5111374265

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/src/lib/misc/zfec/zfec.cpp

/*
* Forward error correction based on Vandermonde matrices
*
* (C) 1997-1998 Luigi Rizzo (luigi@iet.unipi.it)
* (C) 2009,2010,2021 Jack Lloyd
* (C) 2011 Billy Brumley (billy.brumley@aalto.fi)
*
* Botan is released under the Simplified BSD License (see license.txt)
*/

#include <botan/zfec.h>

#include <botan/exceptn.h>
#include <botan/mem_ops.h>
#include <botan/internal/cpuid.h>
#include <cstring>
#include <vector>

namespace Botan {

namespace {

/* Tables for arithetic in GF(2^8) using 1+x^2+x^3+x^4+x^8
*
* See Lin & Costello, Appendix A, and Lee & Messerschmitt, p. 453.
*
* Generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m]
* Lookup tables:
*     index->polynomial form           gf_exp[] contains j= \alpha^i;
*     polynomial form -> index form    gf_log[ j = \alpha^i ] = i
* \alpha=x is the primitive element of GF(2^m)
*/
alignas(256) const uint8_t GF_EXP[255] = {
   0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1D, 0x3A, 0x74, 0xE8, 0xCD, 0x87, 0x13, 0x26, 0x4C, 0x98, 0x2D,
   0x5A, 0xB4, 0x75, 0xEA, 0xC9, 0x8F, 0x03, 0x06, 0x0C, 0x18, 0x30, 0x60, 0xC0, 0x9D, 0x27, 0x4E, 0x9C, 0x25, 0x4A,
   0x94, 0x35, 0x6A, 0xD4, 0xB5, 0x77, 0xEE, 0xC1, 0x9F, 0x23, 0x46, 0x8C, 0x05, 0x0A, 0x14, 0x28, 0x50, 0xA0, 0x5D,
   0xBA, 0x69, 0xD2, 0xB9, 0x6F, 0xDE, 0xA1, 0x5F, 0xBE, 0x61, 0xC2, 0x99, 0x2F, 0x5E, 0xBC, 0x65, 0xCA, 0x89, 0x0F,
   0x1E, 0x3C, 0x78, 0xF0, 0xFD, 0xE7, 0xD3, 0xBB, 0x6B, 0xD6, 0xB1, 0x7F, 0xFE, 0xE1, 0xDF, 0xA3, 0x5B, 0xB6, 0x71,
   0xE2, 0xD9, 0xAF, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0D, 0x1A, 0x34, 0x68, 0xD0, 0xBD, 0x67, 0xCE, 0x81, 0x1F,
   0x3E, 0x7C, 0xF8, 0xED, 0xC7, 0x93, 0x3B, 0x76, 0xEC, 0xC5, 0x97, 0x33, 0x66, 0xCC, 0x85, 0x17, 0x2E, 0x5C, 0xB8,
   0x6D, 0xDA, 0xA9, 0x4F, 0x9E, 0x21, 0x42, 0x84, 0x15, 0x2A, 0x54, 0xA8, 0x4D, 0x9A, 0x29, 0x52, 0xA4, 0x55, 0xAA,
   0x49, 0x92, 0x39, 0x72, 0xE4, 0xD5, 0xB7, 0x73, 0xE6, 0xD1, 0xBF, 0x63, 0xC6, 0x91, 0x3F, 0x7E, 0xFC, 0xE5, 0xD7,
   0xB3, 0x7B, 0xF6, 0xF1, 0xFF, 0xE3, 0xDB, 0xAB, 0x4B, 0x96, 0x31, 0x62, 0xC4, 0x95, 0x37, 0x6E, 0xDC, 0xA5, 0x57,
   0xAE, 0x41, 0x82, 0x19, 0x32, 0x64, 0xC8, 0x8D, 0x07, 0x0E, 0x1C, 0x38, 0x70, 0xE0, 0xDD, 0xA7, 0x53, 0xA6, 0x51,
   0xA2, 0x59, 0xB2, 0x79, 0xF2, 0xF9, 0xEF, 0xC3, 0x9B, 0x2B, 0x56, 0xAC, 0x45, 0x8A, 0x09, 0x12, 0x24, 0x48, 0x90,
   0x3D, 0x7A, 0xF4, 0xF5, 0xF7, 0xF3, 0xFB, 0xEB, 0xCB, 0x8B, 0x0B, 0x16, 0x2C, 0x58, 0xB0, 0x7D, 0xFA, 0xE9, 0xCF,
   0x83, 0x1B, 0x36, 0x6C, 0xD8, 0xAD, 0x47, 0x8E,
};

alignas(256) const uint8_t GF_LOG[256] = {
   0xFF, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1A, 0xC6, 0x03, 0xDF, 0x33, 0xEE, 0x1B, 0x68, 0xC7, 0x4B, 0x04, 0x64, 0xE0,
   0x0E, 0x34, 0x8D, 0xEF, 0x81, 0x1C, 0xC1, 0x69, 0xF8, 0xC8, 0x08, 0x4C, 0x71, 0x05, 0x8A, 0x65, 0x2F, 0xE1, 0x24,
   0x0F, 0x21, 0x35, 0x93, 0x8E, 0xDA, 0xF0, 0x12, 0x82, 0x45, 0x1D, 0xB5, 0xC2, 0x7D, 0x6A, 0x27, 0xF9, 0xB9, 0xC9,
   0x9A, 0x09, 0x78, 0x4D, 0xE4, 0x72, 0xA6, 0x06, 0xBF, 0x8B, 0x62, 0x66, 0xDD, 0x30, 0xFD, 0xE2, 0x98, 0x25, 0xB3,
   0x10, 0x91, 0x22, 0x88, 0x36, 0xD0, 0x94, 0xCE, 0x8F, 0x96, 0xDB, 0xBD, 0xF1, 0xD2, 0x13, 0x5C, 0x83, 0x38, 0x46,
   0x40, 0x1E, 0x42, 0xB6, 0xA3, 0xC3, 0x48, 0x7E, 0x6E, 0x6B, 0x3A, 0x28, 0x54, 0xFA, 0x85, 0xBA, 0x3D, 0xCA, 0x5E,
   0x9B, 0x9F, 0x0A, 0x15, 0x79, 0x2B, 0x4E, 0xD4, 0xE5, 0xAC, 0x73, 0xF3, 0xA7, 0x57, 0x07, 0x70, 0xC0, 0xF7, 0x8C,
   0x80, 0x63, 0x0D, 0x67, 0x4A, 0xDE, 0xED, 0x31, 0xC5, 0xFE, 0x18, 0xE3, 0xA5, 0x99, 0x77, 0x26, 0xB8, 0xB4, 0x7C,
   0x11, 0x44, 0x92, 0xD9, 0x23, 0x20, 0x89, 0x2E, 0x37, 0x3F, 0xD1, 0x5B, 0x95, 0xBC, 0xCF, 0xCD, 0x90, 0x87, 0x97,
   0xB2, 0xDC, 0xFC, 0xBE, 0x61, 0xF2, 0x56, 0xD3, 0xAB, 0x14, 0x2A, 0x5D, 0x9E, 0x84, 0x3C, 0x39, 0x53, 0x47, 0x6D,
   0x41, 0xA2, 0x1F, 0x2D, 0x43, 0xD8, 0xB7, 0x7B, 0xA4, 0x76, 0xC4, 0x17, 0x49, 0xEC, 0x7F, 0x0C, 0x6F, 0xF6, 0x6C,
   0xA1, 0x3B, 0x52, 0x29, 0x9D, 0x55, 0xAA, 0xFB, 0x60, 0x86, 0xB1, 0xBB, 0xCC, 0x3E, 0x5A, 0xCB, 0x59, 0x5F, 0xB0,
   0x9C, 0xA9, 0xA0, 0x51, 0x0B, 0xF5, 0x16, 0xEB, 0x7A, 0x75, 0x2C, 0xD7, 0x4F, 0xAE, 0xD5, 0xE9, 0xE6, 0xE7, 0xAD,
   0xE8, 0x74, 0xD6, 0xF4, 0xEA, 0xA8, 0x50, 0x58, 0xAF};

