Low-power error correction code computation in gf (2r)

A computer implemented method of performing division operations in an error correction code, comprising the steps of:

• receiving an output ω of an error correction code (ECC) algorithm, wherein ω∈F*=F\{0} wherein F=GF(2r) be a Galois field of 2r elements, r=2s, r and s are integers, ω=Σ0≤i≤r−1βi×αi wherein α is a fixed primitive element of F, and βi∈GF(2), wherein K=GF(2s) is a subfield of F, and {1, α} is a basis of F in a linear subspace of K;
• choosing a primitive element δ∈K, wherein ω=ω1+α×ω2, ω1=Σ0≤i≤s−1γi×δi∈K, ω2=Σ0≤i≤s−1γi+s×δi∈K, and γ=[γ0, . . . , γr−1]T∈GF(2)2;
• accessing a first table with ω1 to obtain ω3=ω1−1 where ω3∈K, and computing ω2×ω3 in field K, when ω1≠0;
• accessing a second table with ω2=ω3 to obtain (1+α×ω2×ω3)−1=ω4+α×ω5, where ω4, ω5∈K, and wherein ω−1=(ω1×(1+α×ω2×ω3))−1=ω3×(ω4+α×ω5)=ω3×ω4+α×ω3×ω5;
• and
• computing products ω3×ω4 and ω3×ω5 in field K to obtain ω−1=Σ0≤i≤s−1θi×δi+α·Σi≤i≤s−1θi+s=δi where θi∈GF(2).