Make XMSSMT also use BDS tree traversal

9 years ago · 4c19fe61e4
--- a/.gitignore
+++ b/.gitignore
@@ -4,5 +4,6 @@ test/test_horst
 test/test_xmss
 test/test_xmss_fast
 test/test_xmssmt
 test/test_xmssmt_fast
 test/speed
 test/gen_testvectors
--- a/+ 6
+++ b/+ 6
@@ -5,6 +5,7 @@ all: test/test_chacha \
 test/test_wots \
 test/test_xmss \
 test/test_xmss_fast \
 test/test_xmssmt_fast \
 test/test_xmssmt

 test/test_chacha: chacha.c prg.c randombytes.c test/test_chacha.c chacha.h prg.h randombytes.h
@@ -22,6 +23,9 @@ test/test_xmss_fast: chacha.c hash.c prg.c randombytes.c wots.c xmss_fast.c xmss
 test/test_xmssmt: chacha.c hash.c prg.c randombytes.c wots.c xmss.c xmss_commons.c test/test_xmssmt.c chacha.h hash.h prg.h randombytes.h wots.h xmss.h xmss_commons.h 
 	$(CC) $(CFLAGS) chacha.c hash.c prg.c randombytes.c wots.c xmss.c xmss_commons.c test/test_xmssmt.c -o $@ -lcrypto -lm
 	
 test/test_xmssmt_fast: chacha.c hash.c prg.c randombytes.c wots.c xmss_fast.c xmss_commons.c test/test_xmssmt_fast.c chacha.h hash.h prg.h randombytes.h wots.h xmss_fast.h xmss_commons.h
 	$(CC) $(CFLAGS) chacha.c hash.c prg.c randombytes.c wots.c xmss_fast.c xmss_commons.c test/test_xmssmt_fast.c -o $@ -lcrypto -lm

 .PHONY: clean

 clean:
@@ -29,6 +33,8 @@ clean:
 	-rm test/test_chacha
 	-rm test/test_wots
 	-rm test/test_xmss
 	-rm test/test_xmss_fast
 	-rm test/test_xmssmt
 	-rm test/test_xmssmt_fast


--- a/test/test_xmss_fast.c
+++ b/test/test_xmss_fast.c
@@ -35,12 +35,13 @@ int main()
  unsigned char auth[h*n];
  unsigned char keep[(h >> 1)*n];
  treehash_inst treehash[h-k];
  unsigned char th_nodes[(h-k)*n];
  unsigned char retain[((1 << k) - k - 1)*n];
  bds_state s;
  bds_state *state = &s;
  for(i=0;i<h-k;i++)
    treehash[i].node = (unsigned char *)malloc(n);
  xmss_set_bds_state(state, stack, stackoffset, stacklevels, auth, keep, treehash, retain);
    treehash[i].node = &th_nodes[n*i];
  xmss_set_bds_state(state, stack, stackoffset, stacklevels, auth, keep, treehash, retain, 0);

  unsigned long long signature_length = 4+m+params->wots_par.keysize+h*n;
  unsigned char mo[MLEN+signature_length];
@@ -97,8 +98,6 @@ int main()
    printf("%llu\n", mlen+1);
  }

  for(i=0;i<h-k;i++)
    free(treehash[i].node);
  fclose(urandom);
  return 0;
 }
--- a/test/test_xmssmt_fast.c
+++ b/test/test_xmssmt_fast.c
@@ -0,0 +1,123 @@
 #include <stdio.h>
 #include <string.h>

 #include "../xmss_fast.h"

