/// <summary>
        /// Calculates the authpath and root for tree in layer h which starts with seed[h]
        /// </summary>
        /// 
        /// <param name="NextStack">Stack used for the treehash instance created by this method</param>
        /// <param name="Seed">Starting seeds</param>
        /// <param name="H">Actual layer</param>
        /// 
        /// <returns>An initialized GMSSRootCalc</returns>
        private GMSSRootCalc GenerateNextAuthpathAndRoot(List<byte[]> NextStack, byte[] Seed, int H)
        {
            byte[] OTSseed = new byte[_numLayer];
            WinternitzOTSignature ots;

            // data structure that constructs the whole tree and stores the initial values for treehash, Auth and retain
            GMSSRootCalc treeToConstruct = new GMSSRootCalc(_heightOfTrees[H], _K[H], GetDigest(_msgDigestType));
            treeToConstruct.Initialize(NextStack);
            int seedForTreehashIndex = 3;
            int count = 0;

            // update the tree 2^(H) times, from the first to the last leaf
            for (int i = 0; i < (1 << _heightOfTrees[H]); i++)
            {
                // initialize the seeds for the leaf generation with index 3 * 2^h
                if (i == seedForTreehashIndex && count < _heightOfTrees[H] - _K[H])
                {
                    treeToConstruct.InitializeTreehashSeed(Seed, count);
                    seedForTreehashIndex *= 2;
                    count++;
                }

                OTSseed = _gmssRand.NextSeed(Seed);
                ots = new WinternitzOTSignature(OTSseed, GetDigest(_msgDigestType), _otsIndex[H]);
                treeToConstruct.Update(ots.GetPublicKey());
            }

            if (treeToConstruct.IsFinished())
                return treeToConstruct;

            return null;
        }
        /// <summary>
        /// Calculates the authpath for tree in layer h which starts with seed[h] additionally computes the rootSignature of underlaying root
        /// </summary>
        /// 
        /// <param name="LowerRoot">Stores the root of the lower tree</param>
        /// <param name="CurrentStack">Stack used for the treehash instance created by this method</param>
        /// <param name="Seed">Starting seeds</param>
        /// <param name="H">Actual layer</param>
        /// <returns>An initialized GMSSRootCalc</returns>
        private GMSSRootCalc GenerateCurrentAuthpathAndRoot(byte[] LowerRoot, List<byte[]> CurrentStack, byte[] Seed, int H)
        {
            byte[] help = new byte[_mdLength];
            byte[] OTSseed = new byte[_mdLength];
            OTSseed = _gmssRand.NextSeed(Seed);
            WinternitzOTSignature ots;
            // data structure that constructs the whole tree and stores the initial values for treehash, Auth and retain
            GMSSRootCalc treeToConstruct = new GMSSRootCalc(_heightOfTrees[H], _K[H], GetDigest(_msgDigestType));
            treeToConstruct.Initialize(CurrentStack);

            // generate the first leaf
            if (H == _numLayer - 1)
            {
                ots = new WinternitzOTSignature(OTSseed, GetDigest(_msgDigestType), _otsIndex[H]);
                help = ots.GetPublicKey();
            }
            else
            {
                // for all layers except the lowest, generate the signature of the underlying root
                // and reuse this signature to compute the first leaf of acual layer more efficiently (by verifiing the signature)
                ots = new WinternitzOTSignature(OTSseed, GetDigest(_msgDigestType), _otsIndex[H]);
                _currentRootSigs[H] = ots.GetSignature(LowerRoot);
                WinternitzOTSVerify otsver = new WinternitzOTSVerify(GetDigest(_msgDigestType), _otsIndex[H]);
                help = otsver.Verify(LowerRoot, _currentRootSigs[H]);
            }

            // update the tree with the first leaf
            treeToConstruct.Update(help);
            int seedForTreehashIndex = 3;
            int count = 0;

            // update the tree 2^(H) - 1 times, from the second to the last leaf
            for (int i = 1; i < (1 << _heightOfTrees[H]); i++)
            {
                // initialize the seeds for the leaf generation with index 3 * 2^h
                if (i == seedForTreehashIndex && count < _heightOfTrees[H] - _K[H])
                {
                    treeToConstruct.InitializeTreehashSeed(Seed, count);
                    seedForTreehashIndex *= 2;
                    count++;
                }

                OTSseed = _gmssRand.NextSeed(Seed);
                ots = new WinternitzOTSignature(OTSseed, GetDigest(_msgDigestType), _otsIndex[H]);
                treeToConstruct.Update(ots.GetPublicKey());
            }

            if (treeToConstruct.IsFinished())
                return treeToConstruct;

            return null;
        }