alignas(256) const uint8_t GF_INVERSE[256] = {
   0x00, 0x01, 0x8E, 0xF4, 0x47, 0xA7, 0x7A, 0xBA, 0xAD, 0x9D, 0xDD, 0x98, 0x3D, 0xAA, 0x5D, 0x96, 0xD8, 0x72, 0xC0,
   0x58, 0xE0, 0x3E, 0x4C, 0x66, 0x90, 0xDE, 0x55, 0x80, 0xA0, 0x83, 0x4B, 0x2A, 0x6C, 0xED, 0x39, 0x51, 0x60, 0x56,
   0x2C, 0x8A, 0x70, 0xD0, 0x1F, 0x4A, 0x26, 0x8B, 0x33, 0x6E, 0x48, 0x89, 0x6F, 0x2E, 0xA4, 0xC3, 0x40, 0x5E, 0x50,
   0x22, 0xCF, 0xA9, 0xAB, 0x0C, 0x15, 0xE1, 0x36, 0x5F, 0xF8, 0xD5, 0x92, 0x4E, 0xA6, 0x04, 0x30, 0x88, 0x2B, 0x1E,
   0x16, 0x67, 0x45, 0x93, 0x38, 0x23, 0x68, 0x8C, 0x81, 0x1A, 0x25, 0x61, 0x13, 0xC1, 0xCB, 0x63, 0x97, 0x0E, 0x37,
   0x41, 0x24, 0x57, 0xCA, 0x5B, 0xB9, 0xC4, 0x17, 0x4D, 0x52, 0x8D, 0xEF, 0xB3, 0x20, 0xEC, 0x2F, 0x32, 0x28, 0xD1,
   0x11, 0xD9, 0xE9, 0xFB, 0xDA, 0x79, 0xDB, 0x77, 0x06, 0xBB, 0x84, 0xCD, 0xFE, 0xFC, 0x1B, 0x54, 0xA1, 0x1D, 0x7C,
   0xCC, 0xE4, 0xB0, 0x49, 0x31, 0x27, 0x2D, 0x53, 0x69, 0x02, 0xF5, 0x18, 0xDF, 0x44, 0x4F, 0x9B, 0xBC, 0x0F, 0x5C,
   0x0B, 0xDC, 0xBD, 0x94, 0xAC, 0x09, 0xC7, 0xA2, 0x1C, 0x82, 0x9F, 0xC6, 0x34, 0xC2, 0x46, 0x05, 0xCE, 0x3B, 0x0D,
   0x3C, 0x9C, 0x08, 0xBE, 0xB7, 0x87, 0xE5, 0xEE, 0x6B, 0xEB, 0xF2, 0xBF, 0xAF, 0xC5, 0x64, 0x07, 0x7B, 0x95, 0x9A,
   0xAE, 0xB6, 0x12, 0x59, 0xA5, 0x35, 0x65, 0xB8, 0xA3, 0x9E, 0xD2, 0xF7, 0x62, 0x5A, 0x85, 0x7D, 0xA8, 0x3A, 0x29,
   0x71, 0xC8, 0xF6, 0xF9, 0x43, 0xD7, 0xD6, 0x10, 0x73, 0x76, 0x78, 0x99, 0x0A, 0x19, 0x91, 0x14, 0x3F, 0xE6, 0xF0,
   0x86, 0xB1, 0xE2, 0xF1, 0xFA, 0x74, 0xF3, 0xB4, 0x6D, 0x21, 0xB2, 0x6A, 0xE3, 0xE7, 0xB5, 0xEA, 0x03, 0x8F, 0xD3,
   0xC9, 0x42, 0xD4, 0xE8, 0x75, 0x7F, 0xFF, 0x7E, 0xFD};

const uint8_t* GF_MUL_TABLE(uint8_t y) {
   class GF_Table final {
      public:
         GF_Table() {
            m_table.resize(256 * 256);

            // x*0 = 0*y = 0 so we iterate over [1,255)
            for(size_t i = 1; i != 256; ++i) {
               for(size_t j = 1; j != 256; ++j) {
                  m_table[256 * i + j] = GF_EXP[(GF_LOG[i] + GF_LOG[j]) % 255];
               }
            }
         }

         const uint8_t* ptr(uint8_t y) const { return &m_table[256 * y]; }

      private:
         std::vector<uint8_t> m_table;
   };

   static GF_Table table;
   return table.ptr(y);
}

/*
* invert_matrix() takes a K*K matrix and produces its inverse
* (Gauss-Jordan algorithm, adapted from Numerical Recipes in C)
*/
void invert_matrix(uint8_t matrix[], size_t K) {
   class pivot_searcher {
      public:
         explicit pivot_searcher(size_t K) : m_ipiv(K) {}

         std::pair<size_t, size_t> operator()(size_t col, const uint8_t matrix[]) {
            /*
            * Zeroing column 'col', look for a non-zero element.
            * First try on the diagonal, if it fails, look elsewhere.
            */

            const size_t K = m_ipiv.size();

            if(m_ipiv[col] == false && matrix[col * K + col] != 0) {
               m_ipiv[col] = true;
               return std::make_pair(col, col);
            }

            for(size_t row = 0; row != K; ++row) {
               if(m_ipiv[row])
                  continue;

               for(size_t i = 0; i != K; ++i) {
                  if(m_ipiv[i] == false && matrix[row * K + i] != 0) {
                     m_ipiv[i] = true;
                     return std::make_pair(row, i);
                  }
               }
            }

            throw Invalid_Argument("ZFEC: pivot not found in invert_matrix");
         }

      private:
         // Marks elements already used as pivots
         std::vector<bool> m_ipiv;
   };

   pivot_searcher pivot_search(K);
   std::vector<size_t> indxc(K);
   std::vector<size_t> indxr(K);

   for(size_t col = 0; col != K; ++col) {
      const auto icolrow = pivot_search(col, matrix);

      const size_t icol = icolrow.first;
      const size_t irow = icolrow.second;

