Papers: (Most papers are in preprint versions, so they may be slightly different from the published versions.)
1. Shuhong Gao, Frank Volny IV and Mingsheng Wang, A New Algorithm for Computing Grobner Bases, Revised, July 2013. PDF file (307k)
2. Jang-Woo Park and Shuhong Gao, Dynamics of x+x^{-1} via elliptic curves, Revised, July 2011. PDF file (221K)
3. Mingfu Zhu, Guangran Jiang and Shuhong Gao, Solving the 100 Swiss Francs Problem, To appear in Mathematics in Computer Science. PDF file (254K)
4. Shuhong Gao, Yinhua Guan and Frank Volny IV, A New Incremental Algorithm for Computing Grobner Bases, ISSAC 2010, pp. 13--19. PDF file (168K)
5. Shuhong Gao and Todd Mateer, Additive Fast Fourier Transforms over Finite Fields, IEEE Transactions on Information Theory 56 (2010), 6265--6272. PDF file (164K)
6. Shuhong Gao and Raymond Heindl, Multivariate Public Key Cryptosystems from Diophantine Equations, preprint 2009 . PDF file (205K)
7. Shuhong Gao, Daqing Wan and Mingsheng Wang,  Primary decomposition of zero-dimensional ideals over finite fields, Mathematics of Computation, 78 (2009), 509--521. PDF file (154K)
8. Shuhong Gao and D. Frank Hsu, Short containers in Cayley graphs, Discrete Applied Mathematics, 157 (2009), 1354--1363.
9. Jessie F. Burkhart, Neil J. Calkin, Justine C. Hyde-Volpe, Shuhong Gao, Kevin James, Hiren Maharaj, Shelly Manber, Jared Ruiz and Ethan Smith, Finite field towers and elements of high order arising from modular curves, Designs, Codes and Cryptography, 51 (2009), 301--314.
10. Guantao Chen, Shuhong Gao and Zhiquan Hu,  Linked Graphs with Restricted Lengths, J. Combinatorial Theory, series B, 98 (2008), 735--751. PDF file (282K)
11. Shuhong Gao and Beth Novick,  Fault Tolerance of Cayley Graphs, Annals of Combinatorics, 11 (2007), 161--171. PDF file (186K)
12. Jeff Farr and Shuhong Gao, Gröbner bases and generalized Padé approximation, Mathematics of Computation, 75 (2006), 461-473. PSfile (424K) or PDF file (154K)
13. Jeff Farr and Shuhong Gao, Computing Grobner bases for vanishing ideals of finite sets of points, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC16), LNCS 3857, 2006, 118--127. PSfile (390K) or PDF file (144K)
14. Jeffrey B. Farr and Shuhong Gao,  Gröbner bases, Padé  approximation, and decoding of linear codes, Coding Theory and Quantum Computing, Contemporary Mathematics, vol.381, Amer. Math. Soc., Providence, RI, 3--18, 2005.    PSfile (404K) or PDF file (147K)
15. Shuhong Gao, Erich Kaltofen, John P. May, Zhengfeng Yang and Lihong Zhi,  Approximate factorization of multivariate polynomials via differential equations, in Proceedings of the 2004 international symposium on Symbolic and algebraic computation (ISSAC 2004, July 4-7, 2004,  University of Cantabria, Santander, Spain), pp. 167-174.  PSfile (232K) or PDF file (171K) Maple software available at Erich Kaltofen or Lihong Zhi
16. Joel V. Brawley and Shuhong Gao, On density of primitive elements for field extensions, preprint, 2004 (6 pages).  PSfile (280K) or PDF file (94K)
17. Shuhong Gao and Alan G.B. Lauder, Fast absolute irreducibility testing via Newton polytopes, preprint 2004 (14 pages). PSfile (273K) or PDF file (95K)
18. Fatima Abu Salem, Shuhong Gao and Alan G.B. Lauder, Factoring polynomials via polytopes, in Proceedings of the 2004 international symposium on Symbolic and algebraic computation (ISSAC 2004, July 4-7, 2004,  University of Cantabria, Santander, Spain), pp.  4-11.  PSfile (419K) or PDF file (231K)
19. Shuhong Gao, Virginia M. Rodrigues and Jeffrey Stroomer, Grobner basis structure of finite sets of points, preprint, 2003 (16 pages). PSfile (441K) or PDF file (166K)
