text: #include "ntt.h"
  #include "params.h"
  #include "poly.h"
  #include "reduce.h"
  #include "rounding.h"
  #include "symmetric.h"
  
  
  /*************************************************
  * Name:        poly_reduce
  *
  * Description: Reduce all coefficients of input polynomial to representative
  *              in [0,2*Q[.
  *
  * Arguments:   - poly *a: pointer to input/output polynomial
  **************************************************/
  void poly_reduce(poly *a) {
      for (size_t i = 0; i < N; ++i) {
          a->coeffs[i] = reduce32(a->coeffs[i]);
      }
  }
  
  /*************************************************
  * Name:        poly_csubq
  *
  * Description: For all coefficients of input polynomial subtract Q if
  *              coefficient is bigger than Q.
  *
  * Arguments:   - poly *a: pointer to input/output polynomial
  **************************************************/
  void poly_csubq(poly *a) {
      for (size_t i = 0; i < N; ++i) {
          a->coeffs[i] = csubq(a->coeffs[i]);
      }
  }
  
  /*************************************************
  * Name:        poly_freeze
  *
  * Description: Reduce all coefficients of the polynomial to standard
  *              representatives.
  *
  * Arguments:   - poly *a: pointer to input/output polynomial
  **************************************************/
  void poly_freeze(poly *a) {
      for (size_t i = 0; i < N; ++i) {
          a->coeffs[i] = freeze(a->coeffs[i]);
      }
  }
  
  /*************************************************
  * Name:        poly_add
  *
  * Description: Add polynomials. No modular reduction is performed.
  *
  * Arguments:   - poly *c: pointer to output polynomial
  *              - const poly *a: pointer to first summand
  *              - const poly *b: pointer to second summand
  **************************************************/
  void poly_add(poly *c, const poly *a, const poly *b) {
      for (size_t i = 0; i < N; ++i) {
          c->coeffs[i] = a->coeffs[i] + b->coeffs[i];
      }
  }
  
  /*************************************************
  * Name:        poly_sub
  *
  * Description: Subtract polynomials. Assumes coefficients of second input
  *              polynomial to be less than 2*Q. No modular reduction is
  *              performed.
  *
  * Arguments:   - poly *c: pointer to output polynomial
  *              - const poly *a: pointer to first input polynomial
  *              - const poly *b: pointer to second input polynomial to be
  *                               subtracted from first input polynomial
  **************************************************/
  void poly_sub(poly *c, const poly *a, const poly *b) {
      for (size_t i = 0; i < N; ++i) {
          c->coeffs[i] = a->coeffs[i] + 2 * Q - b->coeffs[i];
      }
  }
  
  /*************************************************
  * Name:        poly_shiftl
  *
  * Description: Multiply polynomial by 2^D without modular reduction. Assumes
  *              input coefficients to be less than 2^{32-D}.
  *
  * Arguments:   - poly *a: pointer to input/output polynomial
  **************************************************/
  void poly_shiftl(poly *a) {
      for (size_t i = 0; i < N; ++i) {
          a->coeffs[i] <<= D;
      }
  }
  
  /*************************************************
  * Name:        poly_ntt
  *
  * Description: Forward NTT. Output coefficients can be up to 16*Q larger than
  *              input coefficients.
  *
  * Arguments:   - poly *a: pointer to input/output polynomial
  **************************************************/
  void poly_ntt(poly *a) {
      ntt(a->coeffs);
  }
  
  /*************************************************
  * Name:        poly_invntt_montgomery
  *
  * Description: Inverse NTT and multiplication with 2^{32}. Input coefficients
  *              need to be less than 2*Q. Output coefficients are less than 2*Q.
  *
  * Arguments:   - poly *a: pointer to input/output polynomial
  **************************************************/
  void poly_invntt_montgomery(poly *a) {
      invntt_frominvmont(a->coeffs);
  }
  
