MA792K Final Project (due Tue, May 8, 5pm).
Please choose one of the two project:

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Your final project is to implement in Maple Sturms theorem.

sturm := proc(f   # f is a univariate polynomial with integer coefficients
             ,x   # the variable in f
             ,a   # the left interval boundary
             ,b   # the right interval boundary, b > a
              )
# returns an k integer >= 0
# such that the number of real roots r of f with a < r <= b is k.

... # your code

end; #sturm
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Your final project is to implement the GGH lattice basis public key crypto system.

You should have at least 3 procedures.

makekeys := proc(n,... # some size parameters
               )
# returns a sequence of 2 lattices (integer Matrices), B,C
# where B is the public key and C is private key

encrypt := proc(text::string, # the clear text
               ,B # the public key
              )            
# returns a Vector of integers, the ciphertext
# uses convert(str, bytes) where str is a string

decrypt := proc(cipher
               ,C
               )
# returns a string, the clear text
# uses convert(lst, bytes) where lst is a list of byte values
# uses IntegerRelations['LLL']
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Good luck!
Yours, Erich