20. Shuhong Gao, A new algorithm for decoding Reed-Solomon codes'', in Communications, Information and Network Security (V. Bhargava, H. V. Poor, V. Tarokh and S. Yoon, Eds.), Kluwer Academic Publishers, 2003, pp. 55-68.  (Correction: In Step 2 of Algorithm 1a,  (d+1)/2 should be (d-1)/2 as pointed out by Professor Sergei Fedorenko.)   PSfile (340K) or PDF file (118K)
21. Shuhong Gao and Virginia M. Rodrigues, Irreducibility of polynomials modulo p via Newton Polytopes'',  Journal of Number Theory 101 (2003), 32-47. PS file (411K) or PDF file (142K)
22. Richard P. Brent, Shuhong Gao and Alan G.B. Lauder, Random Krylov spaces over finite fields,'' SIAM J. on Discrete Mathematics 16 (2003), 276-287. PS file (340K) or PDF file (131K)
23. Shuhong Gao, Erich Kaltofen and Alan G.B. Lauder, Deterministic distinct degree factorization for polynomials over finite fields'', to appear in  Journal of Symbolic Computation (10 pages). PDF file (210K)
24. Shuhong Gao and D. Frank Hsu, Short containers in Cayley graphs'',  DIMACS tech report 2001-18, May 2001. (15 pages) PS file (336K) or PDF file (135K)
25. Shuhong Gao, Factoring multivariate polynomials via partial differential equations,''  Mathematics of Computation 72 (2003), 801-822. PS file (502K) or PDF file (201K)
26. Shuhong Gao and Alan G.B. Lauder, Hensel lifting and polynomial factorisation,'' Mathematics of Computation 71 (2002), 1663-1676. PS file (396K) or PDF file (150K)
27. Huapeng Wu, M. Anwar Hasan, Ian F. Blake and Shuhong Gao, Finite fields multiplier using redundant representation'', IEEE Transactions on Computers, vol. 51, no. 11, 2002, 1306-1316. PDF file (150K)
28. Joel V. Brawley, Shuhong Gao and Donald Mills, Associative Rational functions in two variables'',  in  Finite Fields and Their Applications  (D. Jungnickel and H. Niederreiter, Eds.), Springer-Verlag, 2001, 43-56. PS file (336K) or PDF file (120K)
29. Shuhong Gao, Abelian groups, Gauss periods, and normal bases,'' Finite Fields and Their Applications 7 (2001), 149-164. PS file (410K) or PDF file (151K)
30. Shuhong Gao, Absolute irreducibility of polynomials via Newton polytopes,'' J. of Algebra 237 (2001), 501-520. gzipped PS file (502K) or PDF file (200K)
31. Shuhong Gao, On the deterministic complexity of polynomial factoring,'' J. Symbolic Computation 31 (2001), 19-36. gzipped PS file (680k) or PDF file (238K)
32. Shuhong Gao and Alan G.B. Lauder, Decomposition of polytopes and polynomials,'' Discrete and Computational Geometry  26 (2001), 89-104. PS file (365K) or PDF file (133K)
33. Shuhong Gao, Joachim von zur Gathen, Daniel Panario and Victor Shoup, Algorithms for exponentiation in finite fields,'' J. Symbolic Computation 29 (2000), 879-889. PDF file (306K)
34. Shuhong Gao and M. Amin Shokrollahi, Computing roots of polynomials over function fields of curves,'' in Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory (D. Joyner, Ed.), Springer, 2000, 214-228. gzipped PS file (79K) or PDF file (212K)
35. Shuhong Gao, Elements of provable high orders in finite fields,'' Proc. American Math. Soc. 127  (1999), 1615-1623. PDF file (153K)
36. Shuhong Gao and Jason Howell, A general polynomial sieve,'' Designs, Codes and Cryptography 18 (1999), 149-157. gzipped PS file (504K) or PDF file (118K)
37. Shuhong Gao, Jason Howell and Daniel Panario, Irreducible polynomials of given forms,'' Contemporary Mathematics, vol. 225, Amer. Math. Soc., Providence, RI, 1999, 43-54. PS file (404K) or PDF file (146K)
38. Joel V. Brawley, Shuhong Gao and Donald Mills, Computing composed products of polynomials,'' Contemporary Mathematics, vol. 225, Amer. Math. Soc., Providence, RI, 1999, 1-15.
