xmss-KAT-generator/xmss.c

/*
xmss.c version 20150811
Andreas Hülsing
Public domain.
*/

#include "xmss.h"
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#include <math.h>

#include "randombytes.h"
#include "wots.h"
#include "hash.h"
#include "prg.h"
#include "xmss_commons.h"

// For testing
#include "stdio.h"

/**
 * Macros used to manipulate the respective fields
 * in the 16byte hash address
 */    
#define SET_OTS_BIT(a, b) {\
  a[9] = (a[9] & 253) | (b << 1);}

#define SET_OTS_ADDRESS(a, v) {\
  a[12] = (a[12] & 1) | ((v << 1) & 255);\
  a[11] = (v >> 7) & 255;\
  a[10] = (v >> 15) & 255;\
  a[9] = (a[9] & 254) | ((v >> 23) & 1);}  
  
#define ZEROISE_OTS_ADDR(a) {\
  a[12] = (a[12] & 254);\
  a[13] = 0;\
  a[14] = 0;\
  a[15] = 0;}
  
#define SET_LTREE_BIT(a, b) {\
  a[9] = (a[9] & 254) | b;}

#define SET_LTREE_ADDRESS(a, v) {\
  a[12] = v & 255;\
  a[11] = (v >> 8) & 255;\
  a[10] = (v >> 16) & 255;}

#define SET_LTREE_TREE_HEIGHT(a, v) {\
  a[13] = (a[13] & 3) | ((v << 2) & 255);}

#define SET_LTREE_TREE_INDEX(a, v) {\
  a[15] = (a[15] & 3) | ((v << 2) & 255);\
  a[14] = (v >> 6) & 255;\
  a[13] = (a[13] & 252) | ((v >> 14) & 3);}
  
#define SET_NODE_PADDING(a) {\
  a[10] = 0;\
  a[11] = a[11] & 3;}  

#define SET_NODE_TREE_HEIGHT(a, v) {\
  a[12] = (a[12] & 3) | ((v << 2) & 255);\
  a[11] = (a[11] & 252) | ((v >> 6) & 3);}

#define SET_NODE_TREE_INDEX(a, v) {\
  a[15] = (a[15] & 3) | ((v << 2) & 255);\
  a[14] = (v >> 6) & 255;\
  a[13] = (v >> 14) & 255;\
  a[12] = (a[12] & 252) | ((v >> 22) & 3);}


  /**
 * Used for pseudorandom keygeneration,
 * generates the seed for the WOTS keypair at address addr
 */
static void get_seed(unsigned char seed[32], const unsigned char *sk_seed, unsigned char addr[16])
{
  // Make sure that chain addr, hash addr, and key bit are 0!
  ZEROISE_OTS_ADDR(addr);
  // Generate pseudorandom value
  prg_with_counter(seed, 32, sk_seed, 32, addr);
}

/**
 * Initialize xmss params struct
 * parameter names are the same as in the draft
 */
void xmss_set_params(xmss_params *params, int m, int n, int h, int w)
{
  params->h = h;
  params->m = m;
  params->n = n;
  wots_params wots_par;
  wots_set_params(&wots_par, m, n, w);
  params->wots_par = &wots_par;
}

/**
 * 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, unsigned char addr[16])
{ 
  uint l = params->wots_par->len;
  uint n = params->n;
  unsigned long i = 0;
  uint height = 0;
  
  //ADRS.setTreeHeight(0);
  SET_LTREE_TREE_HEIGHT(addr,height);
  unsigned long bound;
  while ( l > 1 ) 
  {
     bound = l >> 1; //floor(l / 2); 
     for ( i = 0; i < bound; i = i + 1 ) {
       //ADRS.setTreeIndex(i);
       SET_LTREE_TREE_INDEX(addr,i);
       //wots_pk[i] = RAND_HASH(pk[2i], pk[2i + 1], SEED, ADRS);
       hash_2n_n(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++;
     SET_LTREE_TREE_HEIGHT(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, unsigned char ltree_addr[16], unsigned char ots_addr[16])
{
  unsigned char seed[32];
  unsigned char pk[params->wots_par->keysize];

  get_seed(seed, sk_seed, ots_addr);
  wots_pkgen(pk, seed, params->wots_par, pub_seed, ots_addr);

  l_tree(leaf, pk, params, pub_seed, ltree_addr); 
}

/**
 * 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(unsigned char *node, int height, int index, const unsigned char *sk_seed, const xmss_params *params, const unsigned char *pub_seed, const unsigned char addr[16])
{

