Algorithm 2: Authentication process
Givena user feature vector 
and the corrected encrypted version of the feature vector, 
Encodethe word 
as a codeword 
of length n
Find 
Set the system 
Set 
Repeat
Find the reduced GrÓ§bner bases G of 
with respected the specified ordering
Set 
Until G takes of the form 
Find the vector 
of unknown syndromes of 
Computethe error vector 
If the word 
equalsthe first k bits of
, then matching is accepted