// Lemma 4.1 private PermutationNetwork CreateBlockCorrectionNetwork(int blockBitLength, int unsortedness) { PermutationNetwork pn = new PermutationNetwork(1 << blockBitLength); SortedSet <int> ySet = new SortedSet <int>(CalculationCache.generateY(blockBitLength)); Debug.Assert(ySet.Count <= 1 << unsortedness); // augment Y with arbitrary elements int ySize = 1 << (unsortedness + 1); int blockSize = 1 << blockBitLength; Random rand = new Random(0); while (ySet.Count < ySize) { ySet.Add(rand.Next(blockSize)); } // here our implementation differs from the paper. The paper first to extract Y then order the X by the permutation pi. // Instead, we will order all of the inputs by the permutation pi, then map Y using the permutation pi and move X to the top of the block // and Y to the bottom so that we can unshuffle X and add Y. int[] pi = CalculationCache.generatePi(blockBitLength); pn.AppendGate(new PermutationGate(pi), 0); int[] mappedY = new int[ySize]; int i = 0; foreach (var yElem in ySet) { mappedY[i++] = pi[yElem]; } pn.AppendGate(PermutationGateFactory.CreateSplitGate(blockSize, mappedY, false), 0); // we now want to unshuffle X into 2^(l+1) groups and add one element of Y to each group pn.AppendGate(PermutationGateFactory.CreateUnshuffleGate(blockSize - ySize, ySize), 0); pn.AppendGate(PermutationGateFactory.CreateMultiGroupInserterGate(blockSize, (blockSize / ySize) - 1, ySize), 0); var treeInsertion = SortingNetworkFactory.CreateBinaryTreeInsertion(blockSize / ySize); // use binary tree insertion to insert the elemnt we just added to each group for (int j = 0; j < ySize; j++) { pn.AppendNetwork(treeInsertion.Clone() as PermutationNetwork, j * blockSize / ySize); } // now shuffle all of the lists back together pn.AppendGate(PermutationGateFactory.CreateShuffleGate(blockSize, ySize), 0); return(pn); }