MpcLib.Circuits.LPSortingCalculationCache.generateY C# (CSharp) Method

        public int[] generateY(int length)
        {
            Debug.Assert(length < MAX_SIZE);
            if (BadSortCache[length] != null)
                return BadSortCache[length];

            List<int> badSortList = new List<int>();

            // we need to figure out when the H function for the bit string is greater than n^(-.178)
            PopulateBetaCacheOuter(length, SMALL);
            PopulateBetaCacheOuter(length, BIG);

            int powLength = 1 << length;

            double threshold = Math.Pow(powLength, -.178);
            double deltaEvalPoints = DeltaFunction(GetSmallBetaEval(length), GetLargeBetaEval(length));
            for (int i = 0; i < powLength; i++)
            {
                double h = HFunction(BetaCache[length, SMALL][i], BetaCache[length, BIG][i], deltaEvalPoints);
                if (h > threshold)
                {
                    badSortList.Add(i);
                }
            }

            BadSortCache[length] = badSortList.ToArray();

            return BadSortCache[length];
        }

        // 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);
        }