thi Nghiờn cu tớnh cht hn lon ca cỏc h ng hc mt chiu, hai chiu vũng Galois (2n , +, ì) T ú a cỏc phng phỏp m rng hm hn lon nhiu chiu phự hp, tha chu k ca hm hn lon ri rc tỡm c l ln nht s nguyờn hu hn hoc Galois GF (2n ) DANH MC CC CễNG TRèNH CễNG B CA LUN N I: CC CễNG TRèNH LIấN QUAN TRC TIP N LUN N NG [C1 ] Ta Thi Kim Hue, Chu Van Lam, Thang Manh Hoang, S El Assad (2012), "Implementation of secure SPN chaos-based cryptosystem on FPGA", In Proceedings of the 12th IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), pp.129-134 [C2 ] Ta Thi Kim Hue, Thang Manh Hoang, Safwan El Assad (2013), "Design and Implementation of A Chaotic Cipher Block Chaining Mode for Image Encryption," In Proceedings of International Conference on Advanced Technologies for Communications (ATC), pp.185-190 [C3 ] Ta Thi Kim Hue, Thang Manh Hoang, Dat Tran (2014), "Chaos based S-box for Lightweight Block cipher," In Proceedings of International Conference on Communications and Electronics (ICCE), pp.572 - 577 [J1 ] Ta Thi Kim Hue, Hoang Van Quan, Nguyen Minh Quang (2013), "A method of creating block cipher using discretized chaotic map," The Journal of Military Science and Technology, Special Issue 05-2013, ISSN 1859 -1043, pp.34-46 [J2 ] Ta Thi Kim Hue, Thang Manh Hoang, An Braeken, Kris Steenhaut (2016), "Design of the Chaos-Based Diffusion Layer for Lightweight Block Cipher," Journal of Science and Technology, ISSN 2354-1083, Vol 113, pp.8692 [J3 ] Ta Thi Kim Hue, Thang Manh Hoang, An Braeken, Kris Steenhaut (2017), "On construction of Multi-Maximum Distance Separable (MDS) matrix generator based on Cat matrices,"(ISI) Optik - International Journal for Light and Electron Optics, Volume 131, February 2017, Pages 454466 98 99 [J4 ] Ta Thi Kim Hue, Thang Manh Hoang (2017), "Complexity and properties of a multidimensional Cat-Hadamard map for pseudo random number generation,"(ISI) EPJ ST Special Issue: Aspects of Statistical Mechanics and Dynamical Complexity, doi:10.1140/epjst/e2016-60401-7, 31 January 2017, Print ISSN 1951-6355 II: CC CễNG TRèNH LIấN QUAN TRC TIP N LUN N ANG CH KT QU PHN BIN [J5 ] Ta Thi Kim Hue, Thang Manh Hoang, An Braeken, Kris Steenhaut (2016), "Key-Dependent Permutation Layer Based on Two Dimensional Discretised Chaotic Maps for Lightweight Block Ciphers," Journal of Cryptologia (Submitted) Ti liu tham kho [1] Adams, C and S Tavares (1990) The structured design of cryptographically good s-boxes Journal of Cryptology (1), 2741 [2] Aihara, K (2012) Chaos and its applications Procedia IUTAM 5, 199 203 [3] Arroyo, D., G Alvarez, S Li, C Li, and V Fernandez (2009) Cryptanalysis of a new chaotic cryptosystem based on ergodicity International Journal of Modern Physics B 23 (05), 651659 [4] Arroyo, D., G Alvarez, S Li, C Li, and J Nunez (2008) Cryptanalysis of a discrete-time synchronous chaotic encryption system Physics Letters A 372 (7), 10341039 [5] Arroyo, D., J Diaz, and F B Rodriguez (2013) Cryptanalysis of a one round chaos-based substitution permutation network Signal Processing 93 (5), 1358 1364 [6] Arroyo, D., C Li, S Li, G Alvarez, and W A Halang (2009) Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm Chaos, Solitons & Fractals 41 (5), 26132616 [7] Aubry, S and G Abramovici (1990) Chaotic trajectories in the standard map the concept of anti-integrability Physica D: Nonlinear Phenomena 43 (23), 199219 [8] Baptista, M (1998) Cryptography with chaos Physics Letters A 240 (1), 5054 [9] Barreto, P and V Rijmen (2000) The khazad