      /*
      * swap rows irow and icol, so afterwards the diagonal
      * element will be correct. Rarely done, not worth
      * optimizing.
      */
      if(irow != icol) {
         for(size_t i = 0; i != K; ++i)
            std::swap(matrix[irow * K + i], matrix[icol * K + i]);
      }

      indxr[col] = irow;
      indxc[col] = icol;
      uint8_t* pivot_row = &matrix[icol * K];
      const uint8_t c = pivot_row[icol];
      pivot_row[icol] = 1;

      if(c == 0)
         throw Invalid_Argument("ZFEC: singlar matrix");

      if(c != 1) {
         const uint8_t* mul_c = GF_MUL_TABLE(GF_INVERSE[c]);
         for(size_t i = 0; i != K; ++i)
            pivot_row[i] = mul_c[pivot_row[i]];
      }

      /*
      * From all rows, remove multiples of the selected row to zero
      * the relevant entry (in fact, the entry is not zero because we
      * know it must be zero).
      */
      for(size_t i = 0; i != K; ++i) {
         if(i != icol) {
            const uint8_t z = matrix[i * K + icol];
            matrix[i * K + icol] = 0;

            // This is equivalent to addmul()
            const uint8_t* mul_z = GF_MUL_TABLE(z);
            for(size_t j = 0; j != K; ++j)
               matrix[i * K + j] ^= mul_z[pivot_row[j]];
         }
      }
   }

   for(size_t i = 0; i != K; ++i) {
      if(indxr[i] != indxc[i]) {
         for(size_t row = 0; row != K; ++row)
            std::swap(matrix[row * K + indxr[i]], matrix[row * K + indxc[i]]);
      }
   }
}

/*
* Generate and invert a Vandermonde matrix.
*
* Only uses the second column of the matrix, containing the p_i's
* (contents - 0, GF_EXP[0...n])
*
* Algorithm borrowed from "Numerical recipes in C", section 2.8, but
* largely revised for my purposes.
*
* p = coefficients of the matrix (p_i)
* q = values of the polynomial (known)
*/
void create_inverted_vdm(uint8_t vdm[], size_t K) {
   if(K == 0) {
      return;
   }

   if(K == 1) /* degenerate case, matrix must be p^0 = 1 */
   {
      vdm[0] = 1;
      return;
   }

   /*
   * c holds the coefficient of P(x) = Prod (x - p_i), i=0..K-1
   * b holds the coefficient for the matrix inversion
   */
   std::vector<uint8_t> b(K);
   std::vector<uint8_t> c(K);

   /*
   * construct coeffs. recursively. We know c[K] = 1 (implicit)
   * and start P_0 = x - p_0, then at each stage multiply by
   * x - p_i generating P_i = x P_{i-1} - p_i P_{i-1}
   * After K steps we are done.
   */
   c[K - 1] = 0; /* really -p(0), but x = -x in GF(2^m) */
   for(size_t i = 1; i < K; ++i) {
      const uint8_t* mul_p_i = GF_MUL_TABLE(GF_EXP[i]);

      for(size_t j = K - 1 - (i - 1); j < K - 1; ++j)
         c[j] ^= mul_p_i[c[j + 1]];
      c[K - 1] ^= GF_EXP[i];
   }

   for(size_t row = 0; row < K; ++row) {
      // synthetic division etc.
      const uint8_t* mul_p_row = GF_MUL_TABLE(row == 0 ? 0 : GF_EXP[row]);

      uint8_t t = 1;
      b[K - 1] = 1; /* this is in fact c[K] */
      for(size_t i = K - 1; i > 0; i--) {
         b[i - 1] = c[i] ^ mul_p_row[b[i]];
         t = b[i - 1] ^ mul_p_row[t];
      }

      const uint8_t* mul_t_inv = GF_MUL_TABLE(GF_INVERSE[t]);
      for(size_t col = 0; col != K; ++col)
         vdm[col * K + row] = mul_t_inv[b[col]];
   }
}

}  // namespace

/*
* addmul() computes z[] = z[] + x[] * y
*/
void ZFEC::addmul(uint8_t z[], const uint8_t x[], uint8_t y, size_t size) {
   if(y == 0)
      return;

   const uint8_t* GF_MUL_Y = GF_MUL_TABLE(y);

   // first align z to 16 bytes
   while(size > 0 && reinterpret_cast<uintptr_t>(z) % 16) {
      z[0] ^= GF_MUL_Y[x[0]];
      ++z;
      ++x;
      size--;
   }

#if defined(BOTAN_HAS_ZFEC_VPERM)
   if(size >= 16 && CPUID::has_vperm()) {
      const size_t consumed = addmul_vperm(z, x, y, size);
      z += consumed;
      x += consumed;
      size -= consumed;
   }
#endif

#if defined(BOTAN_HAS_ZFEC_SSE2)
   if(size >= 64 && CPUID::has_sse2()) {
      const size_t consumed = addmul_sse2(z, x, y, size);
      z += consumed;
      x += consumed;
      size -= consumed;
   }
#endif

   while(size >= 16) {
      z[0] ^= GF_MUL_Y[x[0]];
      z[1] ^= GF_MUL_Y[x[1]];
      z[2] ^= GF_MUL_Y[x[2]];
      z[3] ^= GF_MUL_Y[x[3]];
      z[4] ^= GF_MUL_Y[x[4]];
      z[5] ^= GF_MUL_Y[x[5]];
      z[6] ^= GF_MUL_Y[x[6]];
      z[7] ^= GF_MUL_Y[x[7]];
      z[8] ^= GF_MUL_Y[x[8]];
      z[9] ^= GF_MUL_Y[x[9]];
      z[10] ^= GF_MUL_Y[x[10]];
      z[11] ^= GF_MUL_Y[x[11]];
      z[12] ^= GF_MUL_Y[x[12]];
      z[13] ^= GF_MUL_Y[x[13]];
      z[14] ^= GF_MUL_Y[x[14]];
      z[15] ^= GF_MUL_Y[x[15]];

      x += 16;
      z += 16;
      size -= 16;
   }

   // Clean up the trailing pieces
   for(size_t i = 0; i != size; ++i)
      z[i] ^= GF_MUL_Y[x[i]];
}

/*
* This section contains the proper FEC encoding/decoding routines.
* The encoding matrix is computed starting with a Vandermonde matrix,
* and then transforming it into a systematic matrix.
*/

/*
* ZFEC constructor
*/
ZFEC::ZFEC(size_t K, size_t N) : m_K(K), m_N(N), m_enc_matrix(N * K) {
   if(m_K == 0 || m_N == 0 || m_K > 256 || m_N > 256 || m_K > N)
      throw Invalid_Argument("ZFEC: violated 1 <= K <= N <= 256");

   std::vector<uint8_t> temp_matrix(m_N * m_K);

   /*
   * quick code to build systematic matrix: invert the top
   * K*K Vandermonde matrix, multiply right the bottom n-K rows
   * by the inverse, and construct the identity matrix at the top.
   */
   create_inverted_vdm(&temp_matrix[0], m_K);

   for(size_t i = m_K * m_K; i != temp_matrix.size(); ++i)
      temp_matrix[i] = GF_EXP[((i / m_K) * (i % m_K)) % 255];

   /*
   * the upper part of the encoding matrix is I
   */
   for(size_t i = 0; i != m_K; ++i)
      m_enc_matrix[i * (m_K + 1)] = 1;