  uint idx = index;
  uint n = params->n;
  // use three different addresses because at this point we use all three formats in parallel
  unsigned char ots_addr[16];
  unsigned char ltree_addr[16];
  unsigned char node_addr[16];
  memcpy(ots_addr, addr, 10);
  SET_OTS_BIT(ots_addr, 1);
  memcpy(ltree_addr, addr, 10);
  SET_OTS_BIT(ltree_addr, 0);
  SET_LTREE_BIT(ltree_addr, 1);
  memcpy(node_addr, ltree_addr, 10);
  SET_LTREE_BIT(node_addr, 0);
  SET_NODE_PADDING(node_addr);
  
  int lastnode,i;
  unsigned char stack[(height+1)*n];
  unsigned int  stacklevels[height+1];
  unsigned int  stackoffset=0;
  
  lastnode = idx+(1<<height);

  for(;idx<lastnode;idx++) 
  {
    SET_LTREE_ADDRESS(ltree_addr,idx);
    SET_OTS_ADDRESS(ots_addr,idx);
    gen_leaf_wots(stack+stackoffset*n,sk_seed,params, pub_seed, ltree_addr, ots_addr);
    stacklevels[stackoffset] = 0;
    stackoffset++;
    while(stackoffset>1 && stacklevels[stackoffset-1] == stacklevels[stackoffset-2])
    {
      SET_NODE_TREE_HEIGHT(node_addr,stacklevels[stackoffset-1]);
      SET_NODE_TREE_INDEX(node_addr, (idx >> (stacklevels[stackoffset-1]+1)));
      hash_2n_n(stack+(stackoffset-2)*n,stack+(stackoffset-2)*n, pub_seed,
          node_addr, n);
      stacklevels[stackoffset-2]++;
      stackoffset--;
    }
  }
  for(i=0;i<n;i++)
    node[i] = stack[i];
}

/**
 * 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, unsigned char addr[16])
{
  uint n = params->n;
  
  int 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++)
  {
    SET_NODE_TREE_HEIGHT(addr,i);
    leafidx >>= 1;
    SET_NODE_TREE_INDEX(addr, leafidx);
    if(leafidx&1)
    {
      hash_2n_n(buffer+n,buffer,pub_seed, addr, n);
      for(j=0;j<n;j++)
        buffer[j] = authpath[j];
    }
    else
    {
      hash_2n_n(buffer,buffer,pub_seed, addr, n);
      for(j=0;j<n;j++)
        buffer[j+n] = authpath[j];
    }
    authpath += n;
  }
  SET_NODE_TREE_HEIGHT(addr, (params->h-1));
  leafidx >>= 1;
  SET_NODE_TREE_INDEX(addr, leafidx);
  hash_2n_n(root,buffer,pub_seed,addr,n);
}

/**
 * Computes the authpath and the root. This method is using a lot of space as we build the whole tree and then select the authpath nodes.
 * For more efficient algorithms see e.g. the chapter on hash-based signatures in Bernstein, Buchmann, Dahmen. "Post-quantum Cryptography", Springer 2009.
 * It returns the authpath in "authpath" with the node on level 0 at index 0.  
 */
static void compute_authpath_wots(unsigned char *root, unsigned char *authpath, unsigned long leaf_idx, const unsigned char *sk_seed, const xmss_params *params, unsigned char *pub_seed, unsigned char addr[16])
{
  uint i, j, level;
  int n = params->n;
  int h = params->h;
  
  unsigned char tree[2*(1<<h)*n];

  unsigned char ots_addr[16];
  unsigned char ltree_addr[16];
  unsigned char node_addr[16];
  
  memcpy(ots_addr, addr, 10);
  SET_OTS_BIT(ots_addr, 1);
  memcpy(ltree_addr, addr, 10);
  SET_OTS_BIT(ltree_addr, 0);
  SET_LTREE_BIT(ltree_addr, 1);
  memcpy(node_addr, ltree_addr, 10);
  SET_LTREE_BIT(node_addr, 0);
  SET_NODE_PADDING(node_addr);

  
  // Compute all leaves
  for(i = 0; i < (1<<h); i++)
  {
    SET_LTREE_ADDRESS(ltree_addr,i);
    SET_OTS_ADDRESS(ots_addr,i);
    gen_leaf_wots(tree+((1<<h)*n + i*n), sk_seed, params, pub_seed, ltree_addr, ots_addr);
  }
  
  
  level = 0;
  // Compute tree:
  // Outer loop: For each inner layer 
  for (i = (1<<h); i > 0; i>>=1)
  {
    SET_NODE_TREE_HEIGHT(node_addr, level);
    // Inner loop: for each pair of sibling nodes
    for (j = 0; j < i; j+=2)
    {
      SET_NODE_TREE_INDEX(node_addr, j>>1);
      hash_2n_n(tree + (i>>1)*n + (j>>1) * n, tree + i*n + j*n, pub_seed, node_addr, n);
    }
    level++;
  }

