The hardness of solving subset sum with preprocessing
Antoine C. Lobstein · IEEE Transactions on Information Theory · 1990
The two problems subset sum and linear decoding (which have given birth to the knapsack and the McEliece public-key cryptosystems) are known to be NP-complete. For linear decoding, it has been proved that, even if one knows the linear code in advance and can preprocess it, the existence of a polynomial-time decoding algorithm would imply that the polynomial-time hierarchy collapses at an early stage. It is proved that the same holds for subset sum. Even if the knapsack is known in advance and can be preprocessed, there is no polynomial-time algorithm solving it, unless the polynomial hierarchy collapses. Also given is the sketch of a new, straightforward proof of this result for linear decoding.>