On Mon, Jan 28, 2013 at 3:16 PM, David Joyner <[email protected]> wrote: > Hi: > > For various reasons, I'm having a hard time using Sage > when I teach a class in coding theory and cryptography. > (Mostly, this is because of a lack of support for non-windows > machines where I teach.) So, I'm trying to find what > sympy, which is easier to install on windows, can do in terms of > basic cryptography and basic error-correcting codes. > My vague memory says the answer is basically nothing, > and a google search doesn't turn up anything. > > Am I missing something? > > If not, I plan on writing up something myself. Should it go in > combinatorics? Or maybe a new module, such as algebra > or codes or crypto? I would like to implement > some classical ciphers, such as > Bifid, > Caesar/shift, > Hill (I hope), > Substitution > Vigenere > and some associated algorithms (repeated squaring > for modular exponentiation, and the extended Euclidean algorithm).
The algorithms should all be implemented already, but none of the codes. The algorithms will be in various places, but in general, check the polys. The extended Euclidean algorithm is gcdex, and works for polynomials or integers. Modular exponentiation is already implemented in Python (pow(a, b, c) is (a**b) % c). SymPy Integers should define the three-arg __pow__ so that this works with them too (if not, it will be easy to fix). The same for finite field stuff (FF, see below). For the codes, I'm not sure. "combinatorics" already contains a bunch of stuff that isn't really combinatorics (like group theory). Maybe we should create "algebra" and put it and group theory there. You will have a better idea than I about where the best place to put things is, since you know what things will do. We definitely welcome the contribution, regardless of where it ends up. I am actually taking a course in algebraic geometry and codes this semester, focusing on error-correcting codes, so maybe this will be useful to me (or maybe not, it sounds like you are focusing more on cryptography than codes). > > For Hill's cipher, I will need to invert a matrix > modulo m. I think I can think of a way to do that, with a little > work (invert over the rationals, find the non-integer terms > and invert them one at a time), but if anyone knows of a > short simple implemention in python, please let me know. You could probably use the fact that the only number that you have to invert is the determinant somehow. Also, you could try using FF (like FF(3)(1) for 1 mod 3). It seems to work in my tests. You'll more likely than not want to use FF(3, symmetric=False) to avoid "negative" numbers. Aaron Meurer > > - David > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > Visit this group at http://groups.google.com/group/sympy?hl=en. > For more options, visit https://groups.google.com/groups/opt_out. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