 #define MLEN 3491
 #define SIGNATURES 1024


 unsigned char mi[MLEN];
 unsigned long long smlen;
 unsigned long long mlen;

 int main()
 {
  int r;
  unsigned long long i,j;
  int m = 32;
  int n = 32;
  int h = 20;
  int d = 5;
  int w = 16;
  int k = 2;

  xmssmt_params p;
  xmssmt_params *params = &p;
  if (xmssmt_set_params(params, m, n, h, d, w, k)) {
    return 1;
  }

  unsigned char stack[2*d * (h-k-1)*n];
  unsigned char stacklevels[2*d * (h-k-1)];
  unsigned char auth[2*d * h*n];
  unsigned char keep[2*d * (h >> 1)*n];
  treehash_inst treehash[2*d * (h-k)];
  unsigned char th_nodes[2*d * (h-k)*n];
  unsigned char retain[2*d * ((1 << k) - k - 1)*n];
  unsigned char wots_sigs[d * params->xmss_par.wots_par.keysize];
  bds_state states[2*d]; // first d are 'regular' states, second d are 'next'

  for (i = 0; i < 2*d; i++) {
    for(j=0;j<h-k;j++)
      treehash[i*(h-k) + j].node = th_nodes + (i*(h-k) + j) * n;
    xmss_set_bds_state(states + i,
      stack + i*(h-k-1)*n, 0, stacklevels + i*(h-k-1),
      auth + i*h*n,
      keep + i*(h >> 1)*n,
      treehash + i*(h-k),
      retain + i*((1 << k) - k - 1)*n,
      0
    );
  }

  unsigned char sk[(params->index_len+2*n+m)];
  unsigned char pk[2*n];

  unsigned long long signature_length = params->index_len + m + (d*params->xmss_par.wots_par.keysize) + h*n;
  unsigned char mo[MLEN+signature_length];
  unsigned char sm[MLEN+signature_length];

  FILE *urandom = fopen("/dev/urandom", "r");
  for(i=0;i<MLEN;i++) mi[i] = fgetc(urandom);

  printf("keypair\n");
  xmssmt_keypair(pk, sk, states, wots_sigs, params);
  // check pub_seed in SK
  for(i=0;i<n;i++)
  {
    if(pk[n+i] != sk[params->index_len+m+n+i]) printf("pk.pub_seed != sk.pub_seed %llu",i);
  }
  printf("pk checked\n");

  unsigned int idx_len = params->index_len;
  // check index
  unsigned long long idx = 0;
  for(i = 0; i < idx_len; i++){
    idx |= ((unsigned long long)sk[i]) << 8*(idx_len - 1 - i);
  }

  if(idx) printf("\nidx != 0: %llu\n",idx);

  for(i=0;i<SIGNATURES;i++){
    printf("sign\n");
    xmssmt_sign(sk, states, wots_sigs, sm, &smlen, mi, MLEN, params);

    idx = 0;
    for(j = 0; j < idx_len; j++){
      idx += ((unsigned long long)sm[j]) << 8*(idx_len - 1 - j);
    }
    printf("\nidx = %llu\n",idx);
    r = memcmp(mi, sm+signature_length,MLEN);
    printf("%d\n", r);

    /* Test valid signature */
    printf("verify\n");
    r = xmssmt_sign_open(mo, &mlen, sm, smlen, pk, params);
    printf("%d\n", r);
    r = memcmp(mi,mo,MLEN);
    printf("%d\n", r);
    printf("%llu\n", MLEN-mlen);

    /* Test with modified message */
    sm[52] ^= 1;
    r = xmssmt_sign_open(mo, &mlen, sm, smlen, pk, params);
    printf("%d\n", r+1);
    r = memcmp(mi,mo,MLEN);
    printf("%d\n", (r!=0) - 1);
    printf("%llu\n", mlen+1);

    /* Test with modified signature */
    sm[260] ^= 1;
    sm[52] ^= 1;
    sm[2] ^= 1;
    r = xmssmt_sign_open(mo, &mlen, sm, smlen, pk, params);
    printf("%d\n", r+1);
    r = memcmp(mi,mo,MLEN);
    printf("%d\n", (r!=0) - 1);
    printf("%llu\n", mlen+1);