   /*
   * computes C = AB where A is n*K, B is K*m, C is n*m
   */
   for(size_t row = m_K; row != m_N; ++row) {
      for(size_t col = 0; col != m_K; ++col) {
         uint8_t acc = 0;
         for(size_t i = 0; i != m_K; i++) {
            const uint8_t row_v = temp_matrix[row * m_K + i];
            const uint8_t row_c = temp_matrix[col + m_K * i];
            acc ^= GF_MUL_TABLE(row_v)[row_c];
         }
         m_enc_matrix[row * m_K + col] = acc;
      }
   }
}

/*
* ZFEC encoding routine
*/
void ZFEC::encode(const uint8_t input[], size_t size, const output_cb_t& output_cb) const {
   if(size % m_K != 0)
      throw Invalid_Argument("ZFEC::encode: input must be multiple of K uint8_ts");

   const size_t share_size = size / m_K;

   std::vector<const uint8_t*> shares;
   for(size_t i = 0; i != m_K; ++i)
      shares.push_back(input + i * share_size);

   this->encode_shares(shares, share_size, output_cb);
}

void ZFEC::encode_shares(const std::vector<const uint8_t*>& shares,
                         size_t share_size,
                         const output_cb_t& output_cb) const {
   if(shares.size() != m_K)
      throw Invalid_Argument("ZFEC::encode_shares must provide K shares");

   // The initial shares are just the original input shares
   for(size_t i = 0; i != m_K; ++i)
      output_cb(i, shares[i], share_size);

   std::vector<uint8_t> fec_buf(share_size);

   for(size_t i = m_K; i != m_N; ++i) {
      clear_mem(fec_buf.data(), fec_buf.size());

      for(size_t j = 0; j != m_K; ++j) {
         addmul(&fec_buf[0], shares[j], m_enc_matrix[i * m_K + j], share_size);
      }

      output_cb(i, &fec_buf[0], fec_buf.size());
   }
}

/*
* ZFEC decoding routine
*/
void ZFEC::decode_shares(const std::map<size_t, const uint8_t*>& shares,
                         size_t share_size,
                         const output_cb_t& output_cb) const {
   /*
   Todo:
   If shares.size() < K:
   signal decoding error for missing shares < K
   emit existing shares < K
   (ie, partial recovery if possible)
   Assert share_size % K == 0
   */

   if(shares.size() < m_K)
      throw Decoding_Error("ZFEC: could not decode, less than K surviving shares");

   std::vector<uint8_t> decoding_matrix(m_K * m_K);
   std::vector<size_t> indexes(m_K);
   std::vector<const uint8_t*> sharesv(m_K);

   auto shares_b_iter = shares.begin();
   auto shares_e_iter = shares.rbegin();

   bool missing_primary_share = false;

   for(size_t i = 0; i != m_K; ++i) {
      size_t share_id = 0;
      const uint8_t* share_data = nullptr;

      if(shares_b_iter->first == i) {
         share_id = shares_b_iter->first;
         share_data = shares_b_iter->second;
         ++shares_b_iter;
      } else {
         // if share i not found, use the unused one closest to n
         share_id = shares_e_iter->first;
         share_data = shares_e_iter->second;
         ++shares_e_iter;
         missing_primary_share = true;
      }

      if(share_id >= m_N)
         throw Decoding_Error("ZFEC: invalid share id detected during decode");

      /*
      This is a systematic code (encoding matrix includes K*K identity
      matrix), so shares less than K are copies of the input data,
      can output_cb directly. Also we know the encoding matrix in those rows
      contains I, so we can set the single bit directly without copying
      the entire row
      */
      if(share_id < m_K) {
         decoding_matrix[i * (m_K + 1)] = 1;
         output_cb(share_id, share_data, share_size);
      } else  // will decode after inverting matrix
      {
         std::memcpy(&decoding_matrix[i * m_K], &m_enc_matrix[share_id * m_K], m_K);
      }

      sharesv[i] = share_data;
      indexes[i] = share_id;
   }

   // If we had the original data shares then no need to perform
   // a matrix inversion, return immediately.
   if(!missing_primary_share) {
      for(size_t i = 0; i != indexes.size(); ++i) {
         BOTAN_ASSERT_NOMSG(indexes[i] < m_K);
      }
      return;
   }

   invert_matrix(&decoding_matrix[0], m_K);

   for(size_t i = 0; i != indexes.size(); ++i) {
      if(indexes[i] >= m_K) {
         std::vector<uint8_t> buf(share_size);
         for(size_t col = 0; col != m_K; ++col) {
            addmul(&buf[0], sharesv[col], decoding_matrix[i * m_K + col], share_size);
         }
         output_cb(i, &buf[0], share_size);
      }
   }
}

std::string ZFEC::provider() const {
#if defined(BOTAN_HAS_ZFEC_VPERM)
   if(CPUID::has_vperm()) {
      return "vperm";
   }
#endif

#if defined(BOTAN_HAS_ZFEC_SSE2)
   if(CPUID::has_sse2()) {
      return "sse2";
   }
#endif

