Curriculum Vitae

Bo-Yin Yang


Research Fellow, Institute of Information Science, Academia Sinica.
2006.8- 2011.1:
Associate Research Fellow, IIS, Academia Sinica

1992.8- 2006.7:
Associate Professor of Mathematics, Tamkang University.
  • Granted retroactive promotion to full Professor, effective 2006.2, before my departure.
  • Tamkang University Research Award 2000 and 2005.

1992.1- 1992.7:
Postdoc, Institute of Mathematics, Academia Sinica.

Contact Information:
Institute of Information Science, Academia Sinica.
128 Section 2 Academia Road, Taipei 115, Taiwan.
Tel: +886-(0)2-27883799#1731. FAX:-(0)2-27824814.

E-Mail: by at, byyang at

February 14, 1969 in Princeton, New Jersey, USA
National Taiwan University B.S. Physics 1987
Massachusetts Institute of Technology Ph.D. Applied Mathematics 1991
    (Prof. Richard Stanley, thesis advisor)  

Current Research Interest:
Cryptography, Analysis of Algorithms, Combinatorics.

  • Academia Sinica Investigator Award 2015-19.
  • Academia Sinica Career Development Award 2010-14.
  • National Science Council Excellent Young Research Investigator Grant 2011-14.

Program Committees:
Indocrypt'06. {PQCrypto, ISC}'08. {PQCrypto, Africacrypt, Pairings}'10. {ICICS, Indocrypt}'11. {CT-RSA, SHARCS, SPACE}'12. {PQCrypto, CHES, SPACE, WISA}'13. {CHES, PQCrypto}'14. {SAC, ProvSec}'15. {PQCrypto, SAC}'16. {ACNS, PQCrypto, SAC}'17
Conference Organization:
PQCrypto Steering Comm since 2008, PQCrypto 2011 PC Chair,
Asiacrypt 2014 organizer, PKC 2016 PC co-Chair, CHES 2017, General co-Chair.
Editorial Boards:
IACR TCHES (Transactions on Cryptographic Hardware and Embedded Systems), 2018.

Invited Talks:
Dec'05, Beijing, Chinese Acad. Sci.; Oct'08, Cincinnati, PQCrypto; Apr'09, TU Eindhoven; Oct'09, Berlin, SPEED-CC; Jan'10, San Francisco, AMS Joint Mathematics Meetings; Apr'10, Guangzhou, South China U. of Technology. Aug'10, CyLab, Carnegie-Mellon U.; Sep'11, CS UMinn; Nov'12, CyLab and Lorentz Center, Leiden, NL; Mar'13, System-Solving in Crypto, Fukuoka; Aug'13, SIAM AG'13, Ft. Collins, US.; Oct'13, CS UMinn; Dec'13, Kyushu U; Mar'14, NIST; Feb'15, Quantum-Resilient Crypto, Fukuoka; Aug'15: SIAM AG'15, Daejeon, KR.

Professional Visits:
  • 2007.9-2007.12: Winter'07 Taft Visiting Lecturer, U. of Cincinnati.
  • 2001.8-2002.7: Visiting Scholar, Department of Mathematics, MIT.

Jointly Supervised Students
with C.-M. Cheng:
  • UROPs (Undergraduate Research Opportunities): Michael Feng-Hao Liu (04-05); Chia-Hsin Chen (05-07); Anna Inn-Tung Chen and Frost Yu-Shuang Li (06-08).
  • M.S.: Kevin Hsieh-Chung Chen, Ming-Yang Chih and Tung Chou (08-10); Jarron Jie-Ren Shih (09-11); Yun-An Chang, Jong-Shian Wu (11-13); Wen-Ding Li (13-15); Will Wei-Cheng Wang (14--).
  • Ph.D.: Ming-Shing Chen (09-), Po-Chun Kuo (10-), Shang-Yi Yang (14-16)
with T. Lange:
Ruben F. Niederhagen (09-12, Ph.D.).

Here is a list of my research papers in a PDF file. Questions to b y @ m o s c i t o . o r g.

Journal or Formally Refereed Conference Articles
LNCS is the series of Lecture Notes in Computer Science by Springer-Verlag, EI.
  1. D. J. Bernstein, B.-Y. Yang, Asymptotically faster quantum algorithms to solve multivariate quadratic equations, accepted to PQCrypto 2018.

  2. R. Niederhagen and K.-C. Ning and B.-Y. Yang, Implementing Joux-Vitse's Crossbred Algorithm for Solving MQ Systems on GPUs, accepted to PQCrypto 2018.

