upstream: Add experimental support for PQC XMSS keys (Extended

Hash-Based Signatures) The code is not compiled in by default (see WITH_XMSS
in Makefile.inc) Joint work with stefan-lukas_gazdag at genua.eu See
https://tools.ietf.org/html/draft-irtf-cfrg-xmss-hash-based-signatures-12 ok
djm@

OpenBSD-Commit-ID: ef3eccb96762a5d6f135d7daeef608df7776a7ac

1 files changed, 1099 insertions, 0 deletions

diff --git a/xmss_fast.c b/xmss_fast.c
new file mode 100644
index 000000000..7ddc92f83
--- /dev/null
+++ b/xmss_fast.c
@@ -0,0 +1,1099 @@
+/*
+xmss_fast.c version 20160722
+Andreas Hülsing
+Joost Rijneveld
+Public domain.
+*/
+
+#include "xmss_fast.h"
+#include <stdlib.h>
+#include <string.h>
+#include <stdint.h>
+
+#include "crypto_api.h"
+#include "xmss_wots.h"
+#include "xmss_hash.h"
+
+#include "xmss_commons.h"
+#include "xmss_hash_address.h"
+// For testing
+#include "stdio.h"
+
+
+
+/**
+ * Used for pseudorandom keygeneration,
+ * generates the seed for the WOTS keypair at address addr
+ *
+ * takes n byte sk_seed and returns n byte seed using 32 byte address addr.
+ */
+static void get_seed(unsigned char *seed, const unsigned char *sk_seed, int n, uint32_t addr[8])
+{
+  unsigned char bytes[32];
+  // Make sure that chain addr, hash addr, and key bit are 0!
+  setChainADRS(addr,0);
+  setHashADRS(addr,0);
+  setKeyAndMask(addr,0);
+  // Generate pseudorandom value
+  addr_to_byte(bytes, addr);
+  prf(seed, bytes, sk_seed, n);
+}
+
+/**
+ * Initialize xmss params struct
+ * parameter names are the same as in the draft
+ * parameter k is K as used in the BDS algorithm
+ */
+int xmss_set_params(xmss_params *params, int n, int h, int w, int k)
+{
+  if (k >= h || k < 2 || (h - k) % 2) {
+    fprintf(stderr, "For BDS traversal, H - K must be even, with H > K >= 2!\n");
+    return 1;
+  }
+  params->h = h;
+  params->n = n;
+  params->k = k;
+  wots_params wots_par;
+  wots_set_params(&wots_par, n, w);
+  params->wots_par = wots_par;
+  return 0;
+}
+
+/**
+ * Initialize BDS state struct
+ * parameter names are the same as used in the description of the BDS traversal
+ */
+void xmss_set_bds_state(bds_state *state, unsigned char *stack, int stackoffset, unsigned char *stacklevels, unsigned char *auth, unsigned char *keep, treehash_inst *treehash, unsigned char *retain, int next_leaf)
+{
+  state->stack = stack;
+  state->stackoffset = stackoffset;
+  state->stacklevels = stacklevels;
+  state->auth = auth;
+  state->keep = keep;
+  state->treehash = treehash;
+  state->retain = retain;
+  state->next_leaf = next_leaf;
+}
+
+/**
+ * Initialize xmssmt_params struct
+ * parameter names are the same as in the draft
+ *
+ * Especially h is the total tree height, i.e. the XMSS trees have height h/d
+ */
+int xmssmt_set_params(xmssmt_params *params, int n, int h, int d, int w, int k)
+{
+  if (h % d) {
+    fprintf(stderr, "d must divide h without remainder!\n");
+    return 1;
+  }
+  params->h = h;
+  params->d = d;
+  params->n = n;
+  params->index_len = (h + 7) / 8;
+  xmss_params xmss_par;
+  if (xmss_set_params(&xmss_par, n, (h/d), w, k)) {
+    return 1;
+  }
+  params->xmss_par = xmss_par;
+  return 0;
+}
+
+/**
+ * Computes a leaf from a WOTS public key using an L-tree.
+ */
+static void l_tree(unsigned char *leaf, unsigned char *wots_pk, const xmss_params *params, const unsigned char *pub_seed, uint32_t addr[8])
+{
+  unsigned int l = params->wots_par.len;
+  unsigned int n = params->n;
+  uint32_t i = 0;
+  uint32_t height = 0;
+  uint32_t bound;
+
+  //ADRS.setTreeHeight(0);
+  setTreeHeight(addr, height);
+  
+  while (l > 1) {
+     bound = l >> 1; //floor(l / 2);
+     for (i = 0; i < bound; i++) {
+       //ADRS.setTreeIndex(i);
+       setTreeIndex(addr, i);
+       //wots_pk[i] = RAND_HASH(pk[2i], pk[2i + 1], SEED, ADRS);
+       hash_h(wots_pk+i*n, wots_pk+i*2*n, pub_seed, addr, n);
+     }
+     //if ( l % 2 == 1 ) {
+     if (l & 1) {
+       //pk[floor(l / 2) + 1] = pk[l];
+       memcpy(wots_pk+(l>>1)*n, wots_pk+(l-1)*n, n);
+       //l = ceil(l / 2);
+       l=(l>>1)+1;
+     }
+     else {
+       //l = ceil(l / 2);
+       l=(l>>1);
+     }
+     //ADRS.setTreeHeight(ADRS.getTreeHeight() + 1);
+     height++;
+     setTreeHeight(addr, height);
+   }
+   //return pk[0];
+   memcpy(leaf, wots_pk, n);
+}
+
+/**
+ * Computes the leaf at a given address. First generates the WOTS key pair, then computes leaf using l_tree. As this happens position independent, we only require that addr encodes the right ltree-address.