  }
  fclose(urandom);
  return 0;
 }
--- a/xmss_fast.c
+++ b/xmss_fast.c
@@ -95,8 +95,12 @@ static void get_seed(unsigned char seed[32], const unsigned char *sk_seed, unsig
 * parameter names are the same as in the draft
 * parameter k is K as used in the BDS algorithm
 */
 void xmss_set_params(xmss_params *params, int m, int n, int h, int w, int k)
 int xmss_set_params(xmss_params *params, int m, 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->m = m;
  params->n = n;
@@ -104,13 +108,14 @@ void xmss_set_params(xmss_params *params, int m, int n, int h, int w, int k)
  wots_params wots_par;
  wots_set_params(&wots_par, m, 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)
 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;
@@ -119,6 +124,7 @@ void xmss_set_bds_state(bds_state *state, unsigned char *stack, int stackoffset,
  state->keep = keep;
  state->treehash = treehash;
  state->retain = retain;
  state->next_leaf = next_leaf;
 }

 /**
@@ -127,11 +133,11 @@ void xmss_set_bds_state(bds_state *state, unsigned char *stack, int stackoffset,
 * 
 * Especially h is the total tree height, i.e. the XMSS trees have height h/d
 */
 void xmssmt_set_params(xmssmt_params *params, int m, int n, int h, int d, int w, int k)
 int xmssmt_set_params(xmssmt_params *params, int m, int n, int h, int d, int w, int k)
 {
  if(h % d){
    fprintf(stderr, "d must devide h without remainder!\n");
    return;
    fprintf(stderr, "d must divide h without remainder!\n");
    return 1;
  }
  params->h = h;
  params->d = d;
@@ -139,8 +145,11 @@ void xmssmt_set_params(xmssmt_params *params, int m, int n, int h, int d, int w,
  params->n = n;
  params->index_len = (h + 7) / 8;
  xmss_params xmss_par;
  xmss_set_params(&xmss_par, m, n, (h/d), w, k);
  if (xmss_set_params(&xmss_par, m, n, (h/d), w, k)) {
    return 1;
  }
  params->xmss_par = xmss_par;
  return 0;
 }

 /**
@@ -386,27 +395,120 @@ static void validate_authpath(unsigned char *root, const unsigned char *leaf, un
  hash_2n_n(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, const unsigned char *sk_seed, const xmss_params *params, unsigned char *pub_seed, const unsigned char addr[16]) {
  unsigned int i;
  int level, l_min, low;
  int h = params->h;
  int k = params->k;

  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) {
    return 1;
  }
  treehash_update(&(state->treehash[level]), state, sk_seed, params, pub_seed, addr);
  return 0;
 }

 /**
 * 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 unsigned char addr[16]) {
  unsigned char ltree_addr[16];
  unsigned char node_addr[16];
  unsigned char ots_addr[16];

  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;
  }

  memcpy(ots_addr, addr, 10);
  SET_OTS_BIT(ots_addr, 1);
  SET_OTS_ADDRESS(ots_addr, idx);

  memcpy(ltree_addr, addr, 10);
  SET_OTS_BIT(ltree_addr, 0);
  SET_LTREE_BIT(ltree_addr, 1);
  SET_LTREE_ADDRESS(ltree_addr, idx);

  memcpy(node_addr, addr, 10);
  SET_LTREE_BIT(node_addr, 0);
  SET_OTS_BIT(node_addr, 0);
  SET_NODE_PADDING(node_addr);

  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);
      }
    }
    SET_NODE_TREE_HEIGHT(node_addr, state->stacklevels[state->stackoffset-1]);
    SET_NODE_TREE_INDEX(node_addr, (idx >> (state->stacklevels[state->stackoffset-1]+1)));
    hash_2n_n(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 compute_authpath_wots_fast(unsigned char *root, unsigned char *authpath, unsigned long leaf_idx, bds_state *state, const unsigned char *sk_seed, const xmss_params *params, unsigned char *pub_seed, unsigned char addr[16])
 static int bds_round(bds_state *state, const unsigned long leaf_idx, const unsigned char *sk_seed, const xmss_params *params, const int updates, unsigned char *pub_seed, unsigned char addr[16])
 {
  unsigned int i, j;
  unsigned int i;
  int n = params->n;
  int h = params->h;
  int k = params->k;

