I am an assistant professor in the Department of Mathematical Sciences at Florida Atlantic University. My research interests are in cryptography and computational number theory.
MAD-2502 Introduction to Computational Mathematics, Spring 2018.
MAS-3203 Introductory Number Theory, Spring 2018.
MAS-6215 Algebraic Number Theory, Fall 2017.
MAD-6478 Cryptanalysis, Spring 2017.
MAC-2311 Calculus-Analytic Geometry I, Spring 2017.
Shi Bai, Pierrick Gaudry, Alexander Kruppa, Emmanuel Thomé and Paul Zimmermann. Factorisation of RSA-220 with CADO-NFS. report, 2016.
Shi Bai, Thijs Laarhoven and Damien Stehlé. Tuple lattice sieving. ANTS-XII -- LMS Journal of Computation and Mathematics, 2016.
Martin Albrecht, Shi Bai and Léo Ducas. A subfield lattice attack on overstretched NTRU assumptions: Cryptanalysis of some FHE and Graded Encoding Schemes. Crypto, 2016.
Shi Bai, Damien Stehlé and Weiqiang Wen. Improved Reduction from the Bounded Distance Decoding Problem to the Unique Shortest Vector Problem in Lattices. ICALP, 2016.
Shi Bai, Adeline Langlois, Tancrède Lepoint, Damien Stehlé and Ron Steinfeld. Improved security proofs in lattice-based cryptography: using the Rényi divergence rather than the statistical distance. Asiacrypt, 2015. (Best paper award).
Shi Bai, Steven Galbraith, Liangze Li and Daniel Sheffield. Improved exponential-time algorithms for inhomogeneous-SIS. preprint,2014.
Shi Bai and Steven Galbraith. Lattice decoding attacks on binary LWE. ACISP, 2014.
Shi Bai and Steven Galbraith. An improved compression technique for signatures based on learning with errors. CT-RSA, 2014.
Shi Bai, Cyril Bouvier, Alexander Kruppa and Paul Zimmermann. Better polynomials for GNFS. Math. Comp. 85 (2016), 861-873.
Shi Bai, Richard Brent and Emmanuel Thomé. Root optimization of polynomials in the number field sieve. Math. Comp. 84 (2015), 2447-2457.
Shi Bai, Emmanuel Thomé and Paul Zimmermann. Factorisation of RSA-704 with CADO-NFS. report, 2012.
CADO-NFS, an implementation of the number field sieve algorithm for integer factorization.
FPLLL, an implementation of several lattice reduction algorithms.
Here are some integers factored by the general number field sieve and their parameters. Some are re-factored due to the lack of communication. I claim no originality for the factorization of those numbers and contributions should be made to those who first factored them. These numbers range from 140 to 212 decimal digits, it might be interested to see various parameters for these numbers.
Acknowledgement goes to Richard Brent, Paul Zimmermann for many suggestions,
Joshua Rich for help on the cluster, authors of "CADO-NFS", "Msieve", "Lasieve" for writing efficient software.
Thanks to MSI of ANU and NeSI of UoA for providing HPC facilities.
Some GNFS polynomials are collected here together with their actual and expected Murphy's E values. The expected values are computed by ignoring the o(1) in the number field sieve asymptotic complexity.