+ */
+static void gen_leaf_wots(unsigned char *leaf, const unsigned char *sk_seed, const xmss_params *params, const unsigned char *pub_seed, uint32_t ltree_addr[8], uint32_t ots_addr[8])
+{
+  unsigned char seed[params->n];
+  unsigned char pk[params->wots_par.keysize];
+
+  get_seed(seed, sk_seed, params->n, ots_addr);
+  wots_pkgen(pk, seed, &(params->wots_par), pub_seed, ots_addr);
+
+  l_tree(leaf, pk, params, pub_seed, ltree_addr);
+}
+
+static int treehash_minheight_on_stack(bds_state* state, const xmss_params *params, const treehash_inst *treehash) {
+  unsigned int r = params->h, i;
+  for (i = 0; i < treehash->stackusage; i++) {
+    if (state->stacklevels[state->stackoffset - i - 1] < r) {
+      r = state->stacklevels[state->stackoffset - i - 1];
+    }
+  }
+  return r;
+}
+
+/**
+ * Merkle's TreeHash algorithm. The address only needs to initialize the first 78 bits of addr. Everything else will be set by treehash.
+ * Currently only used for key generation.
+ *
+ */
+static void treehash_setup(unsigned char *node, int height, int index, bds_state *state, const unsigned char *sk_seed, const xmss_params *params, const unsigned char *pub_seed, const uint32_t addr[8])
+{
+  unsigned int idx = index;
+  unsigned int n = params->n;
+  unsigned int h = params->h;
+  unsigned int k = params->k;
+  // use three different addresses because at this point we use all three formats in parallel
+  uint32_t ots_addr[8];
+  uint32_t ltree_addr[8];
+  uint32_t  node_addr[8];
+  // only copy layer and tree address parts
+  memcpy(ots_addr, addr, 12);
+  // type = ots
+  setType(ots_addr, 0);
+  memcpy(ltree_addr, addr, 12);
+  setType(ltree_addr, 1);
+  memcpy(node_addr, addr, 12);
+  setType(node_addr, 2);
+
+  uint32_t lastnode, i;
+  unsigned char stack[(height+1)*n];
+  unsigned int stacklevels[height+1];
+  unsigned int stackoffset=0;
+  unsigned int nodeh;
+
+  lastnode = idx+(1<<height);
+
+  for (i = 0; i < h-k; i++) {
+    state->treehash[i].h = i;
+    state->treehash[i].completed = 1;
+    state->treehash[i].stackusage = 0;
+  }
+
+  i = 0;
+  for (; idx < lastnode; idx++) {
+    setLtreeADRS(ltree_addr, idx);
+    setOTSADRS(ots_addr, idx);
+    gen_leaf_wots(stack+stackoffset*n, sk_seed, params, pub_seed, ltree_addr, ots_addr);
+    stacklevels[stackoffset] = 0;
+    stackoffset++;
+    if (h - k > 0 && i == 3) {
+      memcpy(state->treehash[0].node, stack+stackoffset*n, n);
+    }
+    while (stackoffset>1 && stacklevels[stackoffset-1] == stacklevels[stackoffset-2])
+    {
+      nodeh = stacklevels[stackoffset-1];
+      if (i >> nodeh == 1) {
+        memcpy(state->auth + nodeh*n, stack+(stackoffset-1)*n, n);
+      }
+      else {
+        if (nodeh < h - k && i >> nodeh == 3) {
+          memcpy(state->treehash[nodeh].node, stack+(stackoffset-1)*n, n);
+        }
+        else if (nodeh >= h - k) {
+          memcpy(state->retain + ((1 << (h - 1 - nodeh)) + nodeh - h + (((i >> nodeh) - 3) >> 1)) * n, stack+(stackoffset-1)*n, n);
+        }
+      }
+      setTreeHeight(node_addr, stacklevels[stackoffset-1]);
+      setTreeIndex(node_addr, (idx >> (stacklevels[stackoffset-1]+1)));
+      hash_h(stack+(stackoffset-2)*n, stack+(stackoffset-2)*n, pub_seed,
+          node_addr, n);
+      stacklevels[stackoffset-2]++;
+      stackoffset--;
+    }
+    i++;
+  }
+
+  for (i = 0; i < n; i++)
+    node[i] = stack[i];
+}
+
+static void treehash_update(treehash_inst *treehash, bds_state *state, const unsigned char *sk_seed, const xmss_params *params, const unsigned char *pub_seed, const uint32_t addr[8]) {
+  int n = params->n;
+
+  uint32_t ots_addr[8];
+  uint32_t ltree_addr[8];
+  uint32_t  node_addr[8];
+  // only copy layer and tree address parts
+  memcpy(ots_addr, addr, 12);
+  // type = ots
+  setType(ots_addr, 0);
+  memcpy(ltree_addr, addr, 12);
+  setType(ltree_addr, 1);
+  memcpy(node_addr, addr, 12);
+  setType(node_addr, 2);
+
+  setLtreeADRS(ltree_addr, treehash->next_idx);
+  setOTSADRS(ots_addr, treehash->next_idx);
+
+  unsigned char nodebuffer[2 * n];
+  unsigned int nodeheight = 0;
+  gen_leaf_wots(nodebuffer, sk_seed, params, pub_seed, ltree_addr, ots_addr);
+  while (treehash->stackusage > 0 && state->stacklevels[state->stackoffset-1] == nodeheight) {
+    memcpy(nodebuffer + n, nodebuffer, n);
+    memcpy(nodebuffer, state->stack + (state->stackoffset-1)*n, n);
+    setTreeHeight(node_addr, nodeheight);
+    setTreeIndex(node_addr, (treehash->next_idx >> (nodeheight+1)));
+    hash_h(nodebuffer, nodebuffer, pub_seed, node_addr, n);
+    nodeheight++;
+    treehash->stackusage--;
+    state->stackoffset--;
+  }
+  if (nodeheight == treehash->h) { // this also implies stackusage == 0
+    memcpy(treehash->node, nodebuffer, n);
+    treehash->completed = 1;
+  }
+  else {
+    memcpy(state->stack + state->stackoffset*n, nodebuffer, n);
+    treehash->stackusage++;
+    state->stacklevels[state->stackoffset] = nodeheight;
+    state->stackoffset++;
+    treehash->next_idx++;
+  }
+}
+
+/**
+ * Computes a root node given a leaf and an authapth
+ */
+static void validate_authpath(unsigned char *root, const unsigned char *leaf, unsigned long leafidx, const unsigned char *authpath, const xmss_params *params, const unsigned char *pub_seed, uint32_t addr[8])
+{
+  unsigned int n = params->n;
+
+  uint32_t i, j;
+  unsigned char buffer[2*n];
+
+  // If leafidx is odd (last bit = 1), current path element is a right child and authpath has to go to the left.