  // the auth path was already computed during the previous round
  memcpy(authpath, state->auth, h*n);
  // TODO but we don't have the root handy yet.
  // memcpy(root, ???, n);

  int tau = h;
  int startidx;
  int offset, rowidx;
  int level, l_min, low;
  unsigned char buf[2 * n];

  unsigned char ots_addr[16];
@@ -463,32 +565,17 @@ static void compute_authpath_wots_fast(unsigned char *root, unsigned char *authp
        state->treehash[i].h = i;
        state->treehash[i].next_idx = startidx;
        state->treehash[i].completed = 0;
        state->treehash[i].stackusage = 0;
      }
    }
  }

  for (i = 0; i < (h - k) >> 1; i++) {
    l_min = h;
    level = h - k;
    for (j = 0; j < h - k; j++) {
      if (state->treehash[j].completed) {
        low = h;
      }
      else if (state->treehash[j].stackusage == 0) {
        low = j;
      }
      else {
        low = treehash_minheight_on_stack(state, params, &(state->treehash[j]));
      }
      if (low < l_min) {
        level = j;
        l_min = low;
      }
    }
    if (level != h - k) {
      treehash_update(&(state->treehash[level]), state, sk_seed, params, pub_seed, addr);
  int remaining = 0;
  for (i = 0; i < updates; i++) {
    if (bds_treehash_update(state, sk_seed, params, pub_seed, addr)) {
      remaining++;
    }
  }
  return remaining;
 }

 /*
@@ -525,8 +612,10 @@ int xmss_keypair(unsigned char *pk, unsigned char *sk, bds_state *state, xmss_pa
 */
 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 m = params->m;
  unsigned int k = params->k;
  
  // Extract SK
  unsigned long idx = ((unsigned long)sk[0] << 24) | ((unsigned long)sk[1] << 16) | ((unsigned long)sk[2] << 8) | sk[3];
@@ -549,7 +638,6 @@ int xmss_sign(unsigned char *sk, bds_state *state, unsigned char *sig_msg, unsig
  unsigned long long i;
  unsigned char R[m];
  unsigned char msg_h[m];
  unsigned char root[n];
  unsigned char ots_seed[n];
  unsigned char ots_addr[16] = {0,0,0,0};
  
@@ -599,7 +687,10 @@ int xmss_sign(unsigned char *sk, bds_state *state, unsigned char *sig_msg, unsig
  sig_msg += params->wots_par.keysize;
  *sig_msg_len += params->wots_par.keysize;

  compute_authpath_wots_fast(root, sig_msg, idx, state, sk_seed, params, pub_seed, ots_addr);
  // the auth path was already computed during the previous round
  memcpy(sig_msg, state->auth, h*n);

  bds_round(state, idx, sk_seed, params, (h - k) >> 1, pub_seed, ots_addr);
  sig_msg += params->h*n;
  *sig_msg_len += params->h*n;
  
@@ -705,11 +796,12 @@ fail:
 * Format sk: [(ceil(h/8) bit) idx || SK_SEED || SK_PRF || PUB_SEED]
 * Format pk: [root || PUB_SEED] omitting algo oid.
 */
 int xmssmt_keypair(unsigned char *pk, unsigned char *sk, bds_state *state, xmssmt_params *params)
 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 m = params->m;
  unsigned int i;
  unsigned char ots_seed[params->n];
  // Set idx = 0
  for (i = 0; i < params->index_len; i++){
    sk[i] = 0;
@@ -721,10 +813,22 @@ int xmssmt_keypair(unsigned char *pk, unsigned char *sk, bds_state *state, xmssm

  // Set address to point on the single tree on layer d-1
  unsigned char addr[16] = {0,0,0,0};
  SET_LAYER_ADDRESS(addr, (params->d-1));
  
