Publications

Books

  • X. Wang, G. Xu, M. Wang, and X. Meng,  Mathematical Foundations of Public Key Cryptography, CRC Press, 2016.

Papers in Refereed Journals and Conferences

  • Z. Zheng, X. Wang, G. Xu, and Y. Yu (∂), Orthogonalized Lattice Enumeration for Solving SVP,  Science China, [Ser. F], (to appear).
  • G. Xu, On Solving a Generalized Chinese Remainder Theorem in the Presence of Remainder Errors,  Springer Proceedings in Math. & Stat. Series —Geometry, Algebra, Number Theory, and Their Information Technology Applications,  (to appear).
  • S. Musa and G. Xu, Fast Scalar Multiplication for Elliptic Curves over Binary Fields by Efficiently Computable Formulas,  IndoCrypt 2017, pp 206–225.
  • S. Huang, X. Wang, G. Xu, M. Wang, and J. Zhao (∂), Conditional Cube Attack on Reduced-Round Keccak Sponge Function,  Advances in Cryptology-EUROCRYPT 2017 II, pp 259-288.
  • Y. Yu, G. Xu, and X. Wang (∂), Provably Secure NTRU Instances over Prime Cyclotomic Rings, 20th International Conference on Practice and Theory of Public-Key Cryptography,  pp. 409-434, 2017.
  • Y. Wei, G. Xu, and Y. Zou, Dynamics of linear systems over finite commutative rings, Applicable Algebra in Engineering, Communication and Computing, 27(2016), 469–479.
  • W. Trost and G. Xu, On the Optimal Pre-Computation of Window τNAF for Koblitz Curves, IEEE Transactions on Computers, 65(2016), 2918-2924
  • K. Giuliani, V. K. Murty, G. Xu, Passwords Management via Split-key, Journal of Information Security, 7(2016), 206-214.
  • G. Xu and Z. Xu,Compressed Sensing Matrices from Fourier Matrices, IEEE Transactions on Information Theory, 61(2015), 469-478.
  • C. Tian, L. Han, and G. Xu (∂), A polynomial time algorithm for GapCVPP in  L1 norm, Science China, [Ser. F] , 57 (3)(2014), 1-7.
  • M. Liu, X. Wang, G. Xu, and X. Zheng,  A note on BDD problems with λ2 gap, Information Processing Letters, 114 (2014) 9-12.
  • C. Tian, M. Liu, and G. Xu (∂),  Measure inequalities and the transference theorem in the geometry of numbers, Proceedings of Amer. Math. Soc., 142(2014) 47-57.  
  • G. Xu and Z. Xu, On the l1 norm invariant convex k-sparse decomposition of signals, Journal of Operations Research Society of China, 1(2013), 537-541.
  • J. Zhang, J. Wang, G. Xu (∂), Predictive compressed-sensing for multislice/multiframe CT image reconstruction, SPIE conference– Medical Imaging, 2012
  • J. Zhang, J. Wang, G. Xu, and J. Thibault (∂), Compressed sensing algorithms for fan-beam CT image reconstruction, Optical Engineering, 51(2012)
  • T. Cai, L. Wang, and G. Xu, New bounds for Restricted Isometry constants, IEEE Transactions on Information Theory, 56(2010), 4388-4394.
  • L. Han, X. Wang, and G. Xu, On an Attack on RSA with Small CRT-Exponents, Science China, [Ser. F] , 53(2010), 1511-1518.
  • Cai, L. Wang, and G. Xu, Stable Recovery of Sparse Signals and an Oracle Inequality, IEEE Transactions on Information Theory, 56(2010), 3516-3522.
  • X. Mu, J. Zhang, W. Hu, T. Zhao, M. Fredette, and G. Xu (∂), Bibliographic Latent Semantic Analysis, International Journal of Information Technology, 6 (2010), 20-33.
  • T. Cai, L. Wang, and G. Xu, Shifting Inequality and Recovery of Sparse Signals, IEEE Transactions on Signal Processing, 58(2010), 1300-1308.
  • K. Jia, X. Wang, Z. Yuan, and G. Xu (∂), Distinguishing and Second-Preimage Attacks on CBC-like MACs, The 8th International Conference on Cryptology And Network Security, 2009, 349-361.
  • Z. Yuan, W. Wang, K. Jia, G. Xu, and X. Wang (∂),New Birthday Attacks on Some MACs Based on Block Ciphers, Advances in CryptologyCRYPTO, 2009, 209-230.
  • L. Han and G. Xu, Generalization of Some Attacks on RSA with Small Prime Combination and Small Private Exponent, 2009 IEEE Asia-Pacific Conference on Information Processing, 445 – 449.
  • D. Liang, G. Xu, H. Wang, K. King, D. Xu, and L. Ying (∂), Toeplitz random encoding MR imaging using compressed sensing, IEEE International Symposium on Biomedical Imaging, 2009, 270-273.
  • T. Cai, G. Xu, and J. Zhang, On Recovery of Sparse Signals via l1 Minimization, IEEE Transactions on Information Theory, 55(2009), 3388-3397.
  • G. Davida , B. Litow, and G. Xu, Fast Arithmetics Using Chinese Remaindering, Information Processing Letters, 109(2009), 660-662.
  • A. Dumitrescu, Cs. D. Tóth, and G. Xu, On  stars and Steiner stars, Discrete Optimization 6(2009), 224-332. [Note: this paper contains results of A. Dumitrescu, Cs. D. Tóth, and G. Xu, On  stars and Steiner stars II, SODA’09]
  • G. Xu and Y. Zou, Linear Dynamical Systems over Finite Rings, Journal of Algebra, 321(2009), 2149-2155.
  • M. Wang, X. Wang, G. Xu, and L. Han, Fast Scalar Multiplication on a Family of Supersingular Curves Over F2m, Proc. of INSCRYPT (short papers), 2008, 12-20.
  • V. K. Murty and G. Xu, Security of storage networks, Proceedings of the International Conference on Security and Cryptography, 2008, Porto/Portugal, 477-480.
  • I. F. Blake and V. K. Murty, and G. Xu,  Nonadjacent radix-τ expansions of integers in Euclidean imaginary quadratic number fields,  Canadian Journal of Mathematics, 60(2008), 1267-1282.
  • A. Dumitrescu and G. Xu, On  a query algorithm for a divisibility problem, ACM Communications in Computer Algebra,  41(2007), 122 -125.
  • A. Dumitrescu and G. Xu, On two representation problems with infinite multiplicity, JP Journal of Algebra, Number Theory and Applications, 9(2007) , 215-236.
  • I. F. Blake, V. K. Murty, and G. Xu, Refinements of Miller’s algorithm for computing the Weil/Tate pairing, Journal of Algorithms, 58(2006), 134-149.
  • V. K. Murty, and G. Xu,  Non-linear secret sharing and prime numbers, Discrete Mathematics and its Applications, editor: M. Sethumadhavan, Narosa, 2006, 1-11.
  • I. F. Blake, V. K. Murty, and G. Xu, A note on window τ-NAF algorithm, Information Processing Letters, 95(2005), no. 5, 496-502.
  • I. F. Blake, V. K. Murty, and G. Xu, Efficient algorithms for Koblitz curves over fields of characteristic three, Journal of Discrete Algorithms, 3(2005), 113-124.
  • G. Baranoski, J. Rokneand G. Xu, Virtual spectrophotometric measurements for biologically and physically based rendering,The Visual Computer, 17(2001), 506-518.
  • G. Baranoski, J. Rokneand G. Xu, Applying the exponential Chebyshev inequality to the nondeterministic computation of form factors, Journal of Quantitive Spectroscopy and  RadiactiveTransfer , 69(2001)447-467.
  • C. Chou, and G. Xu, The weak closure of the set of left translation operators, Proceedings of Amer. Math. Soc., 127 (1999) 465-471.
  • G. Xu, Herz-Schur multipliers and weakly almost periodic functions on locally compact groups, Transactions of Amer. Math. Soc., 349(1997) 2525-2536.
  • Z-J. Ruan, and G. Xu,  Splitting properties of operator bimodules and operator amenability of Kac algebras,   Proceedings of OT16,(1996), Romania, 193-216.
  • G. Xu, Amenability and uniformly continuous functionals on the algebras Ap(G) for discrete groups, Proceedings of Amer. Math. Soc.,123(1995) 3425-3429.
  • G. Xu, E-disjunctive inverse semigroups,Kexue Tongbao (Science Bulletin),  36(1991), 555, (Chinese).
  • G. Xu, Endomorphism semigroups of a finite distributive lattice, Journal of Xi’an JiaotongUniversity, 24(1990), no.3, 95-99, (Chinese).
  • G. Xu, and L. Zhang, The structures of quasimaxmal hypercodes and completely semiprime hypercodes, Adv. in Math.(Beijing), 17(1988), 408-412, (Chinese).
  • Y. Guo, G. Thierrin, and G. Xu, Disjunctive decomposition of languages, Theoret. Comput. Sci., 46(1986), no.1, 47-51.
  • Xu, Commutatively closed ideal languages and their primary decompositions, Kexue Tongbao (Science Bulletin), 31(1986), no.17, 1163-1166.
  • Y. Guo, L. Li, and G. Xu, The union decompositions of dense languages in terms of disjunctive languages, Acta Math. Sinica, 29(1986), no.2, 184-188 (Chinese).
  • Y. Guo, L. Li, and G. Xu,  On the disjunctive structure of dense languages,  Science China, Ser.A, 28(1985)1233-1238.
  • G. Xu, The Goldbach theorems for polynomials over a unique factorization domain,Journal of Lanzhou University, 20(1984)115-118, (Chinese).