   return "base";
}

}  // namespace Botan

1	/*
2	* Forward error correction based on Vandermonde matrices
3	*
4	* (C) 1997-1998 Luigi Rizzo (luigi@iet.unipi.it)
5	* (C) 2009,2010,2021 Jack Lloyd
6	* (C) 2011 Billy Brumley (billy.brumley@aalto.fi)
7	*
8	* Botan is released under the Simplified BSD License (see license.txt)
9	*/
10
11	#include <botan/zfec.h>
12
13	#include <botan/exceptn.h>
14	#include <botan/mem_ops.h>
15	#include <botan/internal/cpuid.h>
16	#include <cstring>
17	#include <vector>
18
19	namespace Botan {
20
21	namespace {
22
23	/* Tables for arithetic in GF(2^8) using 1+x^2+x^3+x^4+x^8
24	*
25	* See Lin & Costello, Appendix A, and Lee & Messerschmitt, p. 453.
26	*
27	* Generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m]
28	* Lookup tables:
29	* index->polynomial form gf_exp[] contains j= \alpha^i;
30	* polynomial form -> index form gf_log[ j = \alpha^i ] = i
31	* \alpha=x is the primitive element of GF(2^m)
32	*/
33	alignas(256) const uint8_t GF_EXP[255] = {
34	0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1D, 0x3A, 0x74, 0xE8, 0xCD, 0x87, 0x13, 0x26, 0x4C, 0x98, 0x2D,
35	0x5A, 0xB4, 0x75, 0xEA, 0xC9, 0x8F, 0x03, 0x06, 0x0C, 0x18, 0x30, 0x60, 0xC0, 0x9D, 0x27, 0x4E, 0x9C, 0x25, 0x4A,
36	0x94, 0x35, 0x6A, 0xD4, 0xB5, 0x77, 0xEE, 0xC1, 0x9F, 0x23, 0x46, 0x8C, 0x05, 0x0A, 0x14, 0x28, 0x50, 0xA0, 0x5D,
37	0xBA, 0x69, 0xD2, 0xB9, 0x6F, 0xDE, 0xA1, 0x5F, 0xBE, 0x61, 0xC2, 0x99, 0x2F, 0x5E, 0xBC, 0x65, 0xCA, 0x89, 0x0F,
38	0x1E, 0x3C, 0x78, 0xF0, 0xFD, 0xE7, 0xD3, 0xBB, 0x6B, 0xD6, 0xB1, 0x7F, 0xFE, 0xE1, 0xDF, 0xA3, 0x5B, 0xB6, 0x71,
39	0xE2, 0xD9, 0xAF, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88, 0x0D, 0x1A, 0x34, 0x68, 0xD0, 0xBD, 0x67, 0xCE, 0x81, 0x1F,
40	0x3E, 0x7C, 0xF8, 0xED, 0xC7, 0x93, 0x3B, 0x76, 0xEC, 0xC5, 0x97, 0x33, 0x66, 0xCC, 0x85, 0x17, 0x2E, 0x5C, 0xB8,
41	0x6D, 0xDA, 0xA9, 0x4F, 0x9E, 0x21, 0x42, 0x84, 0x15, 0x2A, 0x54, 0xA8, 0x4D, 0x9A, 0x29, 0x52, 0xA4, 0x55, 0xAA,
42	0x49, 0x92, 0x39, 0x72, 0xE4, 0xD5, 0xB7, 0x73, 0xE6, 0xD1, 0xBF, 0x63, 0xC6, 0x91, 0x3F, 0x7E, 0xFC, 0xE5, 0xD7,
43	0xB3, 0x7B, 0xF6, 0xF1, 0xFF, 0xE3, 0xDB, 0xAB, 0x4B, 0x96, 0x31, 0x62, 0xC4, 0x95, 0x37, 0x6E, 0xDC, 0xA5, 0x57,
44	0xAE, 0x41, 0x82, 0x19, 0x32, 0x64, 0xC8, 0x8D, 0x07, 0x0E, 0x1C, 0x38, 0x70, 0xE0, 0xDD, 0xA7, 0x53, 0xA6, 0x51,
45	0xA2, 0x59, 0xB2, 0x79, 0xF2, 0xF9, 0xEF, 0xC3, 0x9B, 0x2B, 0x56, 0xAC, 0x45, 0x8A, 0x09, 0x12, 0x24, 0x48, 0x90,
46	0x3D, 0x7A, 0xF4, 0xF5, 0xF7, 0xF3, 0xFB, 0xEB, 0xCB, 0x8B, 0x0B, 0x16, 0x2C, 0x58, 0xB0, 0x7D, 0xFA, 0xE9, 0xCF,
47	0x83, 0x1B, 0x36, 0x6C, 0xD8, 0xAD, 0x47, 0x8E,
48	};
49
50	alignas(256) const uint8_t GF_LOG[256] = {
51	0xFF, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1A, 0xC6, 0x03, 0xDF, 0x33, 0xEE, 0x1B, 0x68, 0xC7, 0x4B, 0x04, 0x64, 0xE0,
52	0x0E, 0x34, 0x8D, 0xEF, 0x81, 0x1C, 0xC1, 0x69, 0xF8, 0xC8, 0x08, 0x4C, 0x71, 0x05, 0x8A, 0x65, 0x2F, 0xE1, 0x24,
53	0x0F, 0x21, 0x35, 0x93, 0x8E, 0xDA, 0xF0, 0x12, 0x82, 0x45, 0x1D, 0xB5, 0xC2, 0x7D, 0x6A, 0x27, 0xF9, 0xB9, 0xC9,
54	0x9A, 0x09, 0x78, 0x4D, 0xE4, 0x72, 0xA6, 0x06, 0xBF, 0x8B, 0x62, 0x66, 0xDD, 0x30, 0xFD, 0xE2, 0x98, 0x25, 0xB3,
55	0x10, 0x91, 0x22, 0x88, 0x36, 0xD0, 0x94, 0xCE, 0x8F, 0x96, 0xDB, 0xBD, 0xF1, 0xD2, 0x13, 0x5C, 0x83, 0x38, 0x46,
56	0x40, 0x1E, 0x42, 0xB6, 0xA3, 0xC3, 0x48, 0x7E, 0x6E, 0x6B, 0x3A, 0x28, 0x54, 0xFA, 0x85, 0xBA, 0x3D, 0xCA, 0x5E,
57	0x9B, 0x9F, 0x0A, 0x15, 0x79, 0x2B, 0x4E, 0xD4, 0xE5, 0xAC, 0x73, 0xF3, 0xA7, 0x57, 0x07, 0x70, 0xC0, 0xF7, 0x8C,
58	0x80, 0x63, 0x0D, 0x67, 0x4A, 0xDE, 0xED, 0x31, 0xC5, 0xFE, 0x18, 0xE3, 0xA5, 0x99, 0x77, 0x26, 0xB8, 0xB4, 0x7C,
59	0x11, 0x44, 0x92, 0xD9, 0x23, 0x20, 0x89, 0x2E, 0x37, 0x3F, 0xD1, 0x5B, 0x95, 0xBC, 0xCF, 0xCD, 0x90, 0x87, 0x97,
60	0xB2, 0xDC, 0xFC, 0xBE, 0x61, 0xF2, 0x56, 0xD3, 0xAB, 0x14, 0x2A, 0x5D, 0x9E, 0x84, 0x3C, 0x39, 0x53, 0x47, 0x6D,
61	0x41, 0xA2, 0x1F, 0x2D, 0x43, 0xD8, 0xB7, 0x7B, 0xA4, 0x76, 0xC4, 0x17, 0x49, 0xEC, 0x7F, 0x0C, 0x6F, 0xF6, 0x6C,
62	0xA1, 0x3B, 0x52, 0x29, 0x9D, 0x55, 0xAA, 0xFB, 0x60, 0x86, 0xB1, 0xBB, 0xCC, 0x3E, 0x5A, 0xCB, 0x59, 0x5F, 0xB0,
63	0x9C, 0xA9, 0xA0, 0x51, 0x0B, 0xF5, 0x16, 0xEB, 0x7A, 0x75, 0x2C, 0xD7, 0x4F, 0xAE, 0xD5, 0xE9, 0xE6, 0xE7, 0xAD,
64	0xE8, 0x74, 0xD6, 0xF4, 0xEA, 0xA8, 0x50, 0x58, 0xAF};
65
66	alignas(256) const uint8_t GF_INVERSE[256] = {
67	0x00, 0x01, 0x8E, 0xF4, 0x47, 0xA7, 0x7A, 0xBA, 0xAD, 0x9D, 0xDD, 0x98, 0x3D, 0xAA, 0x5D, 0x96, 0xD8, 0x72, 0xC0,
68	0x58, 0xE0, 0x3E, 0x4C, 0x66, 0x90, 0xDE, 0x55, 0x80, 0xA0, 0x83, 0x4B, 0x2A, 0x6C, 0xED, 0x39, 0x51, 0x60, 0x56,
69	0x2C, 0x8A, 0x70, 0xD0, 0x1F, 0x4A, 0x26, 0x8B, 0x33, 0x6E, 0x48, 0x89, 0x6F, 0x2E, 0xA4, 0xC3, 0x40, 0x5E, 0x50,
70	0x22, 0xCF, 0xA9, 0xAB, 0x0C, 0x15, 0xE1, 0x36, 0x5F, 0xF8, 0xD5, 0x92, 0x4E, 0xA6, 0x04, 0x30, 0x88, 0x2B, 0x1E,
71	0x16, 0x67, 0x45, 0x93, 0x38, 0x23, 0x68, 0x8C, 0x81, 0x1A, 0x25, 0x61, 0x13, 0xC1, 0xCB, 0x63, 0x97, 0x0E, 0x37,
