Data Integrity Functions

This chapter describes Intel® Integrated Performance Primitives (Intel® IPP) functions for data integrity. These functions implement error-correcting coding, which is featured in [Berl68], [Mor02], and [Bla84].

The data integrity functions are based on operations over finite fields. A field may be defined as a set of elements where

The results of the addition (+) and multiplication (*) operations on two arbitrary elements are defined uniquely.
The associative and commutative laws are applicable to both addition and multiplication, and multiplication is distributional with respect to addition: u*(v+w) = u*v+u*w.
An additive identity element 0 and multiplicative identity 1 ≠ 0 exist.
Each field element u has a unique additive inverse element -u, such that u+(-u) = 0.
Each non-zero field element u has a unique multiplicative inverse element 1/u, such that u*(1/u) = 1.

For each field element u, the following equations are true:

0+u = u

1*u = u

0*u = 0.

A field that contains only finitely many elements is called a finite field (or Galois field). The order of a finite field is the number of elements q it contains. It is traditional to denote the finite field of order q by GF(q).

The error-correcting codes implemented in Intel IPP deal with binary finite fields GF(2^m), consisting of 2^m possible bit strings of length m, and essentially use polynomials over GF(2^m).

Accordingly, the Intel IPP data integrity functions are divided into groups described in the following sections:

GF(2^m) Arithmetic Functions

Arithmetic Functions for Polynomials over GF(2 ^m)

Reed-Solomon Code Functions.