ARM Architecture Reference Manual ARMv7-A and ARMv7-R edition

A2.8 Polynomial arithmetic over {0,1}
Application Level Programmers’ Model
The polynomial data type represents a polynomial in x of the form bn–1x n–1 + … + b1x + b0 where bk is
bit [k] of the value.
The coefficients 0 and 1 are manipulated using the rules of Boolean arithmetic:
0 + 0 = 1 + 1 = 0
0 + 1 = 1 + 0 = 1
0 * 0 = 0 * 1 = 1 * 0 = 0
1 * 1 = 1.
That is:
adding two polynomials over {0,1} is the same as a bitwise exclusive OR
multiplying two polynomials over {0,1} is the same as integer multiplication except that partial
products are exclusive-ORed instead of being added.
A2.8.1 Pseudocode details of polynomial multiplication
In pseudocode, polynomial addition is described by the EOR operation on bitstrings.
Polynomial multiplication is described by the PolynomialMult() function:
// PolynomialMult()
// ================
bits(M+N) PolynomialMult(bits(M) op1, bits(N) op2)
result = Zeros(M+N);
extended_op2 = Zeros(M) : op2;
for i=0 to M-1
if op1 == ‘1’ then
result = result EOR LSL(extended_op2, i);
return result;
ARM DDI 0406B Copyright © 1996-1998, 2000, 2004-2008 ARM Limited. All rights reserved. A2-67