72	0x41, 0x24, 0x57, 0xCA, 0x5B, 0xB9, 0xC4, 0x17, 0x4D, 0x52, 0x8D, 0xEF, 0xB3, 0x20, 0xEC, 0x2F, 0x32, 0x28, 0xD1,
73	0x11, 0xD9, 0xE9, 0xFB, 0xDA, 0x79, 0xDB, 0x77, 0x06, 0xBB, 0x84, 0xCD, 0xFE, 0xFC, 0x1B, 0x54, 0xA1, 0x1D, 0x7C,
74	0xCC, 0xE4, 0xB0, 0x49, 0x31, 0x27, 0x2D, 0x53, 0x69, 0x02, 0xF5, 0x18, 0xDF, 0x44, 0x4F, 0x9B, 0xBC, 0x0F, 0x5C,
75	0x0B, 0xDC, 0xBD, 0x94, 0xAC, 0x09, 0xC7, 0xA2, 0x1C, 0x82, 0x9F, 0xC6, 0x34, 0xC2, 0x46, 0x05, 0xCE, 0x3B, 0x0D,
76	0x3C, 0x9C, 0x08, 0xBE, 0xB7, 0x87, 0xE5, 0xEE, 0x6B, 0xEB, 0xF2, 0xBF, 0xAF, 0xC5, 0x64, 0x07, 0x7B, 0x95, 0x9A,
77	0xAE, 0xB6, 0x12, 0x59, 0xA5, 0x35, 0x65, 0xB8, 0xA3, 0x9E, 0xD2, 0xF7, 0x62, 0x5A, 0x85, 0x7D, 0xA8, 0x3A, 0x29,
78	0x71, 0xC8, 0xF6, 0xF9, 0x43, 0xD7, 0xD6, 0x10, 0x73, 0x76, 0x78, 0x99, 0x0A, 0x19, 0x91, 0x14, 0x3F, 0xE6, 0xF0,
79	0x86, 0xB1, 0xE2, 0xF1, 0xFA, 0x74, 0xF3, 0xB4, 0x6D, 0x21, 0xB2, 0x6A, 0xE3, 0xE7, 0xB5, 0xEA, 0x03, 0x8F, 0xD3,
80	0xC9, 0x42, 0xD4, 0xE8, 0x75, 0x7F, 0xFF, 0x7E, 0xFD};
81
82	const uint8_t* GF_MUL_TABLE(uint8_t y) {	7,305,523✔
83	class GF_Table final {	7,305,523✔
84	public:
85	GF_Table() {	5✔
86	m_table.resize(256 * 256);	5✔
87
88	// x0 = 0y = 0 so we iterate over [1,255)
89	for(size_t i = 1; i != 256; ++i) {	1,280✔
90	for(size_t j = 1; j != 256; ++j) {	326,400✔
91	m_table[256 * i + j] = GF_EXP[(GF_LOG[i] + GF_LOG[j]) % 255];	325,125✔
92	}
93	}
94	}	5✔
95
96	const uint8_t* ptr(uint8_t y) const { return &m_table[256 * y]; }	7,305,523✔
97
98	private:
99	std::vector<uint8_t> m_table;
100	};
101
102	static GF_Table table;	7,305,523✔
103	return table.ptr(y);	7,305,523✔
104	}
105
106	/*
107	* invert_matrix() takes a K*K matrix and produces its inverse
108	* (Gauss-Jordan algorithm, adapted from Numerical Recipes in C)
109	*/
110	void invert_matrix(uint8_t matrix[], size_t K) {	87,705✔
111	class pivot_searcher {	263,115✔
112	public:
113	explicit pivot_searcher(size_t K) : m_ipiv(K) {}	87,705✔
114
115	std::pair<size_t, size_t> operator()(size_t col, const uint8_t matrix[]) {	337,030✔
116	/*
117	* Zeroing column 'col', look for a non-zero element.
118	* First try on the diagonal, if it fails, look elsewhere.
119	*/
120
121	const size_t K = m_ipiv.size();	337,030✔
122
123	if(m_ipiv[col] == false && matrix[col * K + col] != 0) {	337,030✔
124	m_ipiv[col] = true;	337,030✔
125	return std::make_pair(col, col);	337,030✔
126	}
127
128	for(size_t row = 0; row != K; ++row) {	×
129	if(m_ipiv[row])	×
130	continue;	×
131
132	for(size_t i = 0; i != K; ++i) {	×
133	if(m_ipiv[i] == false && matrix[row * K + i] != 0) {	×
134	m_ipiv[i] = true;	×
135	return std::make_pair(row, i);	×
136	}
137	}
138	}
139
140	throw Invalid_Argument("ZFEC: pivot not found in invert_matrix");	×
141	}
142
143	private:
144	// Marks elements already used as pivots
145	std::vector<bool> m_ipiv;
146	};
147
148	pivot_searcher pivot_search(K);	87,705✔
149	std::vector<size_t> indxc(K);	87,705✔
150	std::vector<size_t> indxr(K);	87,705✔
151
152	for(size_t col = 0; col != K; ++col) {	424,735✔
153	const auto icolrow = pivot_search(col, matrix);	337,030✔
154
155	const size_t icol = icolrow.first;	337,030✔
156	const size_t irow = icolrow.second;	337,030✔
157
158	/*
159	* swap rows irow and icol, so afterwards the diagonal
160	* element will be correct. Rarely done, not worth
161	* optimizing.
162	*/
163	if(irow != icol) {	337,030✔
164	for(size_t i = 0; i != K; ++i)	×
165	std::swap(matrix[irow * K + i], matrix[icol * K + i]);	×
166	}
167
168	indxr[col] = irow;	337,030✔
169	indxc[col] = icol;	337,030✔
170	uint8_t* pivot_row = &matrix[icol * K];	337,030✔
171	const uint8_t c = pivot_row[icol];	337,030✔
172	pivot_row[icol] = 1;	337,030✔
173
174	if(c == 0)	337,030✔
175	throw Invalid_Argument("ZFEC: singlar matrix");	×
176
177	if(c != 1) {	337,030✔
178	const uint8_t* mul_c = GF_MUL_TABLE(GF_INVERSE[c]);	158,771✔
179	for(size_t i = 0; i != K; ++i)	774,333✔
180	pivot_row[i] = mul_c[pivot_row[i]];	615,562✔
181	}
182
183	/*
184	* From all rows, remove multiples of the selected row to zero
185	* the relevant entry (in fact, the entry is not zero because we
186	* know it must be zero).
187	*/
188	for(size_t i = 0; i != K; ++i) {	1,650,506✔
189	if(i != icol) {	1,313,476✔
190	const uint8_t z = matrix[i * K + icol];	976,446✔
191	matrix[i * K + icol] = 0;	976,446✔
192
193	// This is equivalent to addmul()
194	const uint8_t* mul_z = GF_MUL_TABLE(z);	976,446✔
195	for(size_t j = 0; j != K; ++j)	4,835,898✔
196	matrix[i * K + j] ^= mul_z[pivot_row[j]];	3,859,452✔
197	}
198	}
199	}
200
201	for(size_t i = 0; i != K; ++i) {	424,735✔
202	if(indxr[i] != indxc[i]) {	337,030✔
203	for(size_t row = 0; row != K; ++row)	×
204	std::swap(matrix[row * K + indxr[i]], matrix[row * K + indxc[i]]);	×
205	}
206	}
207	}	175,410✔
208
209	/*
210	* Generate and invert a Vandermonde matrix.
211	*
212	* Only uses the second column of the matrix, containing the p_i's
213	* (contents - 0, GF_EXP[0...n])
214	*
215	* Algorithm borrowed from "Numerical recipes in C", section 2.8, but
