GF(2^n) multiplication for IA 32 x86 NASM with n=9 as example

GF(2^n) multiplication for IA x86-64 architecture with n=29 as an example

32-bit version:

samira> nasm -f elf -g -F stabs gf2.asm -l gf2.lst

samira> gcc -m32 gf2.o -o gf2

samira> ./gf2

Result: f912

64-bit version:

samirita> nasm -f elf64 -l gf2.lst gf2.asm

samirita> gcc -o gf2 gf2.o

samirita> ./gf2

Result: 155cdbff5519200

Understand the algorithm

Follow the call stack closely

Careful attention to calling convetions and instructions...

For example shl required operands

mov [ebp+12],edx and not dl...

cmp a,b will compare the full contents of both registers...

we compute accordingly

test as you go...

start with simple input test vectors, then scale up

32-bit version:

samira> nasm -v

NASM version 2.10.09 compiled on Dec 29 2013

samira> uname -a

Linux ubuntu 4.4.0-116-generic #140~14.04.1-Ubuntu SMP Fri Feb 16 09:25:20 UTC 2018 x86_64 x86_64 x86_64 GNU/Linux

IDE: TextEditor

64-bit version:

samirita> nasm -v

NASM version 2.15.05 compiled on Nov 3 2021

samirita> uname -a

Linux fedora 5.14.10-300.fc35.x86_64 #1 SMP Thu Oct 7 20:48:44 UTC 2021 x86_64 x86_64 x86_64 GNU/Linux

https://www.cs.dartmouth.edu/~sergey/cs258/tiny-guide-to-x86-assembly.pdf

https://flint.cs.yale.edu/cs421/papers/x86-asm/asm.html

https://cs.lmu.edu/~ray/notes/nasmtutorial/ (for 64-bit registers with rax, rbx, etc.)

https://www.csee.umbc.edu/portal/help/nasm/ (excellent resource and examples for instruction conventions)

You can find the equivalent program in C in this file: https://github.com/olivamadrigal/jenkins_pipeline/blob/main/gf2_9_mul.c

You can put that in new file with main, same test vectors, and create an object file:

samira> gcc -O -g -o main.c

Then do an object dump to see the machine code and assembly code from gcc compiler:

samirita> nasm -v

samira> objdump -d main.c

main.o: file format elf64-x86-64

Disassembly of section .text:

(relative addr) // (object code in hex) // assembly ;)

0000000000000000

and compare...