Martin Albrecht's (malb) SAGE projects

Part of my Thesis

• My thesis deals with algebraic attacks on block ciphers namely the Courtois Toy Cipher. So I will implement/have implemented several algebraic attack algorithms like XL,XSL,F4 and DR. Though those might not be of general interest.

Other stuff I'm working on

• Memory consumption analogous to cputime(). This is tricky because some grep on top et al. doesn't provide the necessary information. E.g. Python never ever frees memory while running, and we also might count shared libraries several times this way.
• Memory profiling similar to %prun or hotshot. The memory profiler would provide hints which part consumes the most memory during a calculation.
• Allow %prun and hotshot to profile pyrex code.

• ["Givaro"] integration. This significantly improves finite field arithmetic (more than ten times) and everything relying on it in SAGE. Try it: k = linbox.GFq(2^8,repr="poly")

• Extremely fast sparse (and dense) linear algebra. Actually I only care about echelon form calculation. We are debating if [http://www.linalg.org LinBox] is a good choice for this. Matrices involved in algebraic attacks are often very sparse and there is no need to have my machine go down because e.g., NTL allocates many zeros (i.e., NTL only knows dense matrices).

• Parallel sparse linear algebra to utilize all 16 cores at sage.math.washington.edu at once. It's either too hard for me (if there is no library) or simple as it would be just another library to expose.

• [http://article.gmane.org/gmane.comp.mathematics.sage.general/193/ SAGEBot] is not dead yet.

• [http://eprint.iacr.org/2006/224.pdf Generalizations of the Karatsuba Algorithm for Efficient Implementations]

• Implement or wrap the [http://eprint.iacr.org/2006/251.pdf "Method of Four Russians"] for row reducing resp. inverting a dense boolean matrix

• NTL wrapper makeover (more SAGEish, avoid function calls, avoid news, deletes)

• [:Factory:cf.CF] makeover (avoid function calls, avoid news, deletes). Also restrict arithmetic to cf.CF (i.e. strongly type it) to avoid casting/coercion overhead.

Done

• Cputime class/function which wraps all the cputime() calls for all the subprocesses for convenience. So only one cputime(all=True) call would be sufficient. (I extended David Harvey's Profiler class for this)

• Consider this example:

     1 sage: R1 = PolynomialRing(GF(2**8),2)
     2 sage: R2 = PolynomialRing(GF(2**8),2000)
     3 sage: x1=R1.gen()
     4 sage: y1=R1.gen(1)
     5 sage: x2=R2.gen()
     6 sage: y2=R2.gen(1)
     7 sage: time for i in range(1000): _ =x2*y2
     8 CPU times: user 1.58 s, sys: 0.03 s, total: 1.61 s
     9 Wall time: 1.63 #ring with 2000 variables
    10 sage: time for i in range(1000): _ =x1*y1
    11 CPU times: user 0.21 s, sys: 0.03 s, total: 0.24 s
    12 Wall time: 0.24 #ring with two variables
  

  This is due to the way multivariate polynomials in SAGE are represented. I want to come up with a more sparse representation which does not add zero to zero 1998 times in the second example. (I rewrote the polynomial representation to use dicts of dicts which map indices to exponents e.g., {{1:2}:3} represents 3*y^2 if y is the second variable in the ring.)

Other stuff

I'm a computer science grad student from Bremen, Germany, with a strong interest in cryptanalysis, right now mainly algebraic attacks on block ciphers. I maintain a blog at http://www.informatik.uni-bremen.de/~malb/blog.php .

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