216	* largely revised for my purposes.
217	*
218	* p = coefficients of the matrix (p_i)
219	* q = values of the polynomial (known)
220	*/
221	void create_inverted_vdm(uint8_t vdm[], size_t K) {	92,530✔
222	if(K == 0) {	92,530✔
223	return;	547✔
224	}
225
226	if(K == 1) /* degenerate case, matrix must be p^0 = 1 */	92,530✔
227	{
228	vdm[0] = 1;	547✔
229	return;	547✔
230	}
231
232	/*
233	* c holds the coefficient of P(x) = Prod (x - p_i), i=0..K-1
234	* b holds the coefficient for the matrix inversion
235	*/
236	std::vector<uint8_t> b(K);	91,983✔
237	std::vector<uint8_t> c(K);	91,983✔
238
239	/*
240	* construct coeffs. recursively. We know c[K] = 1 (implicit)
241	* and start P_0 = x - p_0, then at each stage multiply by
242	* x - p_i generating P_i = x P_{i-1} - p_i P_{i-1}
243	* After K steps we are done.
244	*/
245	c[K - 1] = 0; /* really -p(0), but x = -x in GF(2^m) */	91,983✔
246	for(size_t i = 1; i < K; ++i) {	353,293✔
247	const uint8_t* mul_p_i = GF_MUL_TABLE(GF_EXP[i]);	261,310✔
248
249	for(size_t j = K - 1 - (i - 1); j < K - 1; ++j)	510,904✔
250	c[j] ^= mul_p_i[c[j + 1]];	249,594✔
251	c[K - 1] ^= GF_EXP[i];	261,310✔
252	}
253
254	for(size_t row = 0; row < K; ++row) {	445,276✔
255	// synthetic division etc.
256	const uint8_t* mul_p_row = GF_MUL_TABLE(row == 0 ? 0 : GF_EXP[row]);	353,293✔
257
258	uint8_t t = 1;	353,293✔
259	b[K - 1] = 1; /* this is in fact c[K] */	353,293✔
260	for(size_t i = K - 1; i > 0; i--) {	1,375,101✔
261	b[i - 1] = c[i] ^ mul_p_row[b[i]];	1,021,808✔
262	t = b[i - 1] ^ mul_p_row[t];	1,021,808✔
263	}
264
265	const uint8_t* mul_t_inv = GF_MUL_TABLE(GF_INVERSE[t]);	353,293✔
266	for(size_t col = 0; col != K; ++col)	1,728,394✔
267	vdm[col * K + row] = mul_t_inv[b[col]];	1,375,101✔
268	}
269	}	183,966✔
270
271	} // namespace
272
273	/*
274	* addmul() computes z[] = z[] + x[] * y
275	*/
276	void ZFEC::addmul(uint8_t z[], const uint8_t x[], uint8_t y, size_t size) {	624,599✔
277	if(y == 0)	624,599✔
278	return;
279
280	const uint8_t* GF_MUL_Y = GF_MUL_TABLE(y);	624,599✔
281
282	// first align z to 16 bytes
283	while(size > 0 && reinterpret_cast<uintptr_t>(z) % 16) {	1,249,198✔
284	z[0] ^= GF_MUL_Y[x[0]];	×
285	++z;	×
286	++x;	×
287	size--;	×
288	}
289
290	#if defined(BOTAN_HAS_ZFEC_VPERM)
291	if(size >= 16 && CPUID::has_vperm()) {	1,249,025✔
292	const size_t consumed = addmul_vperm(z, x, y, size);	618,416✔
293	z += consumed;	618,416✔
294	x += consumed;	618,416✔
295	size -= consumed;	618,416✔
296	}
297	#endif
298
299	#if defined(BOTAN_HAS_ZFEC_SSE2)
300	if(size >= 64 && CPUID::has_sse2()) {	629,268✔
301	const size_t consumed = addmul_sse2(z, x, y, size);	2,350✔
302	z += consumed;	2,350✔
303	x += consumed;	2,350✔
304	size -= consumed;	2,350✔
305	}
306	#endif
307
308	while(size >= 16) {	655,974✔
309	z[0] ^= GF_MUL_Y[x[0]];	31,375✔
310	z[1] ^= GF_MUL_Y[x[1]];	31,375✔
311	z[2] ^= GF_MUL_Y[x[2]];	31,375✔
312	z[3] ^= GF_MUL_Y[x[3]];	31,375✔
313	z[4] ^= GF_MUL_Y[x[4]];	31,375✔
314	z[5] ^= GF_MUL_Y[x[5]];	31,375✔
315	z[6] ^= GF_MUL_Y[x[6]];	31,375✔
316	z[7] ^= GF_MUL_Y[x[7]];	31,375✔
317	z[8] ^= GF_MUL_Y[x[8]];	31,375✔
318	z[9] ^= GF_MUL_Y[x[9]];	31,375✔
319	z[10] ^= GF_MUL_Y[x[10]];	31,375✔
320	z[11] ^= GF_MUL_Y[x[11]];	31,375✔
321	z[12] ^= GF_MUL_Y[x[12]];	31,375✔
322	z[13] ^= GF_MUL_Y[x[13]];	31,375✔
323	z[14] ^= GF_MUL_Y[x[14]];	31,375✔
324	z[15] ^= GF_MUL_Y[x[15]];	31,375✔
325
326	x += 16;	31,375✔
327	z += 16;	31,375✔
328	size -= 16;	31,375✔
329	}
330
331	// Clean up the trailing pieces
332	for(size_t i = 0; i != size; ++i)	5,450,899✔
333	z[i] ^= GF_MUL_Y[x[i]];	4,826,300✔
334	}
335
336	/*
337	* This section contains the proper FEC encoding/decoding routines.
338	* The encoding matrix is computed starting with a Vandermonde matrix,
339	* and then transforming it into a systematic matrix.
340	*/
341
342	/*
343	* ZFEC constructor
344	*/
345	ZFEC::ZFEC(size_t K, size_t N) : m_K(K), m_N(N), m_enc_matrix(N * K) {	92,532✔
346	if(m_K == 0 \|\| m_N == 0 \|\| m_K > 256 \|\| m_N > 256 \|\| m_K > N)	92,532✔
347	throw Invalid_Argument("ZFEC: violated 1 <= K <= N <= 256");	2✔
348
349	std::vector<uint8_t> temp_matrix(m_N * m_K);	92,530✔
350
351	/*
352	* quick code to build systematic matrix: invert the top
353	* K*K Vandermonde matrix, multiply right the bottom n-K rows
354	* by the inverse, and construct the identity matrix at the top.
355	*/
356	create_inverted_vdm(&temp_matrix[0], m_K);	92,530✔
357
358	for(size_t i = m_K * m_K; i != temp_matrix.size(); ++i)	1,266,595✔
359	temp_matrix[i] = GF_EXP[((i / m_K) * (i % m_K)) % 255];	1,174,065✔
360
361	/*
362	* the upper part of the encoding matrix is I
363	*/
364	for(size_t i = 0; i != m_K; ++i)	446,370✔
365	m_enc_matrix[i * (m_K + 1)] = 1;	353,840✔
366
367	/*
368	* computes C = AB where A is nK, B is Km, C is n*m
369	*/
370	for(size_t row = m_K; row != m_N; ++row) {	398,398✔
371	for(size_t col = 0; col != m_K; ++col) {	1,479,933✔
372	uint8_t acc = 0;
373	for(size_t i = 0; i != m_K; i++) {	5,751,876✔
