### Publications

1. Toward an $\epsilon$-Approximation Scheme for Generalized Satisfiability, with K. Lieberherr, Proceedings of 1982 Princeton Conference on Information Sciences and Syetems (1982), 268-273.
2. A Hierarchical Compaction Algorithm with Low Page-Fault Complexity, with K. Steiglitz, Proc. MIT Conference on Advanced Research in VLSI (1984), 203-212.
3. On a Simple Primality Testing Algorithm, Proc. 1984 International Symposium on Symbolic and Algebraic Computation (ISSAC) (1984), 321-332.
4. Factorization of Polynomials over Finite Fields and Factorization of Primes in Algebraic Number Fields, Proc. 16th Annual ACM Symposium on Theory of Computing (STOC) (1984), 175-182.
5. Implications of Forbidden Structures for Extremal Algorithmic Problems, with K. Lieberherr, Journal of Theoretical Computer Science, 40 (1985), 195-210.
6. Riemann Hypothesis and Finding Roots over Finite Fields, Proc. 17th Annual ACM Symposium on Theory of Computing (STOC) (1985), 175-182.
7. Solving Some Graph Problems with Optimal or Near-Optimal Speedup on Mesh-of-Trees Networks, Proc. 26th Annual IEEE Symposium on the Foundations of Computer Science (FOCS) (1985), 232-240.
8. Recognizing Primes in Random Polynomial Time, with L.M. Adleman, Proc. 19th ACM Symposium on Theory of Computing (STOC) (1987), 462-469.
9. Network Complexity of Sorting and Graph Problems and Simulating CRCW PRAMS by Interconnection Networks, with A. Aggarwal, Proc. 1988 Aegean Workshop on Computing: 3rd International Workshop on Parallel Computation and VLSI Theory.
10. Secure and Verifiable Schemes for Election and General Distributed Computing Problems, with S.H. Teng, Proc. 7th Annual ACM Symp. on Principles of Distributed Computing (1988), 182-196.
11. A Universal Problem in Secure and Verifiable Distributed Computation, with S.H. Teng, 1988 CRYPTO Conference.
12. Simplifying Nested Radicals and Solving Polynomials by Radicals in Minimum Depth, with Gwoboa Horng, Proc. 31st IEEE Annual Symp. on Foundations of Computer Science (FOCS) (1990), 847-856.
13. Security, Verifiability, and Universality in Distributed Computing, with S.H. Teng, Journal of Algorithms, 11 (1990), 492-521.
14. Factorization of Polynomials over Finite Fields and Decomposition of Primes in Algebraic Number Fields, Journal of Algorithms, 12 (1991), 482-489.
15. Generalized Riemann Hypothesis and Factoring Polynomials over Finite Fields, Journal of Algorithms, 12 (1991), 464-481.
16. Efficient Algorithms for the Riemann-Roch Problem and Addition in the Jacobian of a Curve with Applications, with D. Ierardi, Proc. 32nd IEEE Annual Symp. on Foundations of Computer Science (FOCS) (1991), 678-687.
17. Primality Testing and Two Dimensional Abelian Varieties over Finite Fields, with L. M. Adleman, monograph in Springer-Verlag Lecture Note Series in Mathematics 1512 (142 pages), 1992.
18. Counting Rational Points on Curves over Finite Fields, with D. Ierardi, Proc. 34th IEEE Annual Symp. on Foundations of Computer Science (FOCS) (1993), 616-625.
19. A Subexponential Algorithm for Discrete Logarithms over the Rational Subgroup of the Jacobian of Large Genus Hyperelliptic Curves over Finite Fields, with L.M. Adleman and J, DeMarrais, Proc. First Int'l Symp. on Algorithmic Number Theory (ANTS-I) (1994), 28-40.
20. Efficient Algorithms for the Riemann-Roch Problem and for Addition in the Jacobian of a Curve, with D. Ierardi, Journal of Symbolic Computation, 18 (1994), 519-539.
21. Efficient Program Checkers for Number Theoretical Computations, with L. M. Adleman and K. Kompella, Information and Computation, 121, (1995), 93-102.