  3. M.-S. Chen, W.-D. Li, B.-Y. Peng, B.-Y. Yang, C.-M. Cheng, Implementing 128-bit Secure MPKC Signatures, IEICE Transactions vol. E101-A(2018) No. 3, pp. 553-569.

  4. M.-H. Tsai, B.-Y. Wang, B.-Y. Yang, Certified Verification of Algebraic Properties on Low-Level Mathematical Constructs in Cryptographic Programs, proc. ACM CCS 2017 (24th ACM Conference on Computer and Communications Security, Dallas, TX, USA, Oct. 30-Nov. 3), pp. 1973-1987.

  5. A. Petzoldt, M.-S. Chen, J. Ding, and B.-Y. Yang, HMFEv - An Efficient Multivariate Signature Scheme, PQCrypto 2017 (Utrecht, the Netherlands, Jun. 26-28), LNCS 10346, pp. 205-223.

  6. S.-Y. Yang, P.-C. Kuo, - and C.-M. Cheng, Gauss Sieve Algorithm on GPUs, CT-RSA 2017 (San Francisco, Feb. 14-17), LNCS 10159, pp. 39-57.

  7. B.-Y. Peng, Y.-C. Hsu, Y.-J. Chen, D.-C. Chueh, C.-M. Cheng, and B.-Y. Yang, Multi-core FPGA Implementation of ECC with Homogeneous Co-Z Coordinate Representation, CANS 2016, (Milan, Italy, Nov. 14-16), LNCS 10052, pp. 637–647.

  8. A. Petzoldt, M.-S. Chen, B.-Y. Yang, C. Tao, J. Ding: Design Principles for HFEv- Based Multivariate Signature Schemes, Asiacrypt 2015 (Auckland, New Zealand, Nov. 29-Dec. 3), LNCS 9452, pp. 311-334.

  9. Y.-A. Chang, M.-S. Chen, J.-S. Wu and B.-Y. Yang, Postquantum SSL/TLS for Embedded Systems, IoTS workshop at IEEE SOCA 2014 (Matsue, Japan, Nov. 17-19).

  10. R. Fitzpatrick, C. Bischof, J. Buchmann, Ö. Dagdelen, F. Göpfert, A. Mariano, B.-Y. Yang, Tuning Gauss Sieve for Speed, Latincrypt 2014 (3rd Latin American Conference on Cryptography and Information Security, Florianopolis, Brazil, Sept. 17-19), LNCS 8895, pp. 288-305.

  11. Y.-F. Chen, C.-H. Hsu, H.-H. Lin, P. Schwabe, M.-H. Tsai, B.-Y. Wang, B.-Y. Yang, and S.-Y. Yang, Verifying Curve25519 Software, presented at ACM CCS 2014 (21st ACM Conference on Computer and Communications Security, Scottsdale, Arizona, USA, Nov. 3-7, 2014).

  12. Y.-A. Chang, W.-C. Hong, M.-C. Hsiao, B.-Y. Yang, A.-Y. Wu and C.-M. Cheng, Hydra: An energy-efficient programmable cryptographic coprocessor supporting elliptic-curve pairings over fields of large characteristics, IWSEC 2014 (The 9th International Workshop on Security, Hirosaki, Japan, Aug. 27-29, 2014), LNCS 8639, pp. 174-186.

  13. J. Y.-C. Yeh, C.-M. Cheng, B.-Y. Yang, Operating Degrees for XL vs. \ensuremath{\mathbf{F_4/F_5}} for Generic \ensuremath{\cal
MQ} with Number of Equations Linear in That of Variables, Number Theory and Cryptography Workshop 2013 (November 21-22, TU Darmstadt, Germany), LNCS 8260, pp. 19-33.

  14. C. Bouillaguet, C.-M. Cheng, T. Chou, R. Niederhagen and B.-Y. Yang, Fast Exhaustive Search for Quadratic Systems in F 2 on FPGAs, SAC 2013 (20th workshop on Selected Areas in Cryptography, Aug. 14-16, Simon Fraser University, Burnaby, BC, Canada); LNCS 8282, pp. 205-222. Current version at ePrint 2014/436.

  15. M.-S. Chen, C.-M. Cheng, B.-Y. Yang, RAIDq: A software-friendly, multiple-parity RAID, USENIX HotStorage 2013 (USENIX Federated Workshops, June 27-28, San Jose, CA, USA).