39. Shuhong Gao, Beth Novick and Ke Qiu, From Hall's matching theorem to optimal routing on hypercubes,'' J. Combinatorial Theory (B) 74 (1998), 291-301. PDF file (138K)
40. S. Gao and J. D. Key, Bases of minimum-weight vectors for codes from designs,'' Finite Fields and Their Applications  4 (1998), 1-15. PDF file (187k)
41. Shuhong Gao, Joachim von zur Gathen and Daniel Panario, Gauss periods: orders and cryptographical applications,'' Mathematics of Computation,  67 (1998), 343-352. gzipped PS file (46k)
42. Shuhong Gao and Daniel Panario, Density of normal elements,'' Finite Fields and Their Applications  3 (1997), 141--150. PS file (169k)
43. Shuhong Gao and Daniel Panario, Tests and constructions of irreducible polynomials over finite fields,'' Foundations of Computational Mathematics  (F. Cucker and M. Shub, Eds.), Springer, 346-361, 1997. PDF file (249k)
44. Ian F. Blake, Shuhong Gao and Ronald C. Mullin, Specific irreducible polynomials with linearly independent roots over finite fields'' Linear Algebra and Its Applications 253 (1997), 227--249. PDF file (157k)
45. Ian F. Blake, Shuhong Gao and Robert L. Lambert, Construction and distribution problems for irreducible trinomials over finite fields,'' in  Applications of Finite Fields (D. Gollmann, Ed.),  Oxford, Clarendon Press,  1996, 19-32. PS file (195k)
46. Shuhong Gao and Scott A. Vanstone, On orders of optimal normal basis generators,'' Mathematics of Computation 64 (1995), 1227--1233. PDF file (92k)
47. Shuhong Gao, Joachim von zur Gathen and Daniel Panario, Gauss periods and fast exponentiation in finite fields,'' in Lecture Notes in Computer Science, vol. 911, Springer-Verlag,  1995, 311--322.
48. Shuhong Gao and Gary L. Mullen, Dickson polynomials and irreducible polynomials over finite fields,'' J. Number Theory  49 (1994), 118-132.
49. Ian F. Blake, Shuhong Gao and Ronald C. Mullin, Normal and self-dual normal bases from factorization of cx q+1+dxq -ax -b,'' SIAM J. on Discrete Mathematics 7 (1994), 499-512. PDF file (141k)
50. Ian F. Blake, Shuhong Gao and Robert L. Lambert, Constructive problems for irreducible polynomials over finite fields,'' in Information Theory and Applications (A. Gulliver and N. Secord, eds), LNCS 793, Springer-Verlag, 1994, 1-23.
51. Shuhong Gao and Joachim von zur Gathen, Berlekamp's and Niederreiter's polynomial factorization algorithms,'' in Proc.  2nd International Conference on Finite Fields: Theory, Applications, and Algorithms, Las Vegas, 1993. Contemporary Mathematics, vol. 168,  1994, 101-116.
52. Ian F. Blake, Shuhong Gao and Ronald C. Mullin, Explicit factorization of x2^k +1 over Fp with prime $p \equiv 3 \bmod 4$,'' Applicable Algebra in Engineering, Communication and Computation 4 (1993), 89--94. PDF file (81k)
53. Shuhong Gao and Wan-Di Wei, On non-Abelian group difference sets,'' Discrete Mathematics 123 (1993), 151-177. PDF file (107k)
54. Wan-Di Wei, Shuhong Gao and Benfu Yang,Cyclic near difference sets of type 1,'' Discrete Mathematics 123 (1993), 151-177.
55. Shuhong Gao and Hendrik W. Lenstra, Jr., Optimal normal bases,'' Designs, Codes and Cryptography 2 (1992), 315-323. PDF file (85k)
56. Wan-Di Wei, Shuhong Gao and Qing Xiang, On extraneous multipliers of Abelian difference sets,'' Combinatorial Designs and Applications  (Huangshan, 1988, W. D. Wallis, H. Shen, W. Wei, L. Zhu, Eds.), Marcel Dekker, Inc., 1990, 165--173.
57. Shuhong Gao, On nonabelian group difference sets,'' Sichuan Daxue Xuebao 26 (1989), Special Issue, 136-139.
Books and Chapters:
1. Alfred J. Menezes (Editor), Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone and Tomic Yaghoobian, Applications of Finite Fields, Kluwer Academic Publishers, Boston/Dordrecht/Lancaster, 1993.
2. Mathematical Models in Classical Cryptology,'' in Applied Mathematical Modeling: A Multidisciplinary Approach , (D. R. Shier and K. T. Wallenius, Eds.), Chapman & Hall/CRC, Boca Raton, 2000, p. 93--113. (With Joel V. Brawley).
3. Mathematical Models in Public-key Cryptology,'' Applied Mathematical Modeling: A Multidisciplinary Approach , (D. R. Shier and K. T. Wallenius, Eds.), Chapman & Hall/CRC, Boca Raton, 2000, p. 93--113. (With Joel V. Brawley). HTML , gzipped PS file (522K) or PDF file (178K)