+  // Otherwise, it is the other way around
+  if (leafidx & 1) {
+    for (j = 0; j < n; j++)
+      buffer[n+j] = leaf[j];
+    for (j = 0; j < n; j++)
+      buffer[j] = authpath[j];
+  }
+  else {
+    for (j = 0; j < n; j++)
+      buffer[j] = leaf[j];
+    for (j = 0; j < n; j++)
+      buffer[n+j] = authpath[j];
+  }
+  authpath += n;
+
+  for (i=0; i < params->h-1; i++) {
+    setTreeHeight(addr, i);
+    leafidx >>= 1;
+    setTreeIndex(addr, leafidx);
+    if (leafidx&1) {
+      hash_h(buffer+n, buffer, pub_seed, addr, n);
+      for (j = 0; j < n; j++)
+        buffer[j] = authpath[j];
+    }
+    else {
+      hash_h(buffer, buffer, pub_seed, addr, n);
+      for (j = 0; j < n; j++)
+        buffer[j+n] = authpath[j];
+    }
+    authpath += n;
+  }
+  setTreeHeight(addr, (params->h-1));
+  leafidx >>= 1;
+  setTreeIndex(addr, leafidx);
+  hash_h(root, buffer, pub_seed, addr, n);
+}
+
+/**
+ * Performs one treehash update on the instance that needs it the most.
+ * Returns 1 if such an instance was not found
+ **/
+static char bds_treehash_update(bds_state *state, unsigned int updates, const unsigned char *sk_seed, const xmss_params *params, unsigned char *pub_seed, const uint32_t addr[8]) {
+  uint32_t i, j;
+  unsigned int level, l_min, low;
+  unsigned int h = params->h;
+  unsigned int k = params->k;
+  unsigned int used = 0;
+
+  for (j = 0; j < updates; j++) {
+    l_min = h;
+    level = h - k;
+    for (i = 0; i < h - k; i++) {
+      if (state->treehash[i].completed) {
+        low = h;
+      }
+      else if (state->treehash[i].stackusage == 0) {
+        low = i;
+      }
+      else {
+        low = treehash_minheight_on_stack(state, params, &(state->treehash[i]));
+      }
+      if (low < l_min) {
+        level = i;
+        l_min = low;
+      }
+    }
+    if (level == h - k) {
+      break;
+    }
+    treehash_update(&(state->treehash[level]), state, sk_seed, params, pub_seed, addr);
+    used++;
+  }
+  return updates - used;
+}
+
+/**
+ * Updates the state (typically NEXT_i) by adding a leaf and updating the stack
+ * Returns 1 if all leaf nodes have already been processed
+ **/
+static char bds_state_update(bds_state *state, const unsigned char *sk_seed, const xmss_params *params, unsigned char *pub_seed, const uint32_t addr[8]) {
+  uint32_t ltree_addr[8];
+  uint32_t node_addr[8];
+  uint32_t ots_addr[8];
+
+  int n = params->n;
+  int h = params->h;
+  int k = params->k;
+
+  int nodeh;
+  int idx = state->next_leaf;
+  if (idx == 1 << h) {
+    return 1;
+  }
+
+  // only copy layer and tree address parts
+  memcpy(ots_addr, addr, 12);
+  // type = ots
+  setType(ots_addr, 0);
+  memcpy(ltree_addr, addr, 12);
+  setType(ltree_addr, 1);
+  memcpy(node_addr, addr, 12);
+  setType(node_addr, 2);
+  
+  setOTSADRS(ots_addr, idx);
+  setLtreeADRS(ltree_addr, idx);
+
+  gen_leaf_wots(state->stack+state->stackoffset*n, sk_seed, params, pub_seed, ltree_addr, ots_addr);
+
+  state->stacklevels[state->stackoffset] = 0;
+  state->stackoffset++;
+  if (h - k > 0 && idx == 3) {
+    memcpy(state->treehash[0].node, state->stack+state->stackoffset*n, n);
+  }
+  while (state->stackoffset>1 && state->stacklevels[state->stackoffset-1] == state->stacklevels[state->stackoffset-2]) {
+    nodeh = state->stacklevels[state->stackoffset-1];
+    if (idx >> nodeh == 1) {
+      memcpy(state->auth + nodeh*n, state->stack+(state->stackoffset-1)*n, n);
+    }
+    else {
+      if (nodeh < h - k && idx >> nodeh == 3) {
+        memcpy(state->treehash[nodeh].node, state->stack+(state->stackoffset-1)*n, n);
+      }
+      else if (nodeh >= h - k) {
+        memcpy(state->retain + ((1 << (h - 1 - nodeh)) + nodeh - h + (((idx >> nodeh) - 3) >> 1)) * n, state->stack+(state->stackoffset-1)*n, n);
+      }
+    }
+    setTreeHeight(node_addr, state->stacklevels[state->stackoffset-1]);
+    setTreeIndex(node_addr, (idx >> (state->stacklevels[state->stackoffset-1]+1)));
+    hash_h(state->stack+(state->stackoffset-2)*n, state->stack+(state->stackoffset-2)*n, pub_seed, node_addr, n);
+
+    state->stacklevels[state->stackoffset-2]++;
+    state->stackoffset--;
+  }
+  state->next_leaf++;
+  return 0;
+}
+
+/**
+ * Returns the auth path for node leaf_idx and computes the auth path for the
+ * next leaf node, using the algorithm described by Buchmann, Dahmen and Szydlo
+ * in "Post Quantum Cryptography", Springer 2009.