  16. J. Ding, B.-Y. Yang, Degree of Regularity for HFEv and HFEv-, PQCrypto 2013 (5th Post-Quantum Cryptography Workshop, June 4-6, Limoges, France), LNCS 7932, pp. 52-66.

  17. J.-R. Shih, Y. Hu, M.-C. Hsiao, M.-S. Chen, W.-T. Shen, B.-Y. Yang, and C.-M. Cheng, Securing M2M with Post-Quantum Public-Key Cryptography, IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 3:1(2013), pp. 106-116.

  18. T. Chou, C.-M. Cheng, R. Niederhagen, and B.-Y. Yang, Solving Quadratic Equations with XL on Parallel Architectures, CHES 2012 (14th workshop on Cryptographic Hardware and Embedded Systems, September 9-12, Leuven, Belgium), LNCS 7428, pp. 356-373.

  19. C.-H. Yu and B.-Y. Yang, Probabilistically Correct Secure Arithmetic Computation for Modular Conversion, Zero Test, Comparison, MOD and Exponentiation, to appear at SCN 2012 (8th Conference on Security and Cryptography for Networks, September 5-7, Amalfi, Italy), LNCS 7485, pp. 426-444.

  20. S. Tanaka, T. Chou, B.-Y. Yang, C.-M. Cheng, K. Sakurai: Efficient Parallel Evaluation of Multivariate Quadratic Polynomials on GPUs, WISA 2012 (13th Workshop on Information Security Applications, August 16-18, Jeju Island, Korea), LNCS 7690, pp. 28-42.

  21. D. J. Bernstein, N. Duif, T. Lange, P. Schwabe, and B.-Y. Yang, High-speed high-security signatures, Journal of Cryptographic Engineering 2:2(2012), pp. 77-89. Earlier version presented at CHES 2011 (13th Workshop on Cryptographic Hardware and Embedded Systems, September 28 - October 1, Nara, Japan), LNCS 6917, pp. 124-142. Also ePrint 2011/368.

  22. P. Schwabe, S.-Y. Yang, and B.-Y. Yang, SHA-3 on ARM11 processors, Africacrypt 2012 (July 10-12, Ifrane, Morocco), LNCS 7374, pp. 324-341.

  23. F.-H. Liu, Y.-J. Huang, and B.-Y. Yang, Public-Key Cryptography from New Multivariate Quadratic Assumptions, PKC 2012 (15th International Workshop for Public Key Cryptography, IACR, May 21-23, Darmstadt, Germany), and LNCS 7293, pp. 190-205.

  24. P.-C. Kuo, M. Schneider, Ö. Dagdelen, J. Reichelt, J. Buchmann, C.-M. Cheng, and B.-Y. Yang, Extreme Enumeration on GPU and in Clouds, CHES 2011 (ibid.), pp. 176-191.

  25. D. J. Bernstein, H.-C. Chen, C.-M. Cheng, T. Lange, R. Niederhagen, P. Schwabe, and B.-Y. Yang, ECC2K-130 on NVIDIA GPUs, Indocrypt 2010 (December 13-15, Hyperabad, India) LNCS 6498, pp. 328-344.

  26. K.-M. Chung, F.-H. Liu, C.-J. Lu, and B.-Y. Yang, Efficient String-Commitment from Weak Bit-Commitment, Asiacrypt 2010 (December 5-9, Singapore), LNCS 6477, pp. 268-282.

  27. C. Bouillaguet, H.-C. K. Chen, C.-M. Cheng, T. Chou, R. Niederhagen, A. Shamir, and B.-Y. Yang, Fast Exhaustive Search for Polynomial Systems in F 2 , CHES 2010 (12th Workshop on Cryptographic Hardware and Embedded Systems, August 17-20, UC Santa Barbara), LNCS 6225, pp. 203-218.

  28. Y.-H. Lin, A. Studer, Y.-H. Chen, H.-C. Hsiao, E. L.-H. Kuo, J. Lee, J. McCune, K.-H. Wang, M. Krohn, A. Perrig, B.-Y. Yang, H.-M. Sun, and P.-L. Lin, SPATE: Small-group PKI-less Authenticated Trust Establishment, IEEE Trans on Mobile Computing 9:12(2010), pp. 1666-1681 (SCI). [Note: Extended from #32 as invited paper of IEEE Trans. TMC.]

  29. C.-I Lee, T.-C. Wu, B.-Y. Yang and W.-G. Tzeng, New Secure Broadcasting Scheme Realizing Information Granularity, J. of Info. Sci. and Eng., 26:4(2010) pp. 1509-1523.

