白石 (Shi Bai)

I have completed my PhD under the supervision of Prof. Richard Brent in the Algorithms & Data group at College of Engineering & Computer Science of ANU. In 2012, I was an IT staff in the Mathematical Sciences Institute of ANU. In 2013/2014, I was a postdoctoral researcher at the University of Auckland, working with Prof. Steven Galbraith. I am currently a postdoctoral researcher at ENS Lyon, working with Prof. Damien Stehlé. My research interests are in cryptography and computational number theory.

My PhD thesis titled "Polynomial selection for the number field sieve" can be found here.

Publication & report

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.

Shi Bai and Richard Brent. On the efficiency of Pollard's rho method for discrete logarithms. The Australasian Theory Symposium (CATS), 2008.

Software

I have written some codes in polynomial selection in CADO-NFS, an implementation of the number field sieve for integer factorization.

Projections for GNFS polynomials

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.

Integer factorization

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.

c142 in 3,678+ (re-factored)
c151 in 3,649-
c160 in 11,275- (re-factored)
c164 in 5,905L
c172 in 5,490+
c173 in Bernoulli(202) (with Bill Hart)
c177 in Bernoulli(226) (with Sam Wagstaff)
RSA180 (re-factored)
RSA190 (stopped at sieving)
c191 in 2,2090M (with Sam Wagstaff)
c191 in 2,2110M (with Sam Wagstaff)
c204 in Bernoulli(200)
RSA704 (report)

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.

Useful links

Jörg Arndt - book "Matters Computational"
Richard Brent
Keith Matthews - Number Theory Web
Jason Papadopoulos - Msieve
Sam Wagstaff - the Cunningham project
Paul Zimmermann
Mersenne Forum
FLINT (fast library for number theory)

Contact

Email:
shih.bai AT gmail.com
Postal Address:
Laboratoire LIP,
Ećole Normale Supérieure de Lyon,
Lyon, France.