+ */
+static void bds_round(bds_state *state, const unsigned long leaf_idx, const unsigned char *sk_seed, const xmss_params *params, unsigned char *pub_seed, uint32_t addr[8])
+{
+  unsigned int i;
+  unsigned int n = params->n;
+  unsigned int h = params->h;
+  unsigned int k = params->k;
+
+  unsigned int tau = h;
+  unsigned int startidx;
+  unsigned int offset, rowidx;
+  unsigned char buf[2 * n];
+
+  uint32_t ots_addr[8];
+  uint32_t ltree_addr[8];
+  uint32_t  node_addr[8];
+  // only copy layer and tree address parts
+  memcpy(ots_addr, addr, 12);
+  // type = ots
+  setType(ots_addr, 0);
+  memcpy(ltree_addr, addr, 12);
+  setType(ltree_addr, 1);
+  memcpy(node_addr, addr, 12);
+  setType(node_addr, 2);
+
+  for (i = 0; i < h; i++) {
+    if (! ((leaf_idx >> i) & 1)) {
+      tau = i;
+      break;
+    }
+  }
+
+  if (tau > 0) {
+    memcpy(buf,     state->auth + (tau-1) * n, n);
+    // we need to do this before refreshing state->keep to prevent overwriting
+    memcpy(buf + n, state->keep + ((tau-1) >> 1) * n, n);
+  }
+  if (!((leaf_idx >> (tau + 1)) & 1) && (tau < h - 1)) {
+    memcpy(state->keep + (tau >> 1)*n, state->auth + tau*n, n);
+  }
+  if (tau == 0) {
+    setLtreeADRS(ltree_addr, leaf_idx);
+    setOTSADRS(ots_addr, leaf_idx);
+    gen_leaf_wots(state->auth, sk_seed, params, pub_seed, ltree_addr, ots_addr);
+  }
+  else {
+    setTreeHeight(node_addr, (tau-1));
+    setTreeIndex(node_addr, leaf_idx >> tau);
+    hash_h(state->auth + tau * n, buf, pub_seed, node_addr, n);
+    for (i = 0; i < tau; i++) {
+      if (i < h - k) {
+        memcpy(state->auth + i * n, state->treehash[i].node, n);
+      }
+      else {
+        offset = (1 << (h - 1 - i)) + i - h;
+        rowidx = ((leaf_idx >> i) - 1) >> 1;
+        memcpy(state->auth + i * n, state->retain + (offset + rowidx) * n, n);
+      }
+    }
+
+    for (i = 0; i < ((tau < h - k) ? tau : (h - k)); i++) {
+      startidx = leaf_idx + 1 + 3 * (1 << i);
+      if (startidx < 1U << h) {
+        state->treehash[i].h = i;
+        state->treehash[i].next_idx = startidx;
+        state->treehash[i].completed = 0;
+        state->treehash[i].stackusage = 0;
+      }
+    }
+  }
+}
+
+/*
+ * Generates a XMSS key pair for a given parameter set.
+ * Format sk: [(32bit) idx || SK_SEED || SK_PRF || PUB_SEED || root]
+ * Format pk: [root || PUB_SEED] omitting algo oid.
+ */
+int xmss_keypair(unsigned char *pk, unsigned char *sk, bds_state *state, xmss_params *params)
+{
+  unsigned int n = params->n;
+  // Set idx = 0
+  sk[0] = 0;
+  sk[1] = 0;
+  sk[2] = 0;
+  sk[3] = 0;
+  // Init SK_SEED (n byte), SK_PRF (n byte), and PUB_SEED (n byte)
+  randombytes(sk+4, 3*n);
+  // Copy PUB_SEED to public key
+  memcpy(pk+n, sk+4+2*n, n);
+
+  uint32_t addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+
+  // Compute root
+  treehash_setup(pk, params->h, 0, state, sk+4, params, sk+4+2*n, addr);
+  // copy root to sk
+  memcpy(sk+4+3*n, pk, n);
+  return 0;
+}
+
+/**
+ * Signs a message.
+ * Returns
+ * 1. an array containing the signature followed by the message AND
+ * 2. an updated secret key!