Conference Presentations

  • G. Xu, Fourier Transform and Poisson Summation for Discrete Gaussian Measure on Lattices, International Workshop on Computational Harmonic Analysis, 2017, Nankai, Tianjin, China.
  • I. F. Blake, B. Li, and G.Xu, Protocol for sharing a product, Algebraic Methods in Cryptography, July, 2005, Beijing.
  • V. K. Murty, and G. Xu, A Tutorial on Elliptic Curve Cryptography,  Indocrypt Pre-conference tutorials, 2004.
  • G. Baranoski, J. Rokne and G. Xu,Virtual spectrophotometric measurements for biologically and physically-based rendering. Proceedings of the Eighth Pacific Conference on Computer Graphics and Applications, Hong Kong, 2000, pp. 398-399.
  • J. R. Cockett, and G. Xu, Decision procedures for distributive logic,  Foundational Methods in Computer Science,1999, Kananaskis, Canada
  • G. Xu, Amenability of diagonal groups and of Banach algebras on groups, Conference on Amenability of Groups and Related Function Spaces , 1997, Vancouver, Canada.
  • G. Xu, Multipliers, completely bounded multipliers and Littlewood functions, West Coast Operator Algebra Seminar, 1996, Prince George, Canada.
  • G. Xu, Semigroups of endomorphisms of Boolean algebras, 1st International Symposium on Algebraic Structures and Number Theory, 1988, Hong Kong.

Other Publications

  • G. Xu, On the fixed point theorems of nonexpanded maps, Selected Graduation papers, Lanzhou University, (1982), (Chinese).
  • G. Xu, A remark on uniform continuity,Journal of Huzhou ShiZhuan, (1982), (Chinese).
    Note: Authors are listed alphabetically, unless labeled with (∂).