polarRLCE: A New Code-Based Cryptosystem Using Polar Codes
Algorithm 1
Stern’s ISD algorithm.
Input: Generator matrix , with parameters t, p, and l.
Output: Codeword , s.t. .
1 Select a random information set from and divide it into two equal size subsets and . Moreover, select a size-l subset of .
2 Permutate randomly, and let denote the systematic form:
where is the identity matrix, is a matrix and is a matrix.
3 Let run through all p-weight vectors of length . Then, put all vectors in a sorted list , sorted according to index , with being the value of a vector in positions to , i.e., .
4 Then, construct another list sorted according to , containing all vectors , where run through all p-weight vectors of length .
5 Add all pairs of vectors and for which and put in a new list .
