跳到主要內容

臺灣博碩士論文加值系統

(18.97.9.171) 您好!臺灣時間:2024/12/10 12:52
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:李仲益
研究生(外文):Li, Chung-Yi
論文名稱:小面積、高輸出率並長週期之非線性偽亂數產生器
論文名稱(外文):Hardware-Efficient, High-Throughput, and Long-Period Nonlinear Pseudo Random Number Generators
指導教授:張慶元張慶元引用關係
指導教授(外文):Chang, Tsin-Yuan
口試委員:謝明得杜其永陳竹一鄭桂忠劉靖家張慶元
口試日期:2011-6-22
學位類別:博士
校院名稱:國立清華大學
系所名稱:電機工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:77
中文關鍵詞:計算機算術多重遞迴產生器NIST SP 800-22測試下一個數的預測子偽亂數產生器混沌映射
外文關鍵詞:computer arithmeticmultiple recursive generatorNIST SP 800-22 test suitenext number predictorpseudo random number generatorchaotic map
相關次數:
  • 被引用被引用:0
  • 點閱點閱:417
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:1
1 Introduction 1
1.1 Importance of random number generators . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Previous works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Organization of this dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Literature Review 6
2.1 Linear Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Linear congruential generator(LCG) . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Multiple recursive generator (MRG) . . . . . . . . . . . . . . . . . . . . . 9
2.1.3 An Efficient MRG: DX generator . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Nonlinear PRNGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Quantization Error and short periods in digitized Chaos-based PRBGs . . 14
2.2.2 Remove short periods and enhance statistical properties . . . . . . . . . . 15
3 Proposed Reseeding-Mixing PRNG (RM-PRNG) 18
3.1 Nonlinear Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.1 Hardware reduction for implementing LGM . . . . . . . . . . . . . . . . . 20
3.1.2 Short periods of LGM in 32-bit precision . . . . . . . . . . . . . . . . . . 22
3.2 Reseeding Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Reseeding-period range selection . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.2 Selection of corresponding optimal fixed pattern . . . . . . . . . . . . . . 25
3.3 Vector Mixing Module and Hardware Implementation of RM-PRNG . . . . . . . 26
3.4 Results and comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.1 Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4.2 Statistical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.3 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 DX Generators with New Parameters and Proposed Security Issue of MRGs 40
4.1 DX Generators with New Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Predicting procedure for MRGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Security issue of MRGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5 Proposed Shuffle-Hiding PRNG (SH-PRNG) 48
5.1 Modified MRG for Better Security . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1.1 NNP for hiding method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.1.2 Shuffling method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.1.3 Proposed shuffle-hiding mechanism . . . . . . . . . . . . . . . . . . . . . . 52
5.2 Hardware Design and Numerical Simulations . . . . . . . . . . . . . . . . . . . . 54
5.2.1 Hardware design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2.2 Hardware savings for efficient MRGs . . . . . . . . . . . . . . . . . . . . . 55
5.2.3 Design of shuffle table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2.4 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2.5 Performance measures for selecting generators . . . . . . . . . . . . . . . . 60
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6 Conclusions and Future Research 65
[1] S. Callegari, R. Rovatti, and G. Setti, “Embeddable adc-based true random number generator
for cryptographic applications exploiting nonlinear signal processing and chaos,” IEEE
Trans. on Signal Processing, vol. 53, no. 2, pp. 793–805, feb. 2005.
[2] G. Tsudik, “Ya-trap: Yet another trivial rfid authentication protocol,” in Proc. of IEEE
Symp. on Pervasive Computing and Communications Workshops, 2006, pp. 640–643.
[3] D. H. Lehmer, “Mathematical methods in large-scale computing units,” in Proc. of the
Second Symp. on Large Scale Digital Computing Machinery. Cambridge, MA.: Harvard
University Press, 1951, pp. 141–146.
[4] J. Hastad and A. Shamir, “The cryptographic security of truncated linearly related variables,”
in Proc. of the 17th ACM Symposium on Theory of Computing. ACM, pp. 356–362.
[5] J. Boyar, “Inferring sequences produced by pseudo-random number generators,” J. the
Association for Computing Machinery, vol. 36, pp. 129–141, 1989.