+ *
+ */
+int xmss_sign(unsigned char *sk, bds_state *state, unsigned char *sig_msg, unsigned long long *sig_msg_len, const unsigned char *msg, unsigned long long msglen, const xmss_params *params)
+{
+  unsigned int h = params->h;
+  unsigned int n = params->n;
+  unsigned int k = params->k;
+  uint16_t i = 0;
+
+  // Extract SK
+  unsigned long idx = ((unsigned long)sk[0] << 24) | ((unsigned long)sk[1] << 16) | ((unsigned long)sk[2] << 8) | sk[3];
+  unsigned char sk_seed[n];
+  memcpy(sk_seed, sk+4, n);
+  unsigned char sk_prf[n];
+  memcpy(sk_prf, sk+4+n, n);
+  unsigned char pub_seed[n];
+  memcpy(pub_seed, sk+4+2*n, n);
+  
+  // index as 32 bytes string
+  unsigned char idx_bytes_32[32];
+  to_byte(idx_bytes_32, idx, 32);
+  
+  unsigned char hash_key[3*n]; 
+  
+  // Update SK
+  sk[0] = ((idx + 1) >> 24) & 255;
+  sk[1] = ((idx + 1) >> 16) & 255;
+  sk[2] = ((idx + 1) >> 8) & 255;
+  sk[3] = (idx + 1) & 255;
+  // -- Secret key for this non-forward-secure version is now updated.
+  // -- A productive implementation should use a file handle instead and write the updated secret key at this point!
+
+  // Init working params
+  unsigned char R[n];
+  unsigned char msg_h[n];
+  unsigned char ots_seed[n];
+  uint32_t ots_addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+
+  // ---------------------------------
+  // Message Hashing
+  // ---------------------------------
+
+  // Message Hash:
+  // First compute pseudorandom value
+  prf(R, idx_bytes_32, sk_prf, n);
+  // Generate hash key (R || root || idx)
+  memcpy(hash_key, R, n);
+  memcpy(hash_key+n, sk+4+3*n, n);
+  to_byte(hash_key+2*n, idx, n);
+  // Then use it for message digest
+  h_msg(msg_h, msg, msglen, hash_key, 3*n, n);
+
+  // Start collecting signature
+  *sig_msg_len = 0;
+
+  // Copy index to signature
+  sig_msg[0] = (idx >> 24) & 255;
+  sig_msg[1] = (idx >> 16) & 255;
+  sig_msg[2] = (idx >> 8) & 255;
+  sig_msg[3] = idx & 255;
+
+  sig_msg += 4;
+  *sig_msg_len += 4;
+
+  // Copy R to signature
+  for (i = 0; i < n; i++)
+    sig_msg[i] = R[i];
+
+  sig_msg += n;
+  *sig_msg_len += n;
+
+  // ----------------------------------
+  // Now we start to "really sign"
+  // ----------------------------------
+
+  // Prepare Address
+  setType(ots_addr, 0);
+  setOTSADRS(ots_addr, idx);
+
+  // Compute seed for OTS key pair
+  get_seed(ots_seed, sk_seed, n, ots_addr);
+
+  // Compute WOTS signature
+  wots_sign(sig_msg, msg_h, ots_seed, &(params->wots_par), pub_seed, ots_addr);
+
+  sig_msg += params->wots_par.keysize;
+  *sig_msg_len += params->wots_par.keysize;
+
+  // the auth path was already computed during the previous round
+  memcpy(sig_msg, state->auth, h*n);
+
+  if (idx < (1U << h) - 1) {
+    bds_round(state, idx, sk_seed, params, pub_seed, ots_addr);
+    bds_treehash_update(state, (h - k) >> 1, sk_seed, params, pub_seed, ots_addr);
+  }
+
+/* TODO: save key/bds state here! */
+
+  sig_msg += params->h*n;
+  *sig_msg_len += params->h*n;
+
+  //Whipe secret elements?
+  //zerobytes(tsk, CRYPTO_SECRETKEYBYTES);
+
+
+  memcpy(sig_msg, msg, msglen);
+  *sig_msg_len += msglen;
+
+  return 0;
+}
+
+/**
+ * Verifies a given message signature pair under a given public key.