  30. H.-C. Hsiao, Y.-H. Lin, A. Studer, C. Studer, K.-H. Wang, H. Kikuchi, A. Perrig, H.-M. Sun, B.-Y. Yang, A Study of User-Friendly Hash Comparison Schemes, pp. 105-114, Proc. ACSAC 2009 (December 7-11, Honolulu).

  31. A. I.-T. Chen, M.-S. Chen, T.-R. Chen, C.-M. Cheng, J. Ding, E. L.-H. Kuo, F. Y.-S. Lee, and B.-Y. Yang, SSE Implementation of Multivariate PKCs on Modern x86 CPUs, CHES 2009 (11th Workshop on Cryptographic Hardware and Embedded Systems, Sept. 6-9, Lausanne, Switzerland), pp. 33-48, LNCS 5747.

  32. Y.-H. Lin, A. Studer, H.-C. Hsiao, J. McCune, K.-H. Wang, M. Krohn, P.-L. Lin, A. Perrig, H.-M. Sun, and B.-Y. Yang, SPATE: Small-group PKI-less Authenticated Trust Establishment, Proc. MobiSys 2009 (7th Int'l Conference on Mobile Systems, Applications, and Services, June 22-25, Wroclaw, Poland), pp. 1-14 (best paper).

  33. D. J. Bernstein, T.-R. Chen, C.-M. Cheng, T. Lange, and B.-Y. Yang, ECM on Graphics Cards, Eurocrypt 2009 (April 25-29, Köln, Germany) LNCS 5479, pp. 483-501.

  34. J. Baena, M.-S. Chen, C. Clough, J. Ding, and B.-Y. Yang, Square, a New Multivariate Encryption Scheme, CT-RSA 2009 (10th Cryptographer's Track RSA Conference, April 20-24, San Francisco), LNCS 5473, pp. 252-264.

  35. A. I.-T. Chen, C.-H. Chen, M.-S. Chen, C.-M. Cheng and B.-Y. Yang, Practical-Sized Instances of Multivariate PKCs: Rainbow, and $\ell$IC-derivatives, PQCrypto 2008 (Second Post-Quantum Cryptography Workshop, Oct. 17-19, Cincinnati, USA) and LNCS 5299, pp. 95-106.

  36. F.-H. Liu, C.-J. Lu, and B.-Y. Yang, Secure PRNGs from Specialized Polynomial Maps over Any F q , PQCrypto'08 and LNCS 5299 (ibid.), pp. 181-202.

  37. C.-H. Chen, C.-W. Chen, C. Kuo, Y.-H. Lai, J. McCune, A. Perrig, A. Studer, and B.-Y. Yang, GAnGS: Gather, Authenticate 'n Group Securely, Proc. MobiCom 2008 (14th Annual International Conference on Mobile Computing and Networking, ACM SigMobile, September 14-19, San Francisco), pp. 92-103.

  38. J. Ding, V. Dubois, B.-Y. Yang, C.-H. Chen, and C.-M. Cheng. Can SFLASH be Repaired?, ICALP 2008 (35th International Colloquium on Automata, Languages and Programming, July 6-13, Reykjavik, Iceland), LNCS 5126, pp. 691-701.

  39. J. Ding, B.-Y. Yang, C.-H. Chen, M.-S. Chen, and C.-M. Cheng, New Differential-Algebraic Attacks and Reparametrization of Rainbow, ACNS 2008 (6th Applied Cryptography and Network Security Conference, June 3-6, New York, USA), LNCS 5037, pp. 242-257. Updates at ePrint 2008/108.

  40. J. Ding and B.-Y. Yang, Multivariate Polynomials for Hashing, Inscrypt 2007, Aug. 31-Sep. 5, Xining, China, LNCS 4990, pp. 358-371.

  41. B.-Y. Yang, C.-H. Chen, D. J. Bernstein, and J.-M. Chen, Analysis of QUAD, FSE 2007 (14th International Workshop for Fast Software Encryption, IACR, Mar. 26-28, Luxemberg City, Luxemberg), LNCS 4593, pp. 290-307.

  42. J. Ding, C. Wolf, and B.-Y. Yang, $\ell$-Invertible Cycles for Multivariate Quadratic Public Key Cryptography, PKC 2007 (10th International Workshop for Public Key Cryptography, IACR, Apr. 21-24, Beijing, China), LNCS 4450, pp. 266-281. [Prior version at Post-Quantum Crypto Workshop '06, KU Leuven, Belgium.]

