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##install necessary packages

iman@debian:~$ sudo apt-get install libncurses5 libncurses5-dev libssl-dev kernel-package fakeroot build-essential util-linux

##get kernel 3.19.3

iman@debian:~$ wget https://www.kernel.org/pub/linux/kernel/v3.x/linux-3.19.3.tar.xz

iman@debian:~$ tar -xvf linux-3.19.3.tar.xz

iman@debian:~$ cd linux-3.19.3

##config-3.16.0-4-686-pae is Debian config file from its current kernel (available in the distribution linux-image .deb)

iman@debian:~/linux-3.19.3$ cp ~/config-3.16.0-4-686-pae .config && yes "" | linux32 make oldconfig

##optional : configure kernel

#iman@debian:~/linux-3.19.3$ make menuconfig

##if not first compilation

#iman@debian:~/linux-3.19.3$ make-kpkg clean

##set compile at full speed

iman@debian:~/linux-3.19.3$ export CONCURRENCY_LEVEL=`grep "cpu cores" /proc/cpuinfo | head -1 | cut -d":" -f2 | cut -c2-`

##compile kernel image and kernel headers (headers are optional)

iman@debian:~/linux-3.19.3$ fakeroot linux32 make-kpkg --cross-compile - --arch=i386 --initrd --revision=1+i --append-to-version=-`date +%Y%m%d` kernel-image kernel-headers

##at this point you have a 32bit kernel inside a linux-image-3.19.3-20150326_1+i_amd64.deb package and headers in linux-headers-3.19.3-20150326_1+i_amd64.deb but both labeled for 64bit arch

##let's label it i386

iman@debian:~/linux-3.19.3$ cd ..

iman@debian:~$ mkdir linux-image-3.19.3-20150326_1+i_i386 && cd linux-image-3.19.3-20150326_1+i_i386

##extract .deb

iman@debian:~/linux-image-3.19.3-20150326_1+i_i386$ ar x ../linux-image-3.19.3-20150326_1+i_amd64.deb

##extract control.tar.gz & data.tar.xz

iman@debian:~/linux-image-3.19.3-20150326_1+i_i386$ mkdir DEBIAN && tar xf control.tar.gz -C DEBIAN && rm control.tar.gz

iman@debian:~/linux-image-3.19.3-20150326_1+i_i386$ tar xf data.tar.xz && rm data.tar.xz

iman@debian:~/linux-image-3.19.3-20150326_1+i_i386$ rm debian-binary

##edit DEBIAN/control and replace "Architecture: amd64" by "Architecture: i386"

iman@debian:~/linux-image-3.19.3-20150326_1+i_i386$ sed -i 's/Architecture: amd64/Architecture: i386/g' DEBIAN/control

cd ..

##repackage the modified .deb

iman@debian:~$ dpkg-deb -b linux-image-3.19.3-20150326_1+i_i386

##now you've got your linux-image-3.19.3-20150326_1+i_i386.deb

##same method applies for linux-headers-3.19.3-20150326_1+i_amd64.deb

##copy .deb to your 32bit machine and install :

iman@msiwind:~$ sudo dpkg -i linux-image-3.19.3-20150326_1+i_i386.deb linux-headers-3.19.3-20150326_1+i_i386.deb

##reboot then :

iman@msiwind:~$ uname -a

Linux msiwind 3.19.3-20150326 #1 SMP Thu Mar 26 20:10:01 CET 2015 i686 GNU/Linux