you are in... Main\gf2^32mult
Function gf2^32mult finds product of two elements, a and b, of a
field GF(2^{32})=GF(4,294,967,296). The output, c=ab,
is written onto the last 32 bits. Inputs a and b must remain unchanged.
Primitive polynomial |
Picture |
Machine-readable version |
Library |
Garbage |
Gate count |
Quantum cost |
Author(s) |
Date |
x^{32}+x^{7}+x^{5}+x^{3}+x^{2}+x+1* |
N/A (too large) |
NCT |
64 |
1,179 |
5,275 |
May, 2014 |
||
x^{32}+x^{9}+x^{3}+x^{2}+1* |
N/A (too large) |
NCT |
64 |
1,117 |
5,213 |
May, 2014 |
________________________________
^{m}
- the number is shown to be minimal
* - Shane Kepley and Prof. Rainer Steinwandt of Florida Atlantic University found an error:
the irreducible polynomial as posted originally read x^{32}+x^{7}+x^{5}+x^{3}+x+1,
whereas the correct irreducible polynomial should have read x^{32}+x^{7}+x^{5}+x^{3}+x^{2}+x+1.
This page was updated on May 12, 2014 to correct the error. The new circuit
file was uploaded, the old circuit file is available here. Also, a new primitive polynomial, x^{32}+x^{9}+x^{3}+x^{2}+1,
has been suggested, and a circuit implementation corresponding to it has been added.