  // Compute root
  treehash_setup(pk, params->xmss_par.h, 0, state, sk+params->index_len, &(params->xmss_par), pk+n, addr);
  SET_OTS_BIT(addr,1);
  SET_TREE_ADDRESS(addr, 0);
  SET_OTS_ADDRESS(addr, 0);
  SET_LAYER_ADDRESS(addr, 0);
  // Set up state and compute wots signatures for all but topmost tree root
  for (i = 0; i < params->d - 1; i++) {
    SET_LAYER_ADDRESS(addr, i);
    SET_TREE_ADDRESS(addr, 0);
    SET_OTS_ADDRESS(addr, 0);
    // 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);
    SET_LAYER_ADDRESS(addr, (i+1));
    get_seed(ots_seed, sk+params->index_len, 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);
  return 0;
 }

@@ -735,26 +839,29 @@ int xmssmt_keypair(unsigned char *pk, unsigned char *sk, bds_state *state, xmssm
 * 2. an updated secret key!
 * 
 */
 int xmssmt_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 xmssmt_params *params)
 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 m = params->m;
  unsigned int tree_h = params->xmss_par.h;
  unsigned int k = params->xmss_par.k;
  unsigned int idx_len = params->index_len;
  unsigned long long idx_tree;
  unsigned long long idx_leaf;
  unsigned long long i;
  
  unsigned long long i, j;
  unsigned int updates;
  unsigned int first_nonwots;

  unsigned char sk_seed[n];
  unsigned char sk_prf[m];
  unsigned char pub_seed[n];
  // Init working params
  unsigned char R[m];
  unsigned char msg_h[m];
  unsigned char root[n];
  unsigned char ots_seed[n];
  unsigned char ots_addr[16] = {0,0,0,0};
  
  bds_state tmp;

  // Extract SK
  unsigned long long idx = 0;
  for(i = 0; i < idx_len; i++){
@@ -820,37 +927,88 @@ int xmssmt_sign(unsigned char *sk, bds_state *state, unsigned char *sig_msg, uns
     
  // 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;

  compute_authpath_wots_fast(root, sig_msg, idx_leaf, state, sk_seed, &(params->xmss_par), pub_seed, ots_addr);
  memcpy(sig_msg, states[0].auth, tree_h*n);
  sig_msg += tree_h*n;
  *sig_msg_len += tree_h*n;
  
  // Now loop over remaining layers...
  unsigned int j;
  for(j = 1; j < params->d; j++){
    // Prepare Address
    idx_leaf = (idx_tree & ((1 << tree_h)-1));
    idx_tree = idx_tree >> tree_h;
    SET_LAYER_ADDRESS(ots_addr,j);
    SET_TREE_ADDRESS(ots_addr, idx_tree);
    SET_OTS_ADDRESS(ots_addr, idx_leaf);
    
    // Compute seed for OTS key pair
    get_seed(ots_seed, sk_seed, ots_addr);
      
    // Compute WOTS signature
    wots_sign(sig_msg, root, ots_seed, &(params->xmss_par.wots_par), pub_seed, ots_addr);
    

  // 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;

    compute_authpath_wots_fast(root, sig_msg, idx_leaf, state, sk_seed, &(params->xmss_par), pub_seed, ots_addr);
    // 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;   
  }

  SET_LAYER_ADDRESS(ots_addr, 0);
  SET_TREE_ADDRESS(ots_addr, (idx_tree + 1));
  // mandatory update for NEXT_0 (does not count towards h-k)
  bds_state_update(&states[params->d], sk_seed, &(params->xmss_par), pub_seed, ots_addr);

  updates = tree_h - k;

  for (i = 0; i < params->d; i++) {
    if (((idx + 1) & ((1 << ((i+1)*tree_h)) - 1)) == 0) {
      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));

      SET_TREE_ADDRESS(ots_addr, ((idx + 1) >> ((i+2) * tree_h)));
      SET_OTS_ADDRESS(ots_addr, (((idx >> ((i+1) * tree_h)) + 1) & ((1 << tree_h)-1)));
      SET_LAYER_ADDRESS(ots_addr, (i+1));

      get_seed(ots_seed, sk+params->index_len, 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

