In one embodiment, a forward substitution component performs forward substitution based on a lower-triangular matrix and an input vector to generate an output vector. The forward substitution component has memory, a first permuter, an XOR gate array, and a second permuter. The memory stores output sub-vectors of the output vector. The first permuter permutates one or more previously generated output sub-vectors stored in the memory based on one or more permutation coefficients corresponding to a current block row of the lower-triangular matrix to generate one or more permuted sub-vectors. The XOR gate array performs exclusive disjunction on (i) the one or more permuted sub-vectors and (ii) a current input sub-vector of the input vector to generate an intermediate sub-vector. The second permuter permutates the intermediate sub-vector based on a permutation coefficient corresponding to another block in the current block row to generate a current output sub-vector of the output vector.