text: #include <stdlib.h>
  #include <stdint.h>
  #include <string.h>
  
  #include "fors.h"
  #include "utils.h"
  #include "hash.h"
  #include "hash_address.h"
  
  static void fors_gen_sk(unsigned char *sk, const unsigned char *sk_seed,
                          uint32_t fors_leaf_addr[8])
  {
      prf_addr(sk, sk_seed, fors_leaf_addr);
  }
  
  static void fors_sk_to_leaf(unsigned char *leaf, const unsigned char *sk,
                              const unsigned char *pub_seed,
                              uint32_t fors_leaf_addr[8])
  {
      thash(leaf, sk, 1, pub_seed, fors_leaf_addr);
  }
  
  static void fors_gen_leaf(unsigned char *leaf, const unsigned char *sk_seed,
                            const unsigned char *pub_seed,
                            uint32_t addr_idx, const uint32_t fors_tree_addr[8])
  {
      uint32_t fors_leaf_adr[8] = {0};
  
      /* Only copy the parts that must be kept in fors_leaf_adr. */
      copy_keypair_addr(fors_leaf_adr, fors_tree_addr);
      set_type(fors_leaf_adr, SPX_ADDR_TYPE_FORSTREE);
      set_tree_index(fors_leaf_adr, addr_idx);
  
      fors_gen_sk(leaf, sk_seed, fors_leaf_adr);
      fors_sk_to_leaf(leaf, leaf, pub_seed, fors_leaf_adr);
  }
  
  /**
   * Interprets m as SPX_FORS_HEIGHT-bit unsigned integers.
   * Assumes m contains at least SPX_FORS_HEIGHT * SPX_FORS_TREES bits.
   * Assumes indices has space for SPX_FORS_TREES integers.
   */
  static void message_to_indices(uint32_t *indices, const unsigned char *m)
  {
      unsigned int i, j;
      unsigned int offset = 0;
  
      for (i = 0; i < SPX_FORS_TREES; i++) {
          indices[i] = 0;
          for (j = 0; j < SPX_FORS_HEIGHT; j++) {
              indices[i] <<= 1;
              indices[i] ^= (m[offset >> 3] >> (offset & 0x7)) & 0x1;
              offset++;
          }
      }
  }
  
  /**
   * Signs a message m, deriving the secret key from sk_seed and the FTS address.
   * Assumes m contains at least SPX_FORS_HEIGHT * SPX_FORS_TREES bits.
   */
  void fors_sign(unsigned char *sig, unsigned char *pk,
                 const unsigned char *m,
                 const unsigned char *sk_seed, const unsigned char *pub_seed,
                 const uint32_t fors_addr[8])
  {
      uint32_t indices[SPX_FORS_TREES];
      unsigned char roots[SPX_FORS_TREES * SPX_N];
      uint32_t fors_tree_addr[8] = {0};
      uint32_t fors_pk_addr[8] = {0};
      uint32_t idx_offset;
      unsigned int i;
  
      copy_keypair_addr(fors_tree_addr, fors_addr);
      copy_keypair_addr(fors_pk_addr, fors_addr);
  
      set_type(fors_tree_addr, SPX_ADDR_TYPE_FORSTREE);
      set_type(fors_pk_addr, SPX_ADDR_TYPE_FORSPK);
  
      message_to_indices(indices, m);
  
      for (i = 0; i < SPX_FORS_TREES; i++) {
          idx_offset = i * (1 << SPX_FORS_HEIGHT);
  
          set_tree_height(fors_tree_addr, 0);
          set_tree_index(fors_tree_addr, indices[i] + idx_offset);
  
          /* Include the secret key part that produces the selected leaf node. */
          fors_gen_sk(sig, sk_seed, fors_tree_addr);
          sig += SPX_N;
  
          /* Compute the authentication path for this leaf node. */
          treehash(roots + i*SPX_N, sig, sk_seed, pub_seed,
                   indices[i], idx_offset, SPX_FORS_HEIGHT, fors_gen_leaf,
                   fors_tree_addr);
          sig += SPX_N * SPX_FORS_HEIGHT;
      }
  
      /* Hash horizontally across all tree roots to derive the public key. */
      thash(pk, roots, SPX_FORS_TREES, pub_seed, fors_pk_addr);
  }
  
  /**
   * Derives the FORS public key from a signature.
   * This can be used for verification by comparing to a known public key, or to
   * subsequently verify a signature on the derived public key. The latter is the
   * typical use-case when used as an FTS below an OTS in a hypertree.
   * Assumes m contains at least SPX_FORS_HEIGHT * SPX_FORS_TREES bits.
   */
  void fors_pk_from_sig(unsigned char *pk,
                        const unsigned char *sig, const unsigned char *m,
                        const unsigned char *pub_seed,
                        const uint32_t fors_addr[8])
  {
      uint32_t indices[SPX_FORS_TREES];
      unsigned char roots[SPX_FORS_TREES * SPX_N];
      unsigned char leaf[SPX_N];
      uint32_t fors_tree_addr[8] = {0};
      uint32_t fors_pk_addr[8] = {0};
      uint32_t idx_offset;
      unsigned int i;
  
      copy_keypair_addr(fors_tree_addr, fors_addr);
      copy_keypair_addr(fors_pk_addr, fors_addr);
  
      set_type(fors_tree_addr, SPX_ADDR_TYPE_FORSTREE);
      set_type(fors_pk_addr, SPX_ADDR_TYPE_FORSPK);
  
      message_to_indices(indices, m);
  
      for (i = 0; i < SPX_FORS_TREES; i++) {
          idx_offset = i * (1 << SPX_FORS_HEIGHT);
  
          set_tree_height(fors_tree_addr, 0);
          set_tree_index(fors_tree_addr, indices[i] + idx_offset);
  
          /* Derive the leaf from the included secret key part. */
          fors_sk_to_leaf(leaf, sig, pub_seed, fors_tree_addr);
          sig += SPX_N;
  
          /* Derive the corresponding root node of this tree. */
          compute_root(roots + i*SPX_N, leaf, indices[i], idx_offset,
                       sig, SPX_FORS_HEIGHT, pub_seed, fors_tree_addr);
          sig += SPX_N * SPX_FORS_HEIGHT;
      }
  
      /* Hash horizontally across all tree roots to derive the public key. */
      thash(pk, roots, SPX_FORS_TREES, pub_seed, fors_pk_addr);
  }
  