I am an associate professor in the Department of Mathematical Sciences at Florida Atlantic University. I am also a faculty member in the Center for Cryptology and Information Security (CCIS). My research interests are in cryptography and computational number theory. My research is (and has been) supported by the NSF CAREER Award, NSF collaborative grant, NIST grants, and CyberFlorida capacity building grant.
MAS-4301. Modern Algebra, Spring 2023.
MAD-6607. Coding Theory, Spring 2022.
MAD-5474/CIS-4362. Cryptography And Info Security, Fall 2021.
STA-2023. Introductory Statistics, Fall 2021.
MAS-5312. Intro Abstract Algebra II, Spring 2021.
MAD-2104. Discrete Mathematics, Spring 2021.
MAS-5311/4304. Intro Abstract Algebra I, Fall 2020.
MAD-2104. Discrete Mathematics, Fall 2020.
MAS-6215. Algebraic Number Theory, Fall 2019.
MAC-2312. Calculus-Analytic Geometry II, Spring 2019.
MAS-3203. Introductory Number Theory, Spring 2019.
MAD-6403. Computational Mathematics, Fall 2018.
MAC-2311. Calculus-Analytic Geometry I, Fall 2018.
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.
Martin R. Albrecht, Shi Bai, Jianwei Li and Joe Rowell. Lattice Reduction with Approximate Enumeration Oracles: Practical Algorithms and Concrete Performance. Crypto, 2021.
Martin R. Albrecht, Shi Bai, Pierre-Alain Fouque, Paul Kirchner, Damien Stehlé and Weiqiang Wen. Faster Enumeration-based Lattice Reduction: Root Hermite Factor k^(1/(2k)) in Time k^(k/8 + o(k)). Crypto, 2020.
Shi Bai, Dipayan Das, Ryo Hiromasa, Miruna Rosca, Amin Sakzad, Damien Stehlé, Ron Steinfeld and Zhenfei Zhang. MPSign: A signature from small-secret middle-product learning with errors. PKC, 2020.
Shi Bai, Katharina Boudgoust, Dipayan Das, Adeline Roux-Langlois, Weiqiang Wen and Zhenfei Zhang. Middle-Product Learning with Rounding Problem and its Applications. Asiacrypt, 2019.
Shi Bai, Shaun Miller and Weiqiang Wen. A refined analysis of the cost for solving LWE via uSVP. Africacrypt, 2019.
Shi Bai, Steven Galbraith, Liangze Li and Daniel Sheffield. Improved exponential-time algorithms for inhomogeneous-SIS. Journal of Cryptology. 32 (2019), 35-83.
Shi Bai, Damien Stehlé and Weiqiang Wen. Measuring, simulating and exploiting the head concavity phenomenon in BKZ. Asiacrypt, 2018.
Shi Bai, Adeline Langlois, Tancrède Lepoint, Damien Stehlé, Amin Sakzad and Ron Steinfeld. Improved security proofs in lattice-based cryptography: using the Rényi divergence rather than the statistical distance. Journal of Cryptology. 31 (2018), 610-640.
Jinming Wen, Chao Tong and Shi Bai. Effects of Some Lattice Reductions on the Success Probability of the Zero-Forcing Decoder. IEEE Communications Letters. 20 (2016), 2031-2034.
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 R. 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, Cyril Bouvier, Alexander Kruppa and Paul Zimmermann. Better polynomials for GNFS. Mathematics of Computation. 85 (2016), 861-873.
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, Richard Brent and Emmanuel Thomé. Root optimization of polynomials in the number field sieve. Mathematics of Computation. 84 (2015), 2447-2457.
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, 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.