  /*************************************************
  * Name:        poly_pointwise_invmontgomery
  *
  * Description: Pointwise multiplication of polynomials in NTT domain
  *              representation and multiplication of resulting polynomial
  *              with 2^{-32}. Output coefficients are less than 2*Q if input
  *              coefficient are less than 22*Q.
  *
  * Arguments:   - poly *c: pointer to output polynomial
  *              - const poly *a: pointer to first input polynomial
  *              - const poly *b: pointer to second input polynomial
  **************************************************/
  void poly_pointwise_invmontgomery(poly *c, const poly *a, const poly *b) {
      for (size_t i = 0; i < N; ++i) {
          c->coeffs[i] = montgomery_reduce((uint64_t)a->coeffs[i] * b->coeffs[i]);
      }
  
  }
  
  /*************************************************
  * Name:        poly_power2round
  *
  * Description: For all coefficients c of the input polynomial,
  *              compute c0, c1 such that c mod Q = c1*2^D + c0
  *              with -2^{D-1} < c0 <= 2^{D-1}. Assumes coefficients to be
  *              standard representatives.
  *
  * Arguments:   - poly *a1: pointer to output polynomial with coefficients c1
  *              - poly *a0: pointer to output polynomial with coefficients Q + a0
  *              - const poly *v: pointer to input polynomial
  **************************************************/
  void poly_power2round(poly *a1, poly *a0, const poly *a) {
      for (size_t i = 0; i < N; ++i) {
          a1->coeffs[i] = power2round(a->coeffs[i], &a0->coeffs[i]);
      }
  }
  
  /*************************************************
  * Name:        poly_decompose
  *
  * Description: For all coefficients c of the input polynomial,
  *              compute high and low bits c0, c1 such c mod Q = c1*ALPHA + c0
  *              with -ALPHA/2 < c0 <= ALPHA/2 except c1 = (Q-1)/ALPHA where we
  *              set c1 = 0 and -ALPHA/2 <= c0 = c mod Q - Q < 0.
  *              Assumes coefficients to be standard representatives.
  *
  * Arguments:   - poly *a1: pointer to output polynomial with coefficients c1
  *              - poly *a0: pointer to output polynomial with coefficients Q + a0
  *              - const poly *c: pointer to input polynomial
  **************************************************/
  void poly_decompose(poly *a1, poly *a0, const poly *a) {
      for (size_t i = 0; i < N; ++i) {
          a1->coeffs[i] = decompose(a->coeffs[i], &a0->coeffs[i]);
      }
  }
  
  /*************************************************
  * Name:        poly_make_hint
  *
  * Description: Compute hint polynomial. The coefficients of which indicate
  *              whether the low bits of the corresponding coefficient of
  *              the input polynomial overflow into the high bits.
  *
  * Arguments:   - poly *h: pointer to output hint polynomial
  *              - const poly *a0: pointer to low part of input polynomial
  *              - const poly *a1: pointer to high part of input polynomial
  *
  * Returns number of 1 bits.
  **************************************************/
  uint32_t poly_make_hint(poly *h, const poly *a0, const poly *a1) {
      uint32_t s = 0;
      for (size_t i = 0; i < N; ++i) {
          h->coeffs[i] = make_hint(a0->coeffs[i], a1->coeffs[i]);
          s += h->coeffs[i];
      }
      return s;
  }
  
  /*************************************************
  * Name:        poly_use_hint
  *
  * Description: Use hint polynomial to correct the high bits of a polynomial.
  *
  * Arguments:   - poly *a: pointer to output polynomial with corrected high bits
  *              - const poly *b: pointer to input polynomial
  *              - const poly *h: pointer to input hint polynomial
  **************************************************/
  void poly_use_hint(poly *a, const poly *b, const poly *h) {
      for (size_t i = 0; i < N; ++i) {
          a->coeffs[i] = use_hint(b->coeffs[i], h->coeffs[i]);
      }
  }
  
