Another simple question: polynomial multiplication modulo 2

AARRRGH

Right,

Thanks everyone for the help so far.

I'm implementing "binary polynomial multiplication" at the moment as part of some cryptography code I'm writing. Nearly finished...

Anyway, this is my simple question:

Multiply the following polynomials:

(x^7 + x^5 + x^3 + x) * (x^27 + x^15 + x^13 + x^12 + x^11 + 1)

The answer:

x^34 + x^32 + x^30 + x^28 + x^22 + 2x^20 + x^19 + 3x^18 + x^17 + 3x^16 + x^15 + 2x^14 + x^13 + x^12 + x^7 + x^5 + x^3 + x

Now, let's say I want to reduce this modulo 2. Should it become -

A: x^34 + x^32 + x^30 + x^28 + x^22 + x^19 + x^18 + x^17 + x^16 + x^15 + x^13 + x^12 + x^7 + x^5 + x^3 + x

or

B: x^34 + x^32 + x^30 + x^28 + x^22 + x^19 + x^17 + x^15 + x^13 + x^12 + x^7 + x^5 + x^3 + x

I think perhaps it should become A, as 3 modulo 2 is 1.

In fact, I'm pretty sure of this, but I just want to double check before I move on to polynomial division and polynomial multiplicative inverse...

Thanks

LeixlipRed

Assuming your multiplication is right then Answer A looks good.