374	const uint8_t row_v = temp_matrix[row * m_K + i];	4,577,811✔
375	const uint8_t row_c = temp_matrix[col + m_K * i];	4,577,811✔
376	acc ^= GF_MUL_TABLE(row_v)[row_c];	4,577,811✔
377	}
378	m_enc_matrix[row * m_K + col] = acc;	1,174,065✔
379	}
380	}
381	}	92,532✔
382
383	/*
384	* ZFEC encoding routine
385	*/
386	void ZFEC::encode(const uint8_t input[], size_t size, const output_cb_t& output_cb) const {	767✔
387	if(size % m_K != 0)	767✔
388	throw Invalid_Argument("ZFEC::encode: input must be multiple of K uint8_ts");	×
389
390	const size_t share_size = size / m_K;	767✔
391
392	std::vector<const uint8_t*> shares;	767✔
393	for(size_t i = 0; i != m_K; ++i)	3,294✔
394	shares.push_back(input + i * share_size);	2,527✔
395
396	this->encode_shares(shares, share_size, output_cb);	767✔
397	}	767✔
398
399	void ZFEC::encode_shares(const std::vector<const uint8_t*>& shares,	767✔
400	size_t share_size,
401	const output_cb_t& output_cb) const {
402	if(shares.size() != m_K)	767✔
403	throw Invalid_Argument("ZFEC::encode_shares must provide K shares");	×
404
405	// The initial shares are just the original input shares
406	for(size_t i = 0; i != m_K; ++i)	3,294✔
407	output_cb(i, shares[i], share_size);	5,054✔
408
409	std::vector<uint8_t> fec_buf(share_size);	767✔
410
411	for(size_t i = m_K; i != m_N; ++i) {	3,045✔
412	clear_mem(fec_buf.data(), fec_buf.size());	2,278✔
413
414	for(size_t j = 0; j != m_K; ++j) {	11,033✔
415	addmul(&fec_buf[0], shares[j], m_enc_matrix[i * m_K + j], share_size);	8,755✔
416	}
417
418	output_cb(i, &fec_buf[0], fec_buf.size());	4,556✔
419	}
420	}	767✔
421
422	/*
423	* ZFEC decoding routine
424	*/
425	void ZFEC::decode_shares(const std::map<size_t, const uint8_t*>& shares,	92,250✔
426	size_t share_size,
427	const output_cb_t& output_cb) const {
428	/*
429	Todo:
430	If shares.size() < K:
431	signal decoding error for missing shares < K
432	emit existing shares < K
433	(ie, partial recovery if possible)
434	Assert share_size % K == 0
435	*/
436
437	if(shares.size() < m_K)	92,250✔
438	throw Decoding_Error("ZFEC: could not decode, less than K surviving shares");	×
439
440	std::vector<uint8_t> decoding_matrix(m_K * m_K);	92,250✔
441	std::vector<size_t> indexes(m_K);	92,250✔
442	std::vector<const uint8_t*> sharesv(m_K);	92,250✔
443
444	auto shares_b_iter = shares.begin();	92,250✔
445	auto shares_e_iter = shares.rbegin();	92,250✔
446
447	bool missing_primary_share = false;	92,250✔
448
449	for(size_t i = 0; i != m_K; ++i) {	445,997✔
450	size_t share_id = 0;	353,747✔
451	const uint8_t* share_data = nullptr;	353,747✔
452
453	if(shares_b_iter->first == i) {	353,747✔
454	share_id = shares_b_iter->first;	194,694✔
455	share_data = shares_b_iter->second;	194,694✔
456	++shares_b_iter;	194,694✔
457	} else {
458	// if share i not found, use the unused one closest to n
459	share_id = shares_e_iter->first;	159,053✔
460	share_data = shares_e_iter->second;	159,053✔
461	++shares_e_iter;	159,053✔
462	missing_primary_share = true;	159,053✔
463	}
464
465	if(share_id >= m_N)	353,747✔
466	throw Decoding_Error("ZFEC: invalid share id detected during decode");	×
467
468	/*
469	This is a systematic code (encoding matrix includes K*K identity
470	matrix), so shares less than K are copies of the input data,
471	can output_cb directly. Also we know the encoding matrix in those rows
472	contains I, so we can set the single bit directly without copying
473	the entire row
474	*/
475	if(share_id < m_K) {	353,747✔
476	decoding_matrix[i * (m_K + 1)] = 1;	194,694✔
477	output_cb(share_id, share_data, share_size);	389,388✔
478	} else // will decode after inverting matrix
479	{
480	std::memcpy(&decoding_matrix[i * m_K], &m_enc_matrix[share_id * m_K], m_K);	159,053✔
481	}
482
483	sharesv[i] = share_data;	353,747✔
484	indexes[i] = share_id;	353,747✔
485	}
486
487	// If we had the original data shares then no need to perform
488	// a matrix inversion, return immediately.
489	if(!missing_primary_share) {	92,250✔
490	for(size_t i = 0; i != indexes.size(); ++i) {	21,262✔
491	BOTAN_ASSERT_NOMSG(indexes[i] < m_K);	16,717✔
492	}
493	return;	4,545✔
494	}
495
496	invert_matrix(&decoding_matrix[0], m_K);	87,705✔
497
498	for(size_t i = 0; i != indexes.size(); ++i) {	424,735✔
499	if(indexes[i] >= m_K) {	337,030✔
500	std::vector<uint8_t> buf(share_size);	159,053✔
501	for(size_t col = 0; col != m_K; ++col) {	774,897✔
502	addmul(&buf[0], sharesv[col], decoding_matrix[i * m_K + col], share_size);	615,844✔
503	}
504	output_cb(i, &buf[0], share_size);	318,106✔
505	}	159,053✔
506	}
507	}	276,750✔
508
509	std::string ZFEC::provider() const {	243✔
510	#if defined(BOTAN_HAS_ZFEC_VPERM)
511	if(CPUID::has_vperm()) {	243✔
512	return "vperm";	81✔
513	}
514	#endif
515
516	#if defined(BOTAN_HAS_ZFEC_SSE2)
517	if(CPUID::has_sse2()) {	162✔
518	return "sse2";	81✔
519	}
520	#endif
521
522	return "base";	81✔
523	}
524
525	} // namespace Botan

randombit / botan / 5111374265

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