  43. W. Yan, B.-Y. Yang, and Y.-N. Yeh, The Behavior of Wiener Indices and Polynomials of Graphs under Five Graph Operators, Appl. Math. Lett. 20(2007) pp. 290-295.

  44. I. Gutman, W. Yan, B.-Y. Yang, and Y.-N. Yeh, Generalized Wiener Indices of Zigzagging Pentachains, J. Math. Chem. 42:2(2007) pp. 103-117.

  45. B.-Y. Yang, C.-M. Cheng, B.-R. Chen, and J.-M. Chen, Implementing Minimized Multivariate Public-Key Cryptosystems on Low-Resource Embedded Systems, SPC 2006 (3rd Security of Pervasive Computing Conference, Apr. 18-21, York, UK) LNCS 3934, pp. 73-88.

  46. L.-C. Wang, B.-Y. Yang, Y.-H. Hu, and F.-P. Lai, A ``Medium-Field'' Multivariate Public-Key Encryption Scheme, CT-RSA 2006 (7th Cryptographer's Track RSA Conference, Feb. 13-17, San Jose CA), LNCS 3860, pp. 132-149.

  47. S.-P. Eu, B.-Y. Yang, and Y. Yeh, Computing the Generalized Wiener Indices of Hex Chains, Int'l J. of Quant. Chem. 106(2006), pp. 426-435 .

  48. B.-Y. Yang and J.-M. Chen, Building Secure Tame-Like Multivariate Public-Key Cryptosystems: the New TTS, ACISP 2005 (10th Australasian Conference on Info. Sec. and Privacy, July 4-6, Brisbane), LNCS 3574, pp. 518-531.

  49. B.-Y. Yang and J.-M. Chen, All in the XL Family: Theory and Practice, ICISC 2004 (7th International Conference on Information Security and Cryptology, Dec. 2-3, Seoul, Korea), LNCS 3506, pp. 67-86.

  50. L.-C. Wang, Y.-H. Hu, F.-P. Lai, C.-Y. Chou, and B.-Y. Yang, Tractable Rational Map Signature, PKC 2005 (8th Int'l Workshop for Public-Key Cryptography, IACR, Jan. 26-28, Diablerets, Switzerland), LNCS 3386, pp. 244-257.

  51. B.-Y. Yang, J.-M. Chen, and N. Courtois, On Asymptotic Security Estimates in XL and Gröbner Bases-Related Algebraic Cryptanalysis, ICICS 2004 (6th International Conference on Information and Communications Security, Oct. 27-29, Malaga, Spain), LNCS 3269, pp. 401-413.

  52. B.-Y. Yang, J.-M. Chen, and Y.-H. Chen, TTS: High-Speed Signatures on a Low-Cost Smart Card, CHES 2004 (6th Workshop on Cryptographic Hardware and Embedded Systems, IACR, Aug. 11-13, Boston MA); LNCS 3156, pp. 371-385.

  53. B.-Y. Yang and J.-M. Chen, Theoretical Analysis of XL over Small Fields, ACISP 2004 (9th Australasian Conference on Info. Sec. and Privacy, July 13-15, Sydney); LNCS 3108, pp. 277-288.

  54. B.-Y. Yang and Y. Yeh, Wiener Polynomials of some Chemically Interesting Graphs, International J. of Quantum Chem. 99:2(2004), pp. 80-91.

  55. B.-Y. Yang and Y. Yeh, A Crowning Moment for Wiener Indices, Studies in Applied Mathematics, 112(2004), pp. 333-340.

  56. J.-M. Chen and B.-Y. Yang, A More Secure and Efficacious TTS Signature Scheme, ICISC 2003 ( 6th Int'l Conference on Info. Sec. & Cryptology, Nov. 27-28, Seoul, Korea), LNCS 2971, pp. 320-338.

  57. H.-K. Hwang, B.-Y. Yang, and Y. Yeh, Presorting algorithms: an average-case point of view, Theo. Comp. Sci. 242(2000), no. 1-2, pp. 29-40.

  58. W.-C. Huang, B.-Y. Yang, and Y. Yeh, From Ternary Strings to Wiener indices of Benzenoid Chains, Discrete Appl. Math. 73(1997), pp. 113-131. (SCI)

  59. I-W. Huang, B.-Y. Yang, and Y. Yeh, Wiener Indices of Hex Carpets-- from Hexagon Models to Square Grids, SE Asia Bull. of Math. 20(1996), pp. 81-102.

