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 Cryptology — CRYPTO, 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, 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).
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.
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 (∂).