legacy-level block cipher Primitive submitted to NESSIE 97 [10] Bassham III, L E., A L Rukhin, J Soto, J R Nechvatal, M E Smid, E B Barker, S D Leigh, M Levenson, M Vangel, D L Banks, et al (2010) Sp 100 101 800-22 rev 1a a statistical test suite for random and pseudorandom number generators for cryptographic applications National Institute of Standards & Technology, [11] Biham, E and A Shamir (1993) Differential Cryptanalysis of the Data Encryption Standard London, UK, UK: Springer-Verlag [12] Boccaletti, S., C Grebogi, Y.-C Lai, H Mancini, and D Maza (2000) The control of chaos: Theory and applications Physics Reports 329, 2000 [13] Bogdanov, A., L R Knudsen, G Leander, C Paar, A Poschmann, M J Robshaw, Y Seurin, and C Vikkelsoe (2007) Present: An ultra-lightweight block cipher In International Workshop on Cryptographic Hardware and Embedded Systems, pp 450466 Springer [14] Borghoff, J., A Canteaut, T Gă uneysu, E B Kavun, M Knezevic, L R Knudsen, G Leander, V Nikov, C Paar, C Rechberger, et al (2012) Princea low-latency block cipher for pervasive computing applications In International Conference on the Theory and Application of Cryptology and Information Security, pp 208225 Springer [15] Bruen, A A., M A Forcinito, A G Konheim, C Cobb, A Young, M Yung, and D Hook (1996) Applied cryptography: protocols, algorithms, and source code in c [16] Brumley, D and D Boneh (2005) Remote timing attacks are practical Computer Networks 48 (5), 701716 [17] Chee, C Y and D Xu (2006) Chaotic encryption using discrete-time synchronous chaos Physics Letters A 348 (3), 284292 [18] Chen, F., X Liao, K.-w Wong, Q Han, and Y Li (2012) Period distribution analysis of some linear maps Communications in Nonlinear Science and Numerical Simulation 17 (10), 38483856 [19] Chen, F., K.-W Wong, X Liao, and T Xiang (2013) Period distribution of the generalized discrete arnold cat map for n = 2e IEEE Transactions on Information Theory, Acoustics Speech and Signal Processing 59 (5), 3249 3255 102 [20] Chen, F., K.-w Wong, X Liao, and T Xiang (2014) Period distribution of generalized discrete arnold cat map Theoretical Computer Science 552, 1325 [21] Chen, G., Y Chen, and X Liao (2007) An extended method for obtaining s-boxes based on three-dimensional chaotic baker maps Chaos, Solitons & Fractals 31 (3), 571 579 [22] Chen, G., Y Mao, and C K Chui (2004a) A symmetric image encryption scheme based on 3d chaotic cat maps Chaos, Solitons & Fractals 21 (3), 749761 [23] Chen, G., Y Mao, and C K Chui (2004b) A symmetric image encryption scheme based on 3d chaotic cat maps Chaos, Solitons & Fractals 21 (3), 749761 [24] Chen, W., J Zhuang, W Yu, and Z Wang (2009) Measuring complexity using FuzzyEn, ApEn, and SampEn Medical Engineering & Physics 31 (1), 6168 [25] Cui, T., C Jin, and Z Kong (2015) On compact cauchy matrices for substitution-permutation networks IEEE Transactions on Computers 64 (7), 20982102 [26] Daemen, J., L Knudsen, and V Rijmen (1997) The block cipher square In International Workshop on Fast Software Encryption, pp 149165 Springer [27] Daemen, J and V Rijmen (2001) The wide trail design strategy In IMA International Conference on Cryptography and Coding, pp 222238 Springer [28] Daemen, J and V Rijmen (2002) Security of a wide trail design In International Conference on Cryptology in India, pp 111 Springer [29] Daemen, J and V Rijmen (2013) The design of Rijndael: AES-the advanced encryption standard Springer Science & Business Media [30] Dam Thanh, P