  /*************************************************
  * Name:        poly_chknorm
  *
  * Description: Check infinity norm of polynomial against given bound.
  *              Assumes input coefficients to be standard representatives.
  *
  * Arguments:   - const poly *a: pointer to polynomial
  *              - uint32_t B: norm bound
  *
  * Returns 0 if norm is strictly smaller than B and 1 otherwise.
  **************************************************/
  int poly_chknorm(const poly *a, uint32_t B) {
      int32_t t;
      /* It is ok to leak which coefficient violates the bound since
         the probability for each coefficient is independent of secret
         data but we must not leak the sign of the centralized representative. */
      for (size_t i = 0; i < N; ++i) {
          /* Absolute value of centralized representative */
          t = (int32_t)((Q - 1) / 2 - a->coeffs[i]);
          t ^= (t >> 31);
          t = (Q - 1) / 2 - t;
  
          if ((uint32_t)t >= B) {
              return 1;
          }
      }
      return 0;
  }
  
  /*************************************************
  * Name:        rej_uniform
  *
  * Description: Sample uniformly random coefficients in [0, Q-1] by
  *              performing rejection sampling using array of random bytes.
  *
  * Arguments:   - uint32_t *a: pointer to output array (allocated)
  *              - size_t len: number of coefficients to be sampled
  *              - const uint8_t *buf: array of random bytes
  *              - size_t buflen: length of array of random bytes
  *
  * Returns number of sampled coefficients. Can be smaller than len if not enough
  * random bytes were given.
  **************************************************/
  static size_t rej_uniform(
      uint32_t *a,
      size_t len,
      const uint8_t *buf,
      size_t buflen) {
      size_t ctr, pos;
      uint32_t t;
  
      ctr = pos = 0;
      while (ctr < len && pos + 3 <= buflen) {
          t  = buf[pos++];
          t |= (uint32_t)buf[pos++] << 8;
          t |= (uint32_t)buf[pos++] << 16;
          t &= 0x7FFFFF;
  
          if (t < Q) {
              a[ctr++] = t;
          }
      }
  
      return ctr;
  }
  
  /*************************************************
  * Name:        poly_uniform
  *
  * Description: Sample polynomial with uniformly random coefficients
  *              in [0,Q-1] by performing rejection sampling using the
  *              output stream from SHAKE256(seed|nonce).
  *
  * Arguments:   - poly *a: pointer to output polynomial
  *              - const uint8_t seed[]: byte array with seed of length
  *                                            SEEDBYTES
  *              - uint16_t nonce: 2-byte nonce
  **************************************************/
  #define POLY_UNIFORM_NBLOCKS ((769 + STREAM128_BLOCKBYTES) / STREAM128_BLOCKBYTES)
  #define POLY_UNIFORM_BUFLEN (POLY_UNIFORM_NBLOCKS * STREAM128_BLOCKBYTES)
  void poly_uniform(poly *a,
          const uint8_t seed[SEEDBYTES],
          uint16_t nonce) {
      size_t ctr, off;
      size_t buflen = POLY_UNIFORM_BUFLEN;
      uint8_t buf[POLY_UNIFORM_BUFLEN + 2];
      stream128_state state;
  
      stream128_init(&state, seed, nonce);
      stream128_squeezeblocks(buf, POLY_UNIFORM_NBLOCKS, &state);
  
      ctr = rej_uniform(a->coeffs, N, buf, buflen);
  
      while (ctr < N) {
          off = buflen % 3;
          for (size_t i = 0; i < off; ++i) {
              buf[i] = buf[buflen - off + i];
          }
  
          buflen = STREAM128_BLOCKBYTES + off;
          stream128_squeezeblocks(buf + off, 1, &state);
          ctr += rej_uniform(a->coeffs + ctr, N - ctr, buf, buflen);
      }
      stream128_ctx_release(&state);
  }
  
