Logisim Implementation of a Finite Field Processor

Requirements

Module	Description	Importance	Difficulty	Accept
is_primitive	Check if an input polynomial is irreducible	Optional	Very hard	N
poly_gen	Generate all 2^n terms of a polynomial in GF(n)	Optional	Hard	Y
add	Add 2 terms	Basic	Easy	Y
mul	Multiply 2 terms	Basic	Medium	Y
div	Divide 2 terms	Basic	Medium	Y
log	Find the log of a term	Basic	Easy	N
twos_comp	Generate the two's complement of an integer	Prerequisite	Medium	N
indices	A priority encoder to find the n-th index	Prerequisite	Medium	Y
control_unit	Control unit of the ALU	Basic	Medium	Y
mem	Memory block(s) of the ALU	Basic	Hard	Y
mem_control	Memory interface of the ALU	Basic	Hard	Y

Supported Instructions

Instruction	Operation code	Description
ldi	000	Load immediate/element value into opand1
add	001	XOR values (e -> e)
mul	010	Mod add values (p -> e)
div	011	Mod subtract values (p -> e)
ld	100	Load memory value/polynomial into opand1
init	101	Initialize polynomial generator constants
gen	110	Generate polynomial terms
rst	111	Reset

Format

	Opcode	Operand
Instruction indices	12-9	8-0

Examples

Example input primitive polynomial: x^3+x^2+1

Convert x^3+x^2+1 to its binary representation:

000000110/0x006

Initialize constants required to compute the values of the polynomial

init 6
101 000000110
1010 0000 0110

In hexadecimal:
0xA06

Generate all the values of the polynomial

gen 6
110 000000110
1100 0000 0110

In hexadecimal:
0xC06

Load immediate value 3 into operand 1

ldi 3
000 000000011
0000 0000 0011

In hexadecimal:
0x003

Load memory value 4 into operand 1

ld 4
100 000000100
1000 0000 0100

In hexadecimal:
0x804

Add immediate value 1 into operand 2 and perform addition

add 1
001 000000001
0010 0000 0001

In hexadecimal:
0x201

Add memory value 2 into operand 2 and perform multiplication

mul 2
010 000000010
0100 0000 0010

In hexadecimal:
0x402

Add memory value 3 into operand 2 and perform division

div 3
011 000000011
0110 0000 0011

In hexadecimal:
0x603