+ */
+int xmss_sign_open(unsigned char *msg, unsigned long long *msglen, const unsigned char *sig_msg, unsigned long long sig_msg_len, const unsigned char *pk, const xmss_params *params)
+{
+  unsigned int n = params->n;
+
+  unsigned long long i, m_len;
+  unsigned long idx=0;
+  unsigned char wots_pk[params->wots_par.keysize];
+  unsigned char pkhash[n];
+  unsigned char root[n];
+  unsigned char msg_h[n];
+  unsigned char hash_key[3*n];
+
+  unsigned char pub_seed[n];
+  memcpy(pub_seed, pk+n, n);
+
+  // Init addresses
+  uint32_t ots_addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+  uint32_t ltree_addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+  uint32_t node_addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+
+  setType(ots_addr, 0);
+  setType(ltree_addr, 1);
+  setType(node_addr, 2);
+
+  // Extract index
+  idx = ((unsigned long)sig_msg[0] << 24) | ((unsigned long)sig_msg[1] << 16) | ((unsigned long)sig_msg[2] << 8) | sig_msg[3];
+  printf("verify:: idx = %lu\n", idx);
+  
+  // Generate hash key (R || root || idx)
+  memcpy(hash_key, sig_msg+4,n);
+  memcpy(hash_key+n, pk, n);
+  to_byte(hash_key+2*n, idx, n);
+  
+  sig_msg += (n+4);
+  sig_msg_len -= (n+4);
+
+  // hash message 
+  unsigned long long tmp_sig_len = params->wots_par.keysize+params->h*n;
+  m_len = sig_msg_len - tmp_sig_len;
+  h_msg(msg_h, sig_msg + tmp_sig_len, m_len, hash_key, 3*n, n);
+
+  //-----------------------
+  // Verify signature
+  //-----------------------
+
+  // Prepare Address
+  setOTSADRS(ots_addr, idx);
+  // Check WOTS signature
+  wots_pkFromSig(wots_pk, sig_msg, msg_h, &(params->wots_par), pub_seed, ots_addr);
+
+  sig_msg += params->wots_par.keysize;
+  sig_msg_len -= params->wots_par.keysize;
+
+  // Compute Ltree
+  setLtreeADRS(ltree_addr, idx);
+  l_tree(pkhash, wots_pk, params, pub_seed, ltree_addr);
+
+  // Compute root
+  validate_authpath(root, pkhash, idx, sig_msg, params, pub_seed, node_addr);
+
+  sig_msg += params->h*n;
+  sig_msg_len -= params->h*n;
+
+  for (i = 0; i < n; i++)
+    if (root[i] != pk[i])
+      goto fail;
+
+  *msglen = sig_msg_len;
+  for (i = 0; i < *msglen; i++)
+    msg[i] = sig_msg[i];
+
+  return 0;
+
+
+fail:
+  *msglen = sig_msg_len;
+  for (i = 0; i < *msglen; i++)
+    msg[i] = 0;
+  *msglen = -1;
+  return -1;
+}
+
+/*
+ * Generates a XMSSMT key pair for a given parameter set.
+ * Format sk: [(ceil(h/8) bit) idx || SK_SEED || SK_PRF || PUB_SEED || root]
+ * Format pk: [root || PUB_SEED] omitting algo oid.
+ */
+int xmssmt_keypair(unsigned char *pk, unsigned char *sk, bds_state *states, unsigned char *wots_sigs, xmssmt_params *params)
+{
+  unsigned int n = params->n;
+  unsigned int i;
+  unsigned char ots_seed[params->n];
+  // Set idx = 0
+  for (i = 0; i < params->index_len; i++) {
+    sk[i] = 0;
+  }
+  // Init SK_SEED (n byte), SK_PRF (n byte), and PUB_SEED (n byte)
+  randombytes(sk+params->index_len, 3*n);
+  // Copy PUB_SEED to public key
+  memcpy(pk+n, sk+params->index_len+2*n, n);
+
+  // Set address to point on the single tree on layer d-1
+  uint32_t addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+  setLayerADRS(addr, (params->d-1));
+  // Set up state and compute wots signatures for all but topmost tree root
+  for (i = 0; i < params->d - 1; i++) {
+    // Compute seed for OTS key pair
+    treehash_setup(pk, params->xmss_par.h, 0, states + i, sk+params->index_len, &(params->xmss_par), pk+n, addr);
+    setLayerADRS(addr, (i+1));
+    get_seed(ots_seed, sk+params->index_len, n, addr);
+    wots_sign(wots_sigs + i*params->xmss_par.wots_par.keysize, pk, ots_seed, &(params->xmss_par.wots_par), pk+n, addr);
+  }
+  treehash_setup(pk, params->xmss_par.h, 0, states + i, sk+params->index_len, &(params->xmss_par), pk+n, addr);
+  memcpy(sk+params->index_len+3*n, pk, n);
+  return 0;
+}
+
+/**
+ * Signs a message.
+ * Returns
+ * 1. an array containing the signature followed by the message AND
+ * 2. an updated secret key!
+ *
+ */
+int xmssmt_sign(unsigned char *sk, bds_state *states, unsigned char *wots_sigs, unsigned char *sig_msg, unsigned long long *sig_msg_len, const unsigned char *msg, unsigned long long msglen, const xmssmt_params *params)
+{
+  unsigned int n = params->n;
+  
+  unsigned int tree_h = params->xmss_par.h;
+  unsigned int h = params->h;
+  unsigned int k = params->xmss_par.k;
+  unsigned int idx_len = params->index_len;
+  uint64_t idx_tree;
+  uint32_t idx_leaf;
+  uint64_t i, j;
+  int needswap_upto = -1;
+  unsigned int updates;
+
+  unsigned char sk_seed[n];
+  unsigned char sk_prf[n];
+  unsigned char pub_seed[n];
+  // Init working params
+  unsigned char R[n];
+  unsigned char msg_h[n];
+  unsigned char hash_key[3*n];
+  unsigned char ots_seed[n];
+  uint32_t addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+  uint32_t ots_addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+  unsigned char idx_bytes_32[32];
+  bds_state tmp;
+
+  // Extract SK 
+  unsigned long long idx = 0;
+  for (i = 0; i < idx_len; i++) {
+    idx |= ((unsigned long long)sk[i]) << 8*(idx_len - 1 - i);
+  }
+
+  memcpy(sk_seed, sk+idx_len, n);
+  memcpy(sk_prf, sk+idx_len+n, n);
+  memcpy(pub_seed, sk+idx_len+2*n, n);
+
+  // Update SK
+  for (i = 0; i < idx_len; i++) {
+    sk[i] = ((idx + 1) >> 8*(idx_len - 1 - i)) & 255;
+  }
+  // -- Secret key for this non-forward-secure version is now updated.
+  // -- A productive implementation should use a file handle instead and write the updated secret key at this point!