  /*************************************************
  * Name:        rej_eta
  *
  * Description: Sample uniformly random coefficients in [-ETA, ETA] by
  *              performing rejection sampling using array of random bytes.
  *
  * Arguments:   - uint32_t *a: pointer to output array (allocated)
  *              - size_t len: number of coefficients to be sampled
  *              - const uint8_t *buf: array of random bytes
  *              - size_t buflen: length of array of random bytes
  *
  * Returns number of sampled coefficients. Can be smaller than len if not enough
  * random bytes were given.
  **************************************************/
  static size_t rej_eta(
      uint32_t *a,
      size_t len,
      const uint8_t *buf,
      size_t buflen) {
      size_t ctr, pos;
      uint32_t t0, t1;
  
      ctr = pos = 0;
      while (ctr < len && pos < buflen) {
          t0 = buf[pos] & 0x07;
          t1 = buf[pos++] >> 5;
  
          if (t0 <= 2 * ETA) {
              a[ctr++] = Q + ETA - t0;
          }
          if (t1 <= 2 * ETA && ctr < len) {
              a[ctr++] = Q + ETA - t1;
          }
      }
  
      return ctr;
  }
  
  /*************************************************
  * Name:        poly_uniform_eta
  *
  * Description: Sample polynomial with uniformly random coefficients
  *              in [-ETA,ETA] by performing rejection sampling using the
  *              output stream from SHAKE256(seed|nonce).
  *
  * Arguments:   - poly *a: pointer to output polynomial
  *              - const uint8_t seed[]: byte array with seed of length
  *                                            SEEDBYTES
  *              - uint16_t nonce: 2-byte nonce
  **************************************************/
  #define POLY_UNIFORM_ETA_NBLOCKS (((N / 2 * (1u << SETABITS)) / (2 * ETA + 1) + STREAM128_BLOCKBYTES) / STREAM128_BLOCKBYTES)
  #define POLY_UNIFORM_ETA_BUFLEN (POLY_UNIFORM_ETA_NBLOCKS*STREAM128_BLOCKBYTES)
  void poly_uniform_eta(poly *a,
          const uint8_t *seed,
          uint16_t nonce) {
      size_t ctr;
      uint8_t buf[POLY_UNIFORM_ETA_BUFLEN];
      stream128_state state;
  
      stream128_init(&state, seed, nonce);
      stream128_squeezeblocks(buf, POLY_UNIFORM_ETA_NBLOCKS, &state);
  
      ctr = rej_eta(a->coeffs, N, buf, POLY_UNIFORM_ETA_BUFLEN);
  
      while (ctr < N) {
          stream128_squeezeblocks(buf, 1, &state);
          ctr += rej_eta(a->coeffs + ctr, N - ctr, buf, STREAM128_BLOCKBYTES);
      }
      stream128_ctx_release(&state);
  }
  
  /*************************************************
  * Name:        rej_gamma1m1
  *
  * Description: Sample uniformly random coefficients
  *              in [-(GAMMA1 - 1), GAMMA1 - 1] by performing rejection sampling
  *              using array of random bytes.
  *
  * Arguments:   - uint32_t *a: pointer to output array (allocated)
  *              - size_t len: number of coefficients to be sampled
  *              - const uint8_t *buf: array of random bytes
  *              - size_t buflen: length of array of random bytes
  *
  * Returns number of sampled coefficients. Can be smaller than len if not enough
  * random bytes were given.
  **************************************************/
  static size_t rej_gamma1m1(
      uint32_t *a,
      size_t len,
      const uint8_t *buf,
      size_t buflen) {
  
      size_t ctr, pos;
      uint32_t t0, t1;
  
      ctr = pos = 0;
      while (ctr < len && pos + 5 <= buflen) {
          t0  = buf[pos];
          t0 |= (uint32_t)buf[pos + 1] << 8;
          t0 |= (uint32_t)buf[pos + 2] << 16;
          t0 &= 0xFFFFF;
  
          t1 = buf[pos + 2] >> 4;
          t1 |= (uint32_t)buf[pos + 3] << 4;
          t1 |= (uint32_t)buf[pos + 4] << 12;
  
          pos += 5;
  
          if (t0 <= 2 * GAMMA1 - 2) {
              a[ctr++] = Q + GAMMA1 - 1 - t0;
          }
          if (t1 <= 2 * GAMMA1 - 2 && ctr < len) {
              a[ctr++] = Q + GAMMA1 - 1 - t1;
          }
      }
  