and C Pham Thuong (2015) Adaptive synchronization of chaotic sc-cnn with uncertain state template Mathematical Problems in Engineering 2015 103 [31] DEDIEU, H and M OGORZALEK (2000) Chaos-based signal processing International Journal of Bifurcation and Chaos 10 (04), 737748 [32] Detombe, J and S E Tavares (1993) Constructing large cryptographically strong s-boxes In Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology, ASIACRYPT 92, London, UK, UK, pp 165181 Springer-Verlag [33] Dyson, F J and H Falk (1992) Period of a discrete cat mapping The American Mathematical Monthly 99 (7), 603614 [34] Eisenbarth, T., S Kumar, C Paar, A Poschmann, and L Uhsadel (2007) A survey of lightweight-cryptography implementations IEEE Design & Test of Computers 24 (6), 522533 [35] El Assad, S., H Noura, and I Taralova (2008) Design and analyses of efficient chaotic generators for crypto-systems In World Congress on Engineering and Computer Science 2008, WCECS08 Advances in Electrical and Electronics Engineering-IAENG Special Edition of the, pp 312 IEEE [36] Elumalai, R and A R Reddy (2011) Improving diffusion power of aes rijndael with 8x8 mds matrix International Journal of Scientific & Engineering Research (3) [37] Falcioni, M., L Palatella, S Pigolotti, and A Vulpiani (2005) Properties making a chaotic system a good pseudo random number generator Physical Review E 72 (1), 016220 [38] Ferguson, N and B Schneier (2003) Practical Cryptography (1 ed.) New York, NY, USA: John Wiley & Sons, Inc [39] Forrộ, R (1990) The strict avalanche criterion: Spectral properties of boolean functions and an extended definition In Proceedings on Advances in Cryptology, CRYPTO 88, New York, NY, USA, pp 450468 Springer-Verlag New York, Inc [40] Fridrich, J (1998) Symmetric ciphers based on two-dimensional chaotic maps International Journal of Bifurcation and chaos (06), 12591284 104 [41] Gao, S and A Lauder (2002) Hensel lifting and bivariate polynomial factorisation over finite fields Mathematics of Computation 71 (240), 1663 1676 [42] Gilmore, R and M Lefranc (2002) The topology of chaos: Alice in stretch and squeezeland Chichester: Wiley [43] Gonchenko, S V., I I Ovsyannikov, and J C Tatjer (2014) Birth of discrete lorenz attractors at the bifurcations of 3d maps with homoclinic tangencies to saddle points Regular and Chaotic Dynamics 19 (4), 495505 [44] Gong, Z., S Nikova, and Y W Law (2011) Klein: a new family of lightweight block ciphers In International Workshop on Radio Frequency Identification: Security and Privacy Issues, pp 118 Springer [45] Grassi, G and S Mascolo (2002) A systematic procedure for synchronizing hyperchaos via observer design Journal of Circuits, Systems, and Computers 11 (01), 116 [46] Guan, Z.-H., F Huang, and W Guan (2005) Chaos-based image encryption algorithm Physics Letters A 346 (1), 153157 [47] Guo, J., T Peyrin, and A Poschmann (2011) The photon family of lightweight hash functions In Annual Cryptology Conference, pp 222239 Springer [48] Guo, J., T Peyrin, A Poschmann, and M Robshaw (2011) The led block cipher In International Workshop on Cryptographic Hardware and Embedded Systems, pp 326341 Springer [49] Gupta, K C and I G Ray (2014) On constructions of circulant mds matrices for lightweight cryptography In International Conference on Information Security Practice and Experience, pp 564576 Springer [50] Henderson, H V., F Pukelsheim, and S R Searle (1983) On the history of the kronecker product Linear and Multilinear Algebra 