22. Interpolation of Sparse Multivariate Polynomials over Large Finite Fields with Applications, with A.J. Rao, Proc. 7th ACM-SIAM Symp. on Discrete Algorithms (SODA), (1996), 508-517.
23. Counting Rational Points on Curves and Abelian Varieties over Finite Fields, with L.M. Adleman, Proc. Second Int'l Algorithmic Number Theory Symposium (ANTS-II), (1996), 1-16.
24. Solving Systems of Polynomial Congruences Modulo a Large Prime, with Y.C. Wong, Proc. 37th IEEE Annual Symp. on Foundations of Computer Science (FOCS) (1996), 115-124.
25. Quantum Computability, with L.M. Adleman and J. DeMarrais, Siam J. Computing, 26, (1997), 1523-1539
26. Counting Points on Curves over Finite Fields, with D. Ierardi, Journal of Symbolic Computation, 25, (1998), 1-21.
27. Extended Hilbert Irreducibility and Applications, with Y.C. Wong, Proc. 9th ACM-SIAM Symp. on Discrete Algorithms (SODA), (1998) , 50-58.
28. A Black-Box Approach to the Algebraic Set Decomposition Problem, with A. Rao, Proc. 1998 ACM Symp. on Theory of Computing (STOC), (1998), 497-506.
29. An Algorithm for Approximate Counting of Points on Algebraic Sets over Finite Fields, with Y.C. Wong, Algorithmic Number Theory, Third Int'l Symp., (ANTS-III), (1998), 514-527.
30. Solving Polynomials by Radicals with Roots of Unity in Minimum Depth, with G. Horng, Mathematics of Computation, 68, (1999), 881-885.
31. A Subexponential Algorithm for Discrete Logarithms over the Jacobians of Large Genus Hyperelliptic Curves over GF($q$), with L.M. Adleman and J, DeMarrais, Journal of Theoretical Computer Science, 226, (1999), 7-18.
32. A Function Field Sieve Method for Discrete Logarithms over Finite Fields, with L.M. Adleman, Journal of Information and Computation, 151, No. 1/2, (1999), 5-16.
33. Interpolation of Sparse Multivariate Polynomials over Large Finite Fields with Applications, with A.J. Rao, J. Algorithms, 33, (1999), 204-228.
34. Some Computational Problems of Cryptographic Significance Concerning Elliptic Curves over Rings, with C. Xing, Journal of Information and Computation, 151, No. 1/2, (1999), 92-99.
35. Solvability of Systems of Polynomial Congruences Modulo a Large Prime, with Y.C. Wong, Journal of Computational Complexity, 8, (1999), 227-257.
36. Function Field Sieve Method for Discrete Logarithms over Finite Fields, with L.M. Adleman, Proc. AMS Conf. on Applications of Curves over Finite Fields, AMS Contemporary Mathematics Series, 245, (1999), 133-143.
37. Extended Hilbert Irreducibility and Applications, with Y.C. Wong, J. Algorithms, 37, (2000), 121-145.
38. Factoring Polynomials over Finite Fields and Stable Colorings of Tournaments, with Qi Cheng, Proc. 4th Int'l Symp. on Algorithmic Number Theory (ANTS-IV), 233-246, 2000.
39. Lifting Elliptic Curves and Solving the Elliptic Curve Discrete Logarithm Problem, with K.L. Kueh and K.-S. Tan, Proc. 4th Int'l Symp. on Algorithmic Number Theory (ANTS-IV), 377-384, 2000.
40. Running time and program size for self-assembled squares, with L. Adleman and Q. Cheng and A. Goel, ACM Symp. on Theoey of Computing (STOC), 2001.
41. Linear Self-Assemblies: Equilibria, Entropy, and Convergence Rates, with L. Adleman, Q. Cheng, A. Goel, and H. Wasserman, Proc. 6th International Conference on Difference Equations and Applications (ICDEA).
42. Combinatorial optimization problems in self-assembly, with L. Adleman, Q. Cheng, A. Goel, D. Kempe, P. Moisset, and P. Rothemund, Proc. ACM Symp. on Theory of Computing (STOC), 2002.
43. On counting and generating curves over small finite fields, with Q. Cheng, J. Complexity, 20/2-3, (2004), 284-296.
44. Deciding whether the $p$-torsion group of the $Q_p$-rational points of an elliptic curve is non-trivial, with I. Burhanuddin, ACM SIGSAM Bulletin, Vol 38, No. 3, 96-98, 2004.