      return ctr;
  }
  
  /*************************************************
  * Name:        poly_uniform_gamma1m1
  *
  * Description: Sample polynomial with uniformly random coefficients
  *              in [-(GAMMA1 - 1), GAMMA1 - 1] by performing rejection
  *              sampling on output stream of SHAKE256(seed|nonce).
  *
  * Arguments:   - poly *a: pointer to output polynomial
  *              - const uint8_t seed[]: byte array with seed of length
  *                                            CRHBYTES
  *              - uint16_t nonce: 16-bit nonce
  **************************************************/
  #define POLY_UNIFORM_GAMMA1M1_NBLOCKS ((641 + STREAM256_BLOCKBYTES) / STREAM256_BLOCKBYTES)
  #define POLY_UNIFORM_GAMMA1M1_BUFLEN (POLY_UNIFORM_GAMMA1M1_NBLOCKS * STREAM256_BLOCKBYTES)
  void poly_uniform_gamma1m1(poly *a,
          const uint8_t seed[CRHBYTES],
          uint16_t nonce) {
      size_t ctr, off;
      size_t buflen = POLY_UNIFORM_GAMMA1M1_BUFLEN;
      uint8_t buf[POLY_UNIFORM_GAMMA1M1_BUFLEN + 4];
      stream256_state state;
  
      stream256_init(&state, seed, nonce);
      stream256_squeezeblocks(buf, POLY_UNIFORM_GAMMA1M1_NBLOCKS, &state);
  
      ctr = rej_gamma1m1(a->coeffs, N, buf, buflen);
  
      while (ctr < N) {
          off = buflen % 5;
          for (size_t i = 0; i < off; ++i) {
              buf[i] = buf[buflen - off + i];
          }
  
          buflen = STREAM256_BLOCKBYTES + off;
          stream256_squeezeblocks(buf + off, 1, &state);
          ctr += rej_gamma1m1(a->coeffs + ctr, N - ctr, buf, buflen);
      }
      stream256_ctx_release(&state);
  }
  
  /*************************************************
  * Name:        polyeta_pack
  *
  * Description: Bit-pack polynomial with coefficients in [-ETA,ETA].
  *              Input coefficients are assumed to lie in [Q-ETA,Q+ETA].
  *
  * Arguments:   - uint8_t *r: pointer to output byte array with at least
  *                                  POLETA_SIZE_PACKED bytes
  *              - const poly *a: pointer to input polynomial
  **************************************************/
  void polyeta_pack(uint8_t *r, const poly *a) {
      uint8_t t[8];
  
      for (size_t i = 0; i < N / 8; ++i) {
          t[0] = (uint8_t)(Q + ETA - a->coeffs[8 * i + 0]);
          t[1] = (uint8_t)(Q + ETA - a->coeffs[8 * i + 1]);
          t[2] = (uint8_t)(Q + ETA - a->coeffs[8 * i + 2]);
          t[3] = (uint8_t)(Q + ETA - a->coeffs[8 * i + 3]);
          t[4] = (uint8_t)(Q + ETA - a->coeffs[8 * i + 4]);
          t[5] = (uint8_t)(Q + ETA - a->coeffs[8 * i + 5]);
          t[6] = (uint8_t)(Q + ETA - a->coeffs[8 * i + 6]);
          t[7] = (uint8_t)(Q + ETA - a->coeffs[8 * i + 7]);
  
          r[3 * i + 0]  = (uint8_t)((t[0] >> 0) | (t[1] << 3) | (t[2] << 6));
          r[3 * i + 1]  = (uint8_t)((t[2] >> 2) | (t[3] << 1) | (t[4] << 4) | (t[5] << 7));
          r[3 * i + 2]  = (uint8_t)((t[5] >> 1) | (t[6] << 2) | (t[7] << 5));
      }
  }
  