  60. B.-Y. Yang, and Y. Yeh, Zigging and Zagging in Pentachains, Adv. in Appl. Math. 16(1995) pp. 72-94. (SCI)

Conference Articles without Journal Proceedings, Books/Book Chapters, Tech Reports
  1. M.-S. Chen, B.-Y. Yang, and D. Smith-Tone, PFLASH - secure asymmetric signatures on smart cards. NIST Lightweight Cryptography Workshop 2015 tone-paper.pdf.
  2. D. J. Bernstein, S. Josefsson, T. Lange, P. Schwabe and B.-Y. Yang, EdDSA for more curves, IACR e-Print Archive,

  3. B.-Y. Yang, ed., Post-Quantum Cryptography, Proc. 4th Post-Quantum Cryptography Workshop, Nov. 29-Dec. 2, 2011, Taipei, Taiwan, LNCS 7071, Springer, ISBN 978-3-642-25404-8.

  4. L. Goubin, J. Patarin, and B.-Y. Yang, Multivariate Cryptosystems, pp. 824-828, in Encyclopedia of Cryptography and Security, H. van Tillborg and S. Jajodia, eds., Springer 2011, ISBN 978-1-4419-5905-8.

  5. D. J. Bernstein, H.-C. Chen, M.-S. Chen, C.-M. Cheng, C.-H. Hsiao, Z.-C. Lin, T. Lange, and B.-Y. Yang, The 1 Billion-Mulmod Personal Computer, Presented at SHARCS 2009 (Sept. 9-10, Lausanne, Switzerland).

  6. J. Ding, B.-Y. Yang, F. Werner, C.-H. Chen, M.-S. Chen, Odd-Field Multivariate Hidden Field Equations, poster at Eurocrypt 2009, ePrint 2008/543.

  7. J. Ding and B.-Y. Yang, Multivariate Public-Key Cryptography, chapter in Post-Quantum Cryptography, pp. 193-241, D. J. Bernstein, J. Buchmann and E. Dahmen, eds., Springer 2009, ISBN: 978-3-540-88701-0.

  8. C.-H. Chen, B.-Y. Yang, and J.-M. Chen, Exploring the Limits of Lazard-Faugère Gröbner Bases Methods, PQCrypto'06 (First Post-Quantum Crypto Workshop), KU Leuven, Belgium.

  9. S.-Y. Wang, C.-S. Laih, and B.-Y. Yang, Partially Ordered Signature Schemes, TFIT'06 (third Taiwan-France Info Tech Conference, Mar. 28-30, Nancy, France).

  10. M. Bardet, J.-C. Faugère, B. Salvy, and B.-Y. Yang, Asymptotic Expansion of the Degree of Regularity for Semi-Regular Systems of Equations, MEGA '05 (8th Conférence des Méthodes Effectives en Géométrie Algebrique, May 27- June 1, Porto Conte, Sardinia, Italy); being re-edited for journal submission.

  11. B.-Y. Yang and J.-M. Chen, Cryptanalysis Today, Chap. 6 in Book 19 of the third Information and Communications Security Series, W.-G. Tzeng, ed., C-S. Laih, series editor, published by the National Science of Council of Taiwan, 2004.

  12. B.-Y. Yang and J.-M. Chen, XL: A Brief on the State of the Art, Best Paper Award, Chinese (Taipei) Cryptology and Info. Sec. Assoc. (CCISA) 2004 conference.

  13. J.-M. Chen, B.-Y. Yang, and B.-Y. Peng, Tame Transformation Signatures and Topsy-Turvy Hashes IWAP '02 (11/29-12/01, Taipei), pp. 93-100.

  14. B.-Y. Yang, and Y. Yeh, About Wiener Numbers and Polynomials, Sec. 5 in Lie Algebras, Rings and Related Topics: Proc. of Second International Tainan-Moscow Algebra Workshop (Tainan, 1997), pp. 203-226, Y. Fong, A. Mikhalev, and E. Zelmanov, eds., Springer-Verlag (Berlin) 2000.

  15. B.-Y. Yang, and Y. Yeh, Chains of Motley Gems and their Wiener Indices, in Proc. of First International Tainan-Moscow Algebra Workshop (Tainan, 1994), pp. 329-349, de Gruyter (Berlin), Y. Fong et al ed., De Gruyter (Berlin) 1996.

B.Y., b y @ m o s c i t o . o r g, b y y a n g @ i i s . s i n i c a . e d u . t w