+
+
+  // ---------------------------------
+  // Message Hashing
+  // ---------------------------------
+
+  // Message Hash:
+  // First compute pseudorandom value
+  to_byte(idx_bytes_32, idx, 32);
+  prf(R, idx_bytes_32, sk_prf, n);
+  // Generate hash key (R || root || idx)
+  memcpy(hash_key, R, n);
+  memcpy(hash_key+n, sk+idx_len+3*n, n);
+  to_byte(hash_key+2*n, idx, n);
+  
+  // Then use it for message digest
+  h_msg(msg_h, msg, msglen, hash_key, 3*n, n);
+
+  // Start collecting signature
+  *sig_msg_len = 0;
+
+  // Copy index to signature
+  for (i = 0; i < idx_len; i++) {
+    sig_msg[i] = (idx >> 8*(idx_len - 1 - i)) & 255;
+  }
+
+  sig_msg += idx_len;
+  *sig_msg_len += idx_len;
+
+  // Copy R to signature
+  for (i = 0; i < n; i++)
+    sig_msg[i] = R[i];
+
+  sig_msg += n;
+  *sig_msg_len += n;
+
+  // ----------------------------------
+  // Now we start to "really sign"
+  // ----------------------------------
+
+  // Handle lowest layer separately as it is slightly different...
+
+  // Prepare Address
+  setType(ots_addr, 0);
+  idx_tree = idx >> tree_h;
+  idx_leaf = (idx & ((1 << tree_h)-1));
+  setLayerADRS(ots_addr, 0);
+  setTreeADRS(ots_addr, idx_tree);
+  setOTSADRS(ots_addr, idx_leaf);
+
+  // Compute seed for OTS key pair
+  get_seed(ots_seed, sk_seed, n, ots_addr);
+
+  // Compute WOTS signature
+  wots_sign(sig_msg, msg_h, ots_seed, &(params->xmss_par.wots_par), pub_seed, ots_addr);
+
+  sig_msg += params->xmss_par.wots_par.keysize;
+  *sig_msg_len += params->xmss_par.wots_par.keysize;
+
+  memcpy(sig_msg, states[0].auth, tree_h*n);
+  sig_msg += tree_h*n;
+  *sig_msg_len += tree_h*n;
+
+  // prepare signature of remaining layers
+  for (i = 1; i < params->d; i++) {
+    // put WOTS signature in place
+    memcpy(sig_msg, wots_sigs + (i-1)*params->xmss_par.wots_par.keysize, params->xmss_par.wots_par.keysize);
+
+    sig_msg += params->xmss_par.wots_par.keysize;
+    *sig_msg_len += params->xmss_par.wots_par.keysize;
+
+    // put AUTH nodes in place
+    memcpy(sig_msg, states[i].auth, tree_h*n);
+    sig_msg += tree_h*n;
+    *sig_msg_len += tree_h*n;
+  }
+
+  updates = (tree_h - k) >> 1;
+
+  setTreeADRS(addr, (idx_tree + 1));
+  // mandatory update for NEXT_0 (does not count towards h-k/2) if NEXT_0 exists
+  if ((1 + idx_tree) * (1 << tree_h) + idx_leaf < (1ULL << h)) {
+    bds_state_update(&states[params->d], sk_seed, &(params->xmss_par), pub_seed, addr);
+  }
+
+  for (i = 0; i < params->d; i++) {
+    // check if we're not at the end of a tree
+    if (! (((idx + 1) & ((1ULL << ((i+1)*tree_h)) - 1)) == 0)) {
+      idx_leaf = (idx >> (tree_h * i)) & ((1 << tree_h)-1);
+      idx_tree = (idx >> (tree_h * (i+1)));
+      setLayerADRS(addr, i);
+      setTreeADRS(addr, idx_tree);
+      if (i == (unsigned int) (needswap_upto + 1)) {
+        bds_round(&states[i], idx_leaf, sk_seed, &(params->xmss_par), pub_seed, addr);
+      }
+      updates = bds_treehash_update(&states[i], updates, sk_seed, &(params->xmss_par), pub_seed, addr);
+      setTreeADRS(addr, (idx_tree + 1));
+      // if a NEXT-tree exists for this level;
+      if ((1 + idx_tree) * (1 << tree_h) + idx_leaf < (1ULL << (h - tree_h * i))) {
+        if (i > 0 && updates > 0 && states[params->d + i].next_leaf < (1ULL << h)) {
+          bds_state_update(&states[params->d + i], sk_seed, &(params->xmss_par), pub_seed, addr);
+          updates--;
+        }
+      }
+    }
+    else if (idx < (1ULL << h) - 1) {
+      memcpy(&tmp, states+params->d + i, sizeof(bds_state));
+      memcpy(states+params->d + i, states + i, sizeof(bds_state));
+      memcpy(states + i, &tmp, sizeof(bds_state));
+
+      setLayerADRS(ots_addr, (i+1));
+      setTreeADRS(ots_addr, ((idx + 1) >> ((i+2) * tree_h)));
+      setOTSADRS(ots_addr, (((idx >> ((i+1) * tree_h)) + 1) & ((1 << tree_h)-1)));
+
+      get_seed(ots_seed, sk+params->index_len, n, ots_addr);
+      wots_sign(wots_sigs + i*params->xmss_par.wots_par.keysize, states[i].stack, ots_seed, &(params->xmss_par.wots_par), pub_seed, ots_addr);
+
+      states[params->d + i].stackoffset = 0;
+      states[params->d + i].next_leaf = 0;
+
+      updates--; // WOTS-signing counts as one update
+      needswap_upto = i;
+      for (j = 0; j < tree_h-k; j++) {
+        states[i].treehash[j].completed = 1;
+      }
+    }
+  }
+
+  //Whipe secret elements?
