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Topic: Long polynomials vs. crypto
Replies: 4   Last Post: May 27, 2012 7:39 AM

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 Joe Snod Posts: 82 Registered: 8/28/10
Long polynomials vs. crypto
Posted: May 26, 2012 1:53 PM

I've noticed that the problem of factoring a polynomial of arbitrary
order seems to involve a lot of the same buzzwords as modern crypto,
specifically elliptic curves and lattices, with the latter being, if I
understand correctly, a generalization of the period matrices of the
former.

Also, the summation that represents a long integer is almost identical
to the one for a long polynomial, except that the polynomial has a
variable in the summation, in the same place that the integer has a
base, ie

polynomial = sum from (k=1 to n) of [(a_n)*x^n], where
a=coefficients, x=independent variable, n=number of terms

integer = sum from (k=1 to n) of [(a_n)*b^n], where
a="coefficients," b=base, n=number of digits

Does this mean that, if the problem of factoring a polynomial of
arbitrarily high order is ever solved, the solution would greatly
advance the problem of cracking public key crypto? If so, how far
would it advance the solution? Would it crack it completely?

Date Subject Author
5/26/12 Joe Snod
5/26/12 Kristian Gjøsteen
5/27/12 Joe Snod
5/27/12 Kristian Gjøsteen
5/27/12 William Elliot