45. Invadable Self-Assembly: Combinig Robustness with Efficiency, with H. Chen Q. Cheng, A. Goel, and P. Moisset, Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), 890-899, 2004.
46. On partial lifting and the elliptic curve discrete logarithm problem, with Q. Cheng, Proc.15th Annual Symposium on Algorithms and Computation (ISAAC) 2004.
47. On partial lifting and the elliptic curve discrete logarithm problem, with Q. Cheng, J. Algorithmica, 59-68, V46, No. 1, 2006.
48. Signature Calculus and Discrete Logarithm Problems, with W. Raskind, Algorithmic Number Theory, 7th Int'l Symp., (ANTS-VII), F. Hess, S. Pauli, M. Pohst (Eds.), Berlin, Germany, 558-572, LNCS 4076, Springer, July, 2006.
49. On the Extended Iterative Proportional Scaling Algorithm, with Q. Luo, Proc. International workshop on Symbolic-Numeric Computation (SNC 2005), Xi'an, China, 2005. Symbolic-Numeric Computation Series: Trends in Mathematics, Dongming Wang and Lihong Zhi (Eds.), Chapter 18, 288-303, Birkhuser Press, 2007.
50. Global Duality, Signature Calculus and the Discrete Logarithm Problem, with W. Raskind, JCM, London Mathematical Society, 228-263, Vol. 12, 2009.
51. Folded Algebraic Geometric Codes From Galois Extensions, with Anand Narayanan, Proc. 9th Int'l Conf. on Finite Fields and their Applications (Fq9), AMS Contemporary Mathematics Series, ed. by G. Mullen. 2010
52. Local Duality and the discrete logarithm problem, Proc. International Workshop on Coding and Cryptology (IWCC 2011), Springer-Verlag LNCS 6639, 213-222, 2011.
53. A Multilinedar Generalization of the Tate Pairing, with W. Raskind, Proc. 9th Int'l Conf. on Finite Fields and their Applications (Fq 9), AMS Contemporary Mathematics Series, ed. by G. Mullen, 2010
54. Elliptic curves with large Shafarevich-Tate groups, with I. A. Burhanuddin, J. Number Theory, 369-374, Vol. 133, Issue 2, 2013.
55. The Discrete logarithm problem from a local duality perspective, Science China Mathematics, 1421-1427, Vol. 56, No. 7, 2013.
56. On the Mathematics of the Law of Mass Action, with L. Adleman, M. Gopalkrishnan, and D. Reishus, Chapter 1 of A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations, Kulkarni, Vishwesh, Stan, Guy-Bart, Raman, Karthik (Eds.), 1-44, Springer, 2014.
57. On the Equation $y^2 = x^3-pqx$, with I.Burhanuddin, Journal of Numbers, (2014)
58. Computing Class Groups of Function Fields Using Stark Units, with A.K. Narayanan, Proc. 11th Int'l Conf. on Finite Fields and their Applications (Fq11), AMS Contemporary Mathematics Series, ed. by G. Mullen. 2015
59. Finding Primitive Elements in Finite Fields of Small Characteristic, with A.K. Narayanan, Proc. 11th Int'l Conf. on Finite Fields and their Applications (Fq11), AMS Contemporary Mathematics Series, ed. by G. Mullen. 2015
60. On $\mathfrak{p}$-adic Expansions of Algebraic Integers, with H.H. Chen, Proc. 2015 ACM International Symposium on Symbolic and Algebraic Computation (ISSAC) (2015), 109-116.
61. Last Fall Degree, HFE, and Weil Descent Attacks on ECDLP, with M. Kosters and S.L. Yeo, 2015 CRYPTO Conference.
62. Character Sums and Generating Sets, with L. Liu, Proc. 12th Int'l Conf. on Finite Fields and their Applications (Fq12), 2016
63. Constructing Small Generating Sets for the Multiplicative Groups of Algebras over Finite Fields, with L. Liu, Proc. 2016 ACM International Symposium on Symbolic and Algebraic Computation (ISSAC) (2016), 287-294.