  // copy authpath
  for(i=0;i<h;i++)
    memcpy(authpath + i*n, tree + ((1<<h)>>i)*n + ((leaf_idx >> i) ^ 1) * n, n);
  
  // copy root
  memcpy(root, tree+n, n);
}


/*
 * Generates a XMSS key pair for a given parameter set.
 * Format sk: [(32bit) idx || SK_SEED || SK_PRF || PUB_SEED]
 * Format pk: [root || PUB_SEED] omitting algo oid.
 */
int xmss_keypair(unsigned char *pk, unsigned char *sk, xmss_params *params)
{
  uint n = params->n;
  uint m = params->m;
  // Set idx = 0
  sk[0] = 0;
  sk[1] = 0;
  sk[2] = 0;
  sk[3] = 0;
  // Init SK_SEED (n byte), SK_PRF (m byte), and PUB_SEED (n byte)
  randombytes(sk+4,2*n+m);
  // Copy PUB_SEED to public key
  memcpy(pk+n, sk+4+n+m,n);

  unsigned char addr[16] = {0,0,0,0};
  // Compute root
  treehash(pk, params->h, 0, sk+4, params, sk+4+n+m, addr);
  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, unsigned char *sig_msg, unsigned long long *sig_msg_len, const unsigned char *msg, unsigned long long msglen, const xmss_params *params, unsigned char* pk)
{
  uint n = params->n;
  uint m = params->m;
  
  // Extract SK
  unsigned long idx = (sk[0] << 24) | (sk[1] << 16) | (sk[2] << 8) || sk[3];
  unsigned char sk_seed[n];
  memcpy(sk_seed,sk+4,n);
  unsigned char sk_prf[m];
  memcpy(sk_prf,sk+4+n,m);
  unsigned char pub_seed[n];
  memcpy(pub_seed,sk+4+n+m,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 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};
  
  // ---------------------------------
  // Message Hashing
  // ---------------------------------
  
  // Message Hash: 
  // First compute pseudorandom key
  prf_m(R, msg, msglen, sk_prf, m); 
  // Then use it for message digest
  hash_m(msg_h, msg, msglen, R, m, m);
  
  // 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<m; i++)
    sig_msg[i] = R[i];

  sig_msg += m;
  *sig_msg_len += m;
  
  // ----------------------------------
  // Now we start to "really sign" 
  // ----------------------------------
  
  // Prepare Address
  SET_OTS_BIT(ots_addr,1);
  SET_OTS_ADDRESS(ots_addr,idx);
  
  // Compute seed for OTS key pair
  get_seed(ots_seed, sk_seed, 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;

  compute_authpath_wots(root, sig_msg, idx, sk_seed, params, pub_seed, ots_addr);
  sig_msg += params->h*n;
  *sig_msg_len += params->h*n;
  
  //DEBUG
  for(i=0;i<n;i++)
    if(root[i] != pk[i])
      printf("Different PK's %llu",i);
  
  //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)
{
  uint n = params->n;
  uint m = params->m;
    
  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[m];
  
  unsigned char pub_seed[n];
  memcpy(pub_seed,pk+n,n);  
  
  // Init addresses
  unsigned char ots_addr[16] = {0,0,0,0};
  unsigned char ltree_addr[16];
  unsigned char node_addr[16];
  
  SET_OTS_BIT(ots_addr, 1);
  
  memcpy(ltree_addr, ots_addr, 10);
  SET_OTS_BIT(ltree_addr, 0);
  SET_LTREE_BIT(ltree_addr, 1);
  
  memcpy(node_addr, ltree_addr, 10);
  SET_LTREE_BIT(node_addr, 0);
  SET_NODE_PADDING(node_addr);  
  
  // Extract index
  idx = (sig_msg[0] << 24) | (sig_msg[1] << 16) | (sig_msg[2] << 8) || sig_msg[3];
  sig_msg += 4;
  sig_msg_len -= 4;
  
  // hash message (recall, R is now on pole position at sig_msg
  unsigned long long tmp_sig_len = m+params->wots_par->keysize+params->h*n;
  m_len = sig_msg_len - tmp_sig_len;
  hash_m(msg_h, sig_msg + tmp_sig_len, m_len, sig_msg, m, m);

  sig_msg += m;
  sig_msg_len -= m;
  
  //-----------------------
  // Verify signature
  //-----------------------
  
  // Prepare Address
  SET_OTS_ADDRESS(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
  SET_LTREE_ADDRESS(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;
}