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. I was an IT staff in the Mathematical
Sciences Institute of ANU. I am currently a postdoc at the University of Auckland, working with Prof. Steven Galbraith.
My PhD thesis titled "Polynomial selection for the number field sieve" can be found here.
Shi Bai, Emmanuel Thomé and Paul Zimmermann. Factorisation of RSA-704 with CADO-NFS, report, 2012.
Shi Bai, Paul Zimmermann. Size Optimization of Sextic Polynomial in the Number Field Sieve, report, 2012.
Shi Bai, Richard Brent and Emmanuel Thomé. Root Optimization of Polynomials in the Number Field Sieve, report, 2011.Shi Bai and Richard Brent. On the Efficiency of Pollard's Rho Method for Discrete Logarithms, The Australasian Theory Symposium(CATS2008), 2008.
I have written some codes in polynomial selection in CADO-NFS, an implementation of the number field sieve for integer factorization.
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.
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.
Acknowledgment 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, and MSI for providing computing facilities.