+  //zerobytes(tsk, CRYPTO_SECRETKEYBYTES);
+
+  memcpy(sig_msg, msg, msglen);
+  *sig_msg_len += msglen;
+
+  return 0;
+}
+
+/**
+ * Verifies a given message signature pair under a given public key.
+ */
+int xmssmt_sign_open(unsigned char *msg, unsigned long long *msglen, const unsigned char *sig_msg, unsigned long long sig_msg_len, const unsigned char *pk, const xmssmt_params *params)
+{
+  unsigned int n = params->n;
+
+  unsigned int tree_h = params->xmss_par.h;
+  unsigned int idx_len = params->index_len;
+  uint64_t idx_tree;
+  uint32_t idx_leaf;
+
+  unsigned long long i, m_len;
+  unsigned long long idx=0;
+  unsigned char wots_pk[params->xmss_par.wots_par.keysize];
+  unsigned char pkhash[n];
+  unsigned char root[n];
+  unsigned char msg_h[n];
+  unsigned char hash_key[3*n];
+
+  unsigned char pub_seed[n];
+  memcpy(pub_seed, pk+n, n);
+
+  // Init addresses
+  uint32_t ots_addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+  uint32_t ltree_addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+  uint32_t node_addr[8] = {0, 0, 0, 0, 0, 0, 0, 0};
+
+  // Extract index
+  for (i = 0; i < idx_len; i++) {
+    idx |= ((unsigned long long)sig_msg[i]) << (8*(idx_len - 1 - i));
+  }
+  printf("verify:: idx = %llu\n", idx);
+  sig_msg += idx_len;
+  sig_msg_len -= idx_len;
+  
+  // Generate hash key (R || root || idx)
+  memcpy(hash_key, sig_msg,n);
+  memcpy(hash_key+n, pk, n);
+  to_byte(hash_key+2*n, idx, n);
+
+  sig_msg += n;
+  sig_msg_len -= n;
+  
+
+  // hash message (recall, R is now on pole position at sig_msg
+  unsigned long long tmp_sig_len = (params->d * params->xmss_par.wots_par.keysize) + (params->h * n);
+  m_len = sig_msg_len - tmp_sig_len;
+  h_msg(msg_h, sig_msg + tmp_sig_len, m_len, hash_key, 3*n, n);
+
+  
+  //-----------------------
+  // Verify signature
+  //-----------------------
+
+  // Prepare Address
+  idx_tree = idx >> tree_h;
+  idx_leaf = (idx & ((1 << tree_h)-1));
+  setLayerADRS(ots_addr, 0);
+  setTreeADRS(ots_addr, idx_tree);
+  setType(ots_addr, 0);
+
+  memcpy(ltree_addr, ots_addr, 12);
+  setType(ltree_addr, 1);
+
+  memcpy(node_addr, ltree_addr, 12);
+  setType(node_addr, 2);
+  
+  setOTSADRS(ots_addr, idx_leaf);
+
+  // Check WOTS signature
+  wots_pkFromSig(wots_pk, sig_msg, msg_h, &(params->xmss_par.wots_par), pub_seed, ots_addr);
+
+  sig_msg += params->xmss_par.wots_par.keysize;
+  sig_msg_len -= params->xmss_par.wots_par.keysize;
+
+  // Compute Ltree
+  setLtreeADRS(ltree_addr, idx_leaf);
+  l_tree(pkhash, wots_pk, &(params->xmss_par), pub_seed, ltree_addr);
+
+  // Compute root
+  validate_authpath(root, pkhash, idx_leaf, sig_msg, &(params->xmss_par), pub_seed, node_addr);
+
+  sig_msg += tree_h*n;
+  sig_msg_len -= tree_h*n;
+
+  for (i = 1; i < params->d; i++) {
+    // Prepare Address
+    idx_leaf = (idx_tree & ((1 << tree_h)-1));
+    idx_tree = idx_tree >> tree_h;
+
+    setLayerADRS(ots_addr, i);
+    setTreeADRS(ots_addr, idx_tree);
+    setType(ots_addr, 0);
+
+    memcpy(ltree_addr, ots_addr, 12);
+    setType(ltree_addr, 1);
+
+    memcpy(node_addr, ltree_addr, 12);
+    setType(node_addr, 2);
+
+    setOTSADRS(ots_addr, idx_leaf);
+
+    // Check WOTS signature
+    wots_pkFromSig(wots_pk, sig_msg, root, &(params->xmss_par.wots_par), pub_seed, ots_addr);
+
+    sig_msg += params->xmss_par.wots_par.keysize;
+    sig_msg_len -= params->xmss_par.wots_par.keysize;
+
+    // Compute Ltree
+    setLtreeADRS(ltree_addr, idx_leaf);
+    l_tree(pkhash, wots_pk, &(params->xmss_par), pub_seed, ltree_addr);
+
+    // Compute root
+    validate_authpath(root, pkhash, idx_leaf, sig_msg, &(params->xmss_par), pub_seed, node_addr);
+
+    sig_msg += tree_h*n;
+    sig_msg_len -= tree_h*n;
+
+  }
+
+  for (i = 0; i < n; i++)
+    if (root[i] != pk[i])
+      goto fail;
+
+  *msglen = sig_msg_len;
+  for (i = 0; i < *msglen; i++)
+    msg[i] = sig_msg[i];
+
+  return 0;
+
+
+fail:
+  *msglen = sig_msg_len;
+  for (i = 0; i < *msglen; i++)
+    msg[i] = 0;
+  *msglen = -1;
+  return -1;
+}