14 (2), 113120 [51] Hilborn, R (2000, December) Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers Oxford University Press, USA 105 [52] Houlrik, J and M Jensen (1993) Theory and applications of coupled map lattices Wiley [53] Jeong, K., H Kang, C Lee, J Sung, S Hong, and J I Lim (2015) Weakness of lightweight block ciphers mcrypton and led against biclique cryptanalysis Peer-to-Peer Networking and Applications (4), 716732 [54] Just, W (1995) Bifurcations in globally coupled map lattices Journal of statistical physics 79 (1-2), 429449 [55] Katagi, M and S Moriai (2008) Lightweight cryptography for the internet of things Sony Corporation, 710 [56] Katz, J and Y Lindell (2007) Introduction to Modern Cryptography (Chapman & Hall/Crc Cryptography and Network Security Series) Chapman & Hall/CRC [57] Kelsey, J., B Schneier, D Wagner, and C Hall (1998) Cryptanalytic attacks on pseudorandom number generators In International Workshop on Fast Software Encryption, pp 168188 Springer [58] Keyvanpour, M and F Merrikh-Bayat (2011) An effective chaos-based image watermarking scheme using fractal coding Procedia Computer Science 3, 8995 [59] Kitsos, P and O Koufopavlou (2004) Efficient architecture and hardware implementation of the whirlpool hash function IEEE Transactions on Consumer Electronics 50 (1), 208213 [60] Knudsen, L., G Leander, A Poschmann, and M J Robshaw (2010) Printcipher: a block cipher for ic-printing In International Workshop on Cryptographic Hardware and Embedded Systems, pp 1632 Springer [61] Kocarev, L (2001) Chaos-based cryptography: a brief overview IEEE Circuits and Systems Magazine (3), 621 [62] Kocarev, L and S Lian (2011) Chaos-based Cryptography: Theory, Algorithms and Applications (1st ed.) Springer Publishing Company, Incorporated 106 [63] Kocarev, L., J Szczepanski, J M Amigo, and I Tomovski (2006, June) Discrete chaos-i: Theory IEEE Transactions on Circuits and Systems I: Regular Papers 53 (6), 13001309 [64] Koeune, F., J.-J Quisquater, and J.-J Quisquater (1999) A timing attack against rijndael [65] KOTULSKI, Z., J SZCZEPANSKI, K GểRSKI, A PASZKIEWICZ, and A ZUGAJ (1999) Application of discrete chaotic dynamical systems in cryptography dcc method International Journal of Bifurcation and Chaos 09 (06), 11211135 [66] Langville, A N and W J Stewart (2004) The kronecker product and stochastic automata networks Journal of computational and applied mathematics 167 (2), 429447 [67] Leander, G and A Poschmann (2007) On the Classification of Bit SBoxes, pp 159176 Berlin, Heidelberg: Springer Berlin Heidelberg [68] LEcuyer, P (1994) Uniform random number generation Annals of Operations Research 53 (1), 77120 [69] Li, Y and M Wang (2016) On the construction of lightweight circulant involutory mds matrices In Fast Software Encryption [70] Lian, S., J Sun, and Z Wang (2005a) A block cipher based on a suitable use of the chaotic standard map Chaos, Solitons & Fractals 26 (1), 117 129 [71] Lian, S., J Sun, and Z Wang (2005b) Security analysis of a chaos-based image encryption algorithm Physica A: Statistical Mechanics and its Applications 351 (2), 645661 [72] Lorenz, E N (1963) Deterministic nonperiodic flow Journal of the Atmospheric Sciences 20 (2), 130141 [73] Malik, M Y and J.