[6] P. C. Wu, “Multiplicative, congruential random-number generators with multiplier ±2k1 ±
2k2 and modulus 2p − 1,” ACM Trans. on Mathematical Software, vol. 23, pp. 255–265,
1997.
[7] L. Y. Deng, “Efficient and portable multiple recursive generators of large order,” ACM
Trans. on Modeling and Computer Simulation, vol. 15, no. 1, pp. 1–13, Jan. 2005.
[8] P. L’Ecuyer and R. Simard, “Testu01: A C library for empirical testing of random number
generators,” ACM Trans. on Mathematical Software, vol. 33, no. 2, pp. 1–40, 2007.
[9] L. Blum, M. Blum, and M. Shub, “A simple unpredictable pseudo-random number generator,”
SIAM Journal on Computing, vol. 15, pp. 364–383, 1986.
[10] M. Bucci and R. Luzzi, “Fully digital random bit generators for cryptographic applications,”
IEEE Trans. on Circuits and Systems I: Fundamental Theory and Applications, vol. 55,
no. 3, pp. 861–875, 2008.
[11] D. E. Eastlake, S. D. Crocker, and J. I. Shiller, RFC 1750: Randomness recommendations
for security. Florida: Internet Society Request for Comments: Internet Engineering Task
Force, 1994.
[12] B. M. Gammel, R. Goettfert, and O. Kniffler, “An NLFSR-based stream cipher,” in Proc.
IEEE Int. Symp. on Circuits and Systems (ISCAS'06), 2006, pp. 2917–2920.
[13] G. Jakimoski and L. Kocarev, “Chaos and cryptography: Block encryption ciphers based
on chaotic maps,” IEEE Trans. on Circuits and Systems I: Fundamental Theory and Ap-
plications, vol. 48, no. 2, pp. 163–169, Feb. 2001.
[14] N. Masuda and K. Aihara, “Cryptosystems with discretized chatoic maps,” IEEE Trans.
on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 1, pp. 28–40,
Jan. 2002.
[15] X. J. Tong, M. G. Cui, and W. Jiang, “The production algorithm of pseudo-random number
generator based on compound non-linear chaos system,” in Proc. of IEEE Symp. on
Intelligent Information Hiding and Multimedia Signal Processing, Dec. 2006, pp. 685–688.
[16] N. Masuda, G. Jakimoski, K. Aihara, and L. Kocarev, “Chaotic block ciphers: From theory
to practical algorithms,” IEEE Trans. on Circuits and Systems I: Fundamental Theory and
Applications, vol. 53, no. 6, pp. 1341–1352, Jan. 2006.
[17] T. Addabbo, M. Alioto, A. Fort, A. Pasini, S. Rocchi, and V. Vignoli, “A class of maximumperiod
nonlinear congruential generators derived from the R´enyi chaotic map,” IEEE Trans.
on Circuits and Systems I: Fundamental Theory and Applications, vol. 54, no. 4, pp. 816–
828, Apr. 2007.
[18] T. Addabbo, M. Alioto, A. Fort, S. Rocchi, and V. Vignoli, “The digital tent map: Performance
analysis and optimized design as a low-complexity source of pseudorandom bits,”
IEEE Trans. on Instrumentation and Measurement, vol. 55, no. 5, pp. 1451–1458, Oct.
2006.
[19] ——, “Low-hardware complexity PRBGs based on a piecewise-linear chaotic map,” IEEE
Trans. on Circuits and Systems II: Express Briefs, vol. 53, no. 5, pp. 329–333, May 2006.
[20] C. Y. Li, J. S. Chen, and T. Y. Chang, “A chaos-based pseudo random number generator
using timing-based reseeding method,” in Proc. IEEE Int. Symp. on Circuits and Systems
(ISCAS'06), May 2006, pp. 3277–3280.
[21] C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos. Boca Raton,
FL: CRC Press, Inc., 2000.
[22] S. J. Li, G. R. Chen, and X. Q. Mou, “On the dynamical degradation of digital piecewise
linear chaotic maps,” Int. J. Bifurcation and Chaos, vol. 15, no. 10, pp. 3119–3151, 2005.
[23] S. J. Li and X. Zheng, “Cryptanalysis of a chaotic image encryption method,” in Proc.
IEEE Int. Symp. on Circuits and Systems (ISCAS'02), vol. 2, 2002, pp. 708–711.
