ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 04 Sep 2017 08:02:35 +0200calculating the modulo of a "number" in a binary finite fieldhttps://ask.sagemath.org/question/38735/calculating-the-modulo-of-a-number-in-a-binary-finite-field/Polynomial equations in binary finite fields are often represented as numbers. eg. $x^2 + 1$ is basically the same thing as $1x^2 + 0x^1 + 1x^0$ and thus would be represented as $101_2$ or $5_{10}$.
In that spirit I'm trying to use a hexadecimal number to represent a polynomial equation. The polynomial equation is larger than the modulo I'm using ($x^{113} + x^9 + 1$) so I'm trying to get the result of the modulo operation.
Here's what I've tried:
BF.<a> = FiniteField(2^113);
X = Integer(0x61661990d3b1f7a608ad095a01d727380850d2592f5b9f88f66a20e8);
X_bf = BF._cache.fetch_int(X);
X_bf.mod(x^113 + x^9 + 1)
Unfortunately, this doesn't seem to work and instead gets me the following error messages:
TypeError Traceback (most recent call last)
<ipython-input-4-dba4addbde0d> in <module>()
2
3 X = Integer(Integer(0x61661990d3b1f7a608ad095a01d727380850d2592f5b9f88f66a20e8));
----> 4 X_bf = BF._cache.fetch_int(X);
5
6 X_bf.mod(x**Integer(113) + x**Integer(9) + Integer(1))
/home/sage/sage-8.0/src/sage/rings/finite_rings/element_ntl_gf2e.pyx in sage.rings.finite_rings.element_ntl_gf2e.Cache_ntl_gf2e.fetch_int (/home/sage/sage/src/build/cythonized/sage/rings/finite_rings/element_ntl_gf2e.cpp:7596)()
400 raise ValueError("Cannot coerce element %s to this field." % e)
401
--> 402 cpdef FiniteField_ntl_gf2eElement fetch_int(self, number):
403 """
404 Given an integer less than `p^n` with base `2`
/home/sage/sage-8.0/src/sage/rings/finite_rings/element_ntl_gf2e.pyx in sage.rings.finite_rings.element_ntl_gf2e.Cache_ntl_gf2e.fetch_int (/home/sage/sage/src/build/cythonized/sage/rings/finite_rings/element_ntl_gf2e.cpp:7212)()
431
432 if number < 0 or number >= self.order():
--> 433 raise TypeError("n must be between 0 and self.order()")
434
435 if isinstance(number, int) or isinstance(number, long):
TypeError: n must be between 0 and self.order()
I realize that what I'm doing isn't technically a finite field but idk how else I might get a "number" turned into a polynomial equation.
Any ideas?neubertMon, 04 Sep 2017 08:02:35 +0200https://ask.sagemath.org/question/38735/pre-reduction multiplication result in binary fieldhttps://ask.sagemath.org/question/38734/pre-reduction-multiplication-result-in-binary-field/The following will do multiplication in a finite field:
X = Integer(0x009D73616F35F4AB1407D73562C10F);
Y = Integer(0x00A52830277958EE84D1315ED31886);
F.<x> = GF(2)[];
p = x^113 + x^9 + 1;
BF = GF(2^113, 'x', modulus=p);
X_bf = BF._cache.fetch_int(X);
Y_bf = BF._cache.fetch_int(Y);
temp = Y * X; temp
The problem with this is that the result you get back has had the reduction step already ran. I'd like to see the multiplication result pre-reduction.
Any ideas?neubertMon, 04 Sep 2017 05:44:52 +0200https://ask.sagemath.org/question/38734/inverse of a polynomial modulo another polynomialhttps://ask.sagemath.org/question/8756/inverse-of-a-polynomial-modulo-another-polynomial/Hi, I'm trying to implement the Baby Step Giant Step algorithm in the group of units of prime fields. I would like to generate the field provided one generator polynomial. But I need to calculate p^(-1) (where p is a polynomial), but can't find a function to do so. This is what I'm doing,
F.<a> = GF(2)[];
R.<b> = PolynomialRing(F)
S.<x> = R.quotient(b^4+b+1)
m = sqrt(S.modulus().degree());
gamma = S.modulus();
alpha = x^3+1;
now i need to calculate (alpha)^(-1) modulo gamma
Any help? Better ways to do the same thing?
Thanks!
inertialFrostTue, 28 Feb 2012 11:47:08 +0100https://ask.sagemath.org/question/8756/