-S No (2011) Dynamic mds matrices for substantial cryptographic strength IACR Cryptology ePrint Archive 2011, 177 [74] Massey, J L., G H Khachatrian, and M K Kuregian (2000) Nomination of safer++ as candidate algorithm for the new european schemes for signatures, 107 integrity, and encryption (nessie) Primitive submitted to NESSIE by Cylink Corp, [75] Masuda, N and K Aihara (2002) Cryptosystems with discretized chaotic maps Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on 49 (1), 2840 [76] Masuda, N., G Jakimoski, K Aihara, and L Kocarev (2006, June) Chaotic block ciphers: from theory to practical algorithms IEEE Transactions on Circuits and Systems I: Regular Papers 53 (6), 13411352 [77] Matsui, M (1993) Linear cryptanalysis method for des cipher In Workshop on the Theory and Application of of Cryptographic Techniques, pp 386397 Springer [78] Mishra, B K., V A Bharadi, B Nemade, M M Potey, C Dhote, and D H Sharma (2016) Proceedings of international conference on communication, computing and virtualization (icccv) 2016 homomorphic encryption for security of cloud data Procedia Computer Science 79, 175 181 [79] Nejati, H., A Beirami, A G Sahebi, and W H Ali (2013, Aug) Variability analysis of tent map-based chaotic-map truly random number generators In 2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS), pp 157160 [80] Ohtsubo, J (2013) Chaos Control and Applications, pp 329351 Berlin, Heidelberg: Springer Berlin Heidelberg [81] Paar, C., A Poschmann, and M Robshaw (2008) New designs in lightweight symmetric encryption In RFID Security, pp 349371 Springer [82] Patidar, V., N Pareek, G Purohit, and K Sud (2011) A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption Optics Communications 284 (19), 43314339 [83] Pesin, Y B (1997) Dimension theory in dynamical systems : contemporary views and applications Chicago lectures in mathematics series Chicago: University of Chicago Press [84] Peterson, G (1997) Arnolds cat map Math45-Linear algebra 108 [85] Phuong, D T and P T Cat (2014) Finite time control of chaotic cellular neural network with uncertain parameters Applied Mathematical Sciences (68), 33933403 [86] Poschmann, A., G Leander, K Schramm, and C Paar (2007) New lightweight crypto algorithms for rfid In 2007 IEEE International Symposium on Circuits and Systems, pp 18431846 IEEE [87] Poschmann, A Y (2009) Lightweight cryptography: cryptographic engineering for a pervasive world In PH D THESIS Citeseer [88] Powell, P D (2011) Calculating determinants of block matrices arXiv preprint arXiv:1112.4379 [89] Rannou, F (1974) Numerical study of discrete plane area-preserving mappings Astronomy and Astrophysics 31, 289 [90] Richman, J S and J R Moorman (2000) Physiological time-series analysis using approximate entropy and sample entropy American Journal of Physiology - Heart and Circulatory Physiology 278 (6), H2039H2049 [91] Rijmen, V., J Daemen, B Preneel, A Bosselaers, and E De Win (1996) The cipher shark In Fast Software Encryption, pp 99111 Springer [92] Ruelle, D (1989) Chaotic evolution and strange attractors, Volume Cambridge University Press [93] Saarinen, M.-J O (2012) Cryptographic Analysis of All ì 4-Bit S-Boxes, pp 118133 Berlin, Heidelberg: Springer Berlin Heidelberg [94] Sajadieh, M., M Dakhilalian, H Mala, and B Omoomi (2012) On construction of involutory mds matrices from vandermonde matrices in gf (2 q) Designs, Codes and Cryptography 64 (3), 287308 [95] Schneier, B (1995) Applied Cryptography (2Nd Ed.): Protocols, Algorithms, and Source Code in C New York, NY, USA: John Wiley & Sons, Inc [96] Schneier, B., J Kelsey, D Whiting, D Wagner, C Hall, and N Ferguson (1998) Twofish: A 128-bit block cipher NIST AES Proposal 15 [97] Shannon, C E (1949) Communication theory of secrecy systems Bell system technical journal 28 (4), 656715 109 [98] Sharmila, D and R Neelaveni (2009) A proposed safer plus security algorithm using fast walsh hadamard transform for bluetooth technology International Journal of Wireless & Mobile Networks (IJWMN) (2) [99] Skrobek, A (2008) Approximation of a chaotic orbit as a cryptanalytical method on baptistas cipher Physics Letters A 372 (6), 849859 [100] Solak, E (2011) Cryptanalysis of Chaotic Ciphers, pp 227256 Berlin, Heidelberg: Springer Berlin Heidelberg [101] SOLAK, E., C C OKAL, O T YILDIZ, and T BIYIKOGLU (2010) Cryptanalysis of fridrichs chaotic image encryption International Journal of Bifurcation and Chaos 20 (05), 14051413 [102] Sprott, J C (2003) Chaos and time-series analysis Oxford, New York: Oxford University Press [103] St Denis, T (2004) Fast pseudo-hadamard transforms Technical report, Cryptology ePrint Archive, Report 2004-010 [104] Stallings, W (2002) Cryptography and Network Security: Principles and Practice (3rd ed.) Pearson Education [105] Standaert, F.-X., G Piret, N Gershenfeld, and J.-J Quisquater (2006) Sea: A scalable encryption algorithm for small embedded applications In International Conference on Smart Card Research and Advanced Applications, pp 222236 Springer [106] Strogatz, S H (1994) Nonlinear dynamics and chaos : with applications to physics, biology, chemistry, and engineering Studies in nonlinearity Cambridge (Mass.): Westview Press Autre(s) tirage(s) : 2000 [107] Suzaki, T., K Minematsu, S Morioka, and E Kobayashi (2012) Twine: A lightweight block cipher for multiple platforms In International Conference on Selected Areas in Cryptography, pp 339354 Springer [108] Svanstrăom, F (2014) Properties of a generalized arnolds discrete cat map http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-35209 [109] Szczepanski, J., J M Amigo, T Michalek, and L Kocarev (2005, Feb) Cryptographically secure substitutions based on the approximation of mixing 110 maps IEEE Transactions on Circuits and Systems I: Regular Papers 52 (2), 443453 [110] Tang, G and X Liao (2005) A method for designing dynamical s-boxes based on discretized chaotic map Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena 23 (5), 19011909 [111] Tang, W K and Y Liu (2011) Formation of high-dimensional chaotic maps and their uses in cryptography In Chaos-Based Cryptography, pp 99 136 Springer [112] Wall, D (1960) Fibonacci series modulo m The American Mathematical Monthly 67 (6), 525532 [113] Wang, Y., K.-W Wong, C Li, and Y Li (2012) A novel method to design s-box based on chaotic map and genetic algorithm Physics Letters A 376 (67), 827 833 [114] Webster, A F and S E Tavares (1986) On the Design of S-Boxes, pp 523534 Berlin, Heidelberg: Springer Berlin Heidelberg [115] Wong, K.-W., B S.-H Kwok, and W.-S Law (2008) A fast image encryption scheme based on chaotic standard map Physics Letters A 372 (15), 26452652 [116] Wu, X and Z.-H Guan (2007) A novel digital watermark algorithm based on chaotic maps Physics Letters A 365 (5), 403406 [117] Wu, Y., S Member, J P Noonan, L Member, S Agaian, and S Member (2011) Npcr and uaci randomness tests for image encryption In Cyber Journals: Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT) [118] Xu, G., G Zhao, and L Min (2009, July) A method for designing dynamical s-boxes based on discrete chaos map system In Communications, Circuits and Systems, 2009 ICCCAS 2009 International Conference on, pp 876880