      // this bds_round is needed to initialise the state, but should not perform updates
      // note that one should still pass the (reduced) current idx, as bds_round sets up for idx+1
      bds_round(&states[i+1], ((idx >> ((i+1)*tree_h))) & ((1 << tree_h)-1), sk_seed, &(params->xmss_par), 0, pub_seed, ots_addr);
      for (j = 0; j < tree_h-k; j++) {
        states[i].treehash[j].completed = 1;
      }
    }
  }

  SET_LAYER_ADDRESS(ots_addr, 0);
  SET_TREE_ADDRESS(ots_addr, idx_tree);

  first_nonwots = (tree_h - k) - updates;

  if (first_nonwots == 0) {
    updates = bds_round(&states[0], idx_leaf, sk_seed, &(params->xmss_par), (tree_h - k) >> 1, pub_seed, ots_addr);
  }

  for (i = 1; updates > 0 && i < params->d; i++) {
    idx_leaf = (idx_tree & ((1 << tree_h)-1));
    idx_tree = idx_tree >> tree_h;
    if (first_nonwots > i) {
      continue;
    }
    SET_LAYER_ADDRESS(ots_addr, i);
    SET_TREE_ADDRESS(ots_addr, idx_tree);
    SET_OTS_ADDRESS(ots_addr, idx_leaf);
    while (updates > 0 && !bds_treehash_update(&states[i], sk_seed, &(params->xmss_par), pub_seed, ots_addr)) {
      updates--;
    }
    SET_TREE_ADDRESS(ots_addr, (idx_tree + 1));
    while (updates > 0 && !bds_state_update(&states[params->d + i], sk_seed, &(params->xmss_par), pub_seed, ots_addr)) {
      updates--;
    }
  }
  
  //Whipe secret elements?  
  //zerobytes(tsk, CRYPTO_SECRETKEYBYTES);
--- a/xmss_fast.h
+++ b/xmss_fast.h
@@ -47,25 +47,26 @@ typedef struct {
  unsigned char *keep;
  treehash_inst *treehash;
  unsigned char *retain;
  int next_leaf;
 } bds_state;

 /**
 * 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);
 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);
 /**
 * Initializes parameter set.
 * Needed, for any of the other methods.
 */
 void xmss_set_params(xmss_params *params, int m, int n, int h, int w, int k);
 int xmss_set_params(xmss_params *params, int m, int n, int h, int w, int k);
 /**
 * 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
 */
 void xmssmt_set_params(xmssmt_params *params, int m, int n, int h, int d, int w, int k);
 int xmssmt_set_params(xmssmt_params *params, int m, int n, int h, int d, int w, int k);
 /**
 * Generates a XMSS key pair for a given parameter set.
 * Format sk: [(32bit) idx || SK_SEED || SK_PRF || PUB_SEED]
@@ -92,7 +93,7 @@ int xmss_sign_open(unsigned char *msg,unsigned long long *msglen, const unsigned
 * Format sk: [(ceil(h/8) bit) idx || SK_SEED || SK_PRF || PUB_SEED]
 * Format pk: [root || PUB_SEED] omitting algo oid.
 */
 int xmssmt_keypair(unsigned char *pk, unsigned char *sk, bds_state *state, xmssmt_params *params);
 int xmssmt_keypair(unsigned char *pk, unsigned char *sk, bds_state *states, unsigned char *wots_sigs, xmssmt_params *params);
 /**
 * Signs a message.
 * Returns 
@@ -100,7 +101,7 @@ int xmssmt_keypair(unsigned char *pk, unsigned char *sk, bds_state *state, xmssm
 * 2. an updated secret key!
 * 
 */
 int xmssmt_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 xmssmt_params *params);
 int xmssmt_sign(unsigned char *sk, bds_state *state, 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);
 /**
 * Verifies a given message signature pair under a given public key.
 */