[24] C. C. Chen, K. Yao, K. Umeno, and E. Biglieri, “Design of spread-spectrum sequences using
chaotic dynamical systems and ergodic theory,” IEEE Trans. on Circuits and Systems I:
Fundamental Theory and Applications, vol. 48, no. 9, pp. 1110–1114, 2001.
[25] H. P. Hu, Y. Xu, and Z. Zhu, “A method of improving the properties of digital chaotic
system,” Chaos, Solitons and Fractals, vol. 38, pp. 439–446, 2009.
[26] P. L’Ecuyer, “Good parameter sets for combined multiple recursive random number generators,”
Operations Research, vol. 47(1), pp. 159–164, 1999.
[27] P. L’Ecuyer, R. Simard, E. J. Chen, and W. D. Kelton, “An object-oriented randomnumber
package with many long streams and substreams,” Operations Research, vol. 50(6),
pp. 1073–1075, 2002.
[28] A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, E. Leigh, M. Levenson, M. Vangel,
D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom
number generators for cryptographic applications special publication 800-22,”
National Institute for Standards and Technology, Tech. Rep., 2008.
[29] J. D. Alanen and D. E. Knuth, “Tables of finite fields,” Sankhy¯a, vol. 26, pp. 305–328, 1964.
[30] D. E. Knuth, The Art of Computer Programming, 3rd ed. Reading, MA.: Addison-Wesley,
1998, vol. 2: Seminumerical Algorithms.
[31] P. L’Ecuyer and R. Simard, “Beware of linear congruential generators with multipliers of
the form a = ±2q±2r,” ACM Trans. on Mathematical Software, vol. 25, pp. 367–374, 1999.
[32] L. Y. Deng and H. Xu, “A system of high-dimensional, efficient, long-cycle and portable
uniform random number generators,” ACM Trans. on Modeling and Computer Simulation,
vol. 13, no. 4, pp. 299–309, 2003.
[33] L. Y. Deng, “Generalized mersenne prime number and its application to random number
generation,” in Monte Carlo and Quasi-Monte Carlo Methods 2002, H. Niederreiter, Ed.
Springer-Verlag, 2004, pp. 167–180.
[34] R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, revised ed.
Cambridge, MA.: Cambridge University Press, 1994.
[35] L. Y. Deng and D. K. J. Lin, “Random number generation for the new century,” American
Statistician, vol. 54, pp. 145–150, 2000.
[36] D. Mukhopadhyay, D. R. Chowdhury, and C. Rebeiro, “Theory of composing non-linear machines
with predictable cyclic structures,” in Proc. of 8th Int. Conf. on Cellular Automata
for Research and Industry (ACRI). Springer, 2008, pp. 210–219.
[37] D. Mukhopadhyay, “Group properties of non-linear cellular automata,” J. Cellular Au-
tomata (JCA), vol. 5, no. 1, pp. 139–155, Oct. 2009.
[38] J. Cermak, “Digital generators of chaos,” Physics Letters A, vol. 214, no. 3-4, pp. 151–160,
1996.
[39] T. Sang, R. Wang, and Y. Yan, “Perturbance-based algorithm to expand cycle length of
chaotic key stream,” Electronics Letters, vol. 34, no. 9, pp. 873–874, Apr. 1998.
[40] ——, “Clock-controlled chaotic keystream generators,” Electronics Letters, vol. 34, no. 20,
pp. 1932–1934, Oct. 1998.
[41] S. Li, X. Mou, and Y. Cai, “Pseudo-random bit generator based on couple chaotic systems
and its application in stream-ciphers cryptography,” in Progress in Cryptology (IN-
DOCRYPT 2001), Lecture Notes in Computer Science, vol. 2247, 2001, pp. 316–329.
[42] T. Stojanovski and L. Kocarev, “Chaos-based random number generators–Part I: analysis,”
IEEE Trans. on Circuits and Systems I. Fundamental theory and applications, vol. 48, no. 3,
pp. 281–288, Mar. 2001.
[43] H. L¨u, S. Wang, X. Li, G. T. J. Kuang, W. Ye, and G. Hu, “A new spatiotemporally
chaotic cryptosystem and its security and performance analyses,” Chaos, vol. 14, no. 3, pp.
