Research Interests
Algebraic number theory: Ideal lattices, well-rounded ideal lattices, log unit lattices, the size function of a number field, and geometry of endomorphism rings of supersingular elliptic curves.
Applying (algebraic) lattices and iosogenies in cryptography and coding theory.
Publications
Rigorous Certification of Fundamental Units in Number Fields, with Randy Yee, Felix Fontein, and Michael J. Jacobson, Jr., in preparation.
Fast arithmetic in the divisor class group, with Jens Dietrich Bauch and Sumin Leem, in preparation.
Well-rounded twists of the ring of integrers of cyclic cubic fields, with Nam H. Le, Dat T. Tran, and David A. Karpuk, submitted.
Gross lattices of supersingular elliptic curves, with Chenfeng He, Gaurish Korpal, and Christelle Vincent, submitted.
Principal well-rounded ideals of quadratic fields, with Morgan Smith, accepted by the Journal of Algebra and Its Applications.
Orientations and cycles in supersingular isogeny graphs, with Sarah Arpin, Mingjie Chen, Kristin E. Lauter, Renate Scheidler, Katherine E. Stange (2024), In: Bucur, A., Ho, W., Scheidler, R. (eds) Research Directions in Number Theory. Association for Women in Mathematics Series, vol 33. Springer, Cham.
Reduced ideals from the reduction algorithm, with Peng Tian, Results in Mathematics, Volume 79, article number 50, (2024).
The size function for imaginary cyclic sextic fields, with Peng Tian and Amy Feaver, Journal de théorie des nombres de Bordeaux, Volume 35 (2023) no. 3, pp. 841-866.
Computing mod $\ell$- Galois representations associated to modular forms for small primes, with Peng Tian and Dung Duong, AIMS Mathematics 2023, Volume 8, Issue 12: 28766-28779.
Well-rounded ideal lattices of cyclic cubic and quartic fields, with Nam H. Le, Dat T. Tran, Communications in Mathematics, October 18, 2023, Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications).
Orienteering with one endomorphism, with Sarah Arpin, Mingjie Chen, Kristin E. Lauter, Renate Scheidler, Katherine E. Stange, La Matematica (2023).
Well-rounded twists of ideal lattices from imaginary quadratic fields, with Nam H. Le, Dat T. Tran, Journal of Algebra and Its Applications, Vol. 21, No. 07, 2250133 (2022). pdf
An efficient multivariate threshold ring signature scheme, with Dung Hoang Duong, Willy Susilo and Le Van Luyen, Computer Standards & Interfaces 74 (2021): 103489. pdf
Lattice Blind Signatures with Forward Security, with Huy Quoc Le, Dung Hoang Duong, Willy Susilo, Viet Cuong Trinh, Josef Pieprzyk, and Thomas Plantard, In Australasian Conference on Information Security and Privacy 2020, Nov 30 (pp. 3--22). Springer, Cham. pdf
A multivariate blind ring signature scheme, with Dung H. Duong and Willy Susilo, The Computer Journal, Volume 63, Issue 8, August 2020, Pages 1194–1202. pdf
Choosing subfields for LUOV and LRainbow Signature Scheme, with Dung Hoang Duong and Le Van Luyen, IET Information Security, 2019. pdf (errata)
Computation of triangular integral bases, with Jens Dietrich Bauch, THE OPEN BOOK SERIES 2 (2019), Thirteenth Algorithmic Number Theory Symposium.
The size function for cyclic cubic fields, with Peng Tian, Int. J. Number Theory 14, 399 (2018). pdf (errata)
The size function of quadratic extensions of complex quadratic fields, Journal de théorie des nombres de Bordeaux, 29 no. 1 (2017), p. 243-259. pdf
Computing dimensions of spaces of Arakelov divisors of number fields, Int. J. Number Theory, March 2017, Vol. 13, No. 02: pp. 487-512 pdf
Well-Rounded Lattices for Coset Coding in MIMO Wiretap Channels, with Oliver W. Gnilke, Amaro Barreal, Alex Karrila, David A. Karpuk and Camilla Hollanti, 26th International Telecommunication Networks and Applications Conference, ITNAC 2016., p. 289-294. pdf
Well-Rounded Lattices for Reliability and Security in Rayleigh Fading SISO Channels, with O. W. Gnilke, A. Karrila and C. Hollanti, Information Theory Workshop (ITW), 2016 IEEE, 359-363. pdf
On reduced Arakelov divisors of real quadratic fields, Acta Arith. 3483 (2016), 297-315. pdf
A generalization of reduced Arakelov divisors of a number field, Journal of Number Theory 167 (2016) 104 - 117. pdf (errata)