617–629, Sep. 2004.
[44] P. Li, Z. Li, W. A. Halang, and G. Chen, “Analysis of a multiple-output pseudo-randombit
generator based on a spatiotemporal chaotic system,” Int. J. Bifurcation and Chaos,
vol. 16, no. 10, pp. 2949–2963, 2006.
[45] T. Addabbo, A. Fort, M. Mugnaini, S. Rocchi, and V. Vignoli, “On the efficient digital
implementation of nonlinear congruential generators derived from the R´enyi chaotic map,”
in Proc. IEEE Int. Conf. on Instrumentation and Measurement Technology, May 2008, pp.
1707–1711.
[46] F. Robert, Disctere iterations: a metric study. New York: Springer-Verlag, 1986, vol. 6.
[47] S. Hellebrand, J. Rajski, S. Tarnick, S. Venkataraman, and B. Courtois, “Built-in test for
circuits with scan based on reseeding of multiple-polynomial linear feedback shift registers,”
IEEE Trans. on Computers, vol. 44, no. 2, pp. 223–233, Feb. 1995.
[48] J. Lee and N. A. Touba, “LFSR-reseeding scheme achieving low-power dissipation during
test,” IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 26,
no. 2, pp. 396–401, Feb. 2007.
[49] C.-Y. Li, Y.-H. Chen, T.-Y. Chang, and J.-N. Chen, “A probabilistic estimation bias circuit
for fixed-width booth multiplier and its dct applications,” IEEE Trans. on Circuits and
Systems II: Express Briefs, vol. 58, no. 4, pp. 215–219, Apr. 2011.
[50] C. Y. Li, T. Y. Chang, and C. C. Huang, “An nonlinear PRNG using digitized Logistic
map with self-reseeding method,” in Proc. IEEE Int. Symp. on VLSI Design, Automation
and Test (VLSI-DAT), Apr. 2010, pp. 108–111.
[51] T. Sang, R. L. Wang, and Y. X. Yan, “Perturbance-based algorithm to expand cycle length
of chaotic key stream,” Electronics Letters, vol. 34, no. 9, pp. 873–874, Apr. 1998.
[52] M. Goresky and A. Klapper, “Periodicity and distribution properties of combined FCSR
sequences,” in Sequences and their applications (SETA06), ser. Lecture Notes in Computer
Science, vol. 4086, 2006, pp. 334–341.
[53] D. R. Stinson, Cryptography: Theory and Practice. Boca Raton, FL: Chapman and
Hall/CRC Press, 2006.
[54] L. Y. Deng, J. J. H. Shiau, and H. H. S. Lu, “Security enhancement on linear random
number generators via mutual shuffling,” University of Memphis and National Chiao Tung
University, Tech. Rep., 2011, preprint.
[55] M. D. MacLaren and G. Marsaglia, “Uniform random number generators,” J. the ACM,
vol. 12, pp. 83–89, 1965.
[56] C. Bays and S. D. Durham, “Improving a poor random number generator,” ACM Trans.
on Mathematical Software, vol. 2, pp. 59–64, 1976.
[57] M. Dichtl, “Cryptographic shuffling of random and pseudorandom sequences,” in Proc.
07021 of Dagstuhl Seminar on Symmetric Cryptography, 2007.
[58] P. L’Ecuyer and R. Touzin, “Fast combined multiple recursive generators with multipliers
of the form a = ±2q ± 2r,” in Proc. IEEE Winter Simulation Conference, J. A. Joines,
R. R. Barton, K. Kang, and P. A. Fishwick, Eds., 2000, pp. 683–689.
[59] J. Hastad and A. Shamir, “The cryptographic security of truncated linearly related variables,”
in Proc. of the 17th ACM Symposium on Theory of Computing. ACM, pp. 356–362.
[60] M. Blum and S. Micali, “How to generate cryptographically strong sequences of pseudorandom
bits,” SIAM Journal on Computing, vol. 13, pp. 850–864, 1984.
[61] D. E. Knuth, “Deciphering a linear congruential encryption,” IEEE Trans. on Information
Theory, vol. 31, pp. 49–52, 1985.
[62] H. Krawczyk, “How to predict congruential generators,” J. Algorithms, vol. 13, pp. 527–545,
1992.
77
連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top