  /*************************************************
  * Name:        polyeta_unpack
  *
  * Description: Unpack polynomial with coefficients in [-ETA,ETA].
  *              Output coefficients lie in [Q-ETA,Q+ETA].
  *
  * Arguments:   - poly *r: pointer to output polynomial
  *              - const uint8_t *a: byte array with bit-packed polynomial
  **************************************************/
  void polyeta_unpack(poly *r, const uint8_t *a) {
      for (size_t i = 0; i < N / 8; ++i) {
          r->coeffs[8 * i + 0] = a[3 * i + 0] & 0x07;
          r->coeffs[8 * i + 1] = (a[3 * i + 0] >> 3) & 0x07;
          r->coeffs[8 * i + 2] = (uint32_t)((a[3 * i + 0] >> 6) | (a[3 * i + 1] << 2)) & 0x07;
          r->coeffs[8 * i + 3] = (a[3 * i + 1] >> 1) & 0x07;
          r->coeffs[8 * i + 4] = (a[3 * i + 1] >> 4) & 0x07;
          r->coeffs[8 * i + 5] = (uint32_t)((a[3 * i + 1] >> 7) | (a[3 * i + 2] << 1)) & 0x07;
          r->coeffs[8 * i + 6] = (a[3 * i + 2] >> 2) & 0x07;
          r->coeffs[8 * i + 7] = (a[3 * i + 2] >> 5) & 0x07;
  
          r->coeffs[8 * i + 0] = Q + ETA - r->coeffs[8 * i + 0];
          r->coeffs[8 * i + 1] = Q + ETA - r->coeffs[8 * i + 1];
          r->coeffs[8 * i + 2] = Q + ETA - r->coeffs[8 * i + 2];
          r->coeffs[8 * i + 3] = Q + ETA - r->coeffs[8 * i + 3];
          r->coeffs[8 * i + 4] = Q + ETA - r->coeffs[8 * i + 4];
          r->coeffs[8 * i + 5] = Q + ETA - r->coeffs[8 * i + 5];
          r->coeffs[8 * i + 6] = Q + ETA - r->coeffs[8 * i + 6];
          r->coeffs[8 * i + 7] = Q + ETA - r->coeffs[8 * i + 7];
      }
  
  }
  
  /*************************************************
  * Name:        polyt1_pack
  *
  * Description: Bit-pack polynomial t1 with coefficients fitting in 9 bits.
  *              Input coefficients are assumed to be standard representatives.
  *
  * Arguments:   - uint8_t *r: pointer to output byte array with at least
  *                                  POLT1_SIZE_PACKED bytes
  *              - const poly *a: pointer to input polynomial
  **************************************************/
  void polyt1_pack(uint8_t *r, const poly *a) {
  
      for (size_t i = 0; i < N / 8; ++i) {
          r[9 * i + 0] = (uint8_t)((a->coeffs[8 * i + 0] >> 0));
          r[9 * i + 1] = (uint8_t)((a->coeffs[8 * i + 0] >> 8) | (a->coeffs[8 * i + 1] << 1));
          r[9 * i + 2] = (uint8_t)((a->coeffs[8 * i + 1] >> 7) | (a->coeffs[8 * i + 2] << 2));
          r[9 * i + 3] = (uint8_t)((a->coeffs[8 * i + 2] >> 6) | (a->coeffs[8 * i + 3] << 3));
          r[9 * i + 4] = (uint8_t)((a->coeffs[8 * i + 3] >> 5) | (a->coeffs[8 * i + 4] << 4));
          r[9 * i + 5] = (uint8_t)((a->coeffs[8 * i + 4] >> 4) | (a->coeffs[8 * i + 5] << 5));
          r[9 * i + 6] = (uint8_t)((a->coeffs[8 * i + 5] >> 3) | (a->coeffs[8 * i + 6] << 6));
          r[9 * i + 7] = (uint8_t)((a->coeffs[8 * i + 6] >> 2) | (a->coeffs[8 * i + 7] << 7));
          r[9 * i + 8] = (uint8_t)((a->coeffs[8 * i + 7] >> 1));
      }
  
  }
  
  /*************************************************
  * Name:        polyt1_unpack
  *
  * Description: Unpack polynomial t1 with 9-bit coefficients.
  *              Output coefficients are standard representatives.
  *
  * Arguments:   - poly *r: pointer to output polynomial
  *              - const uint8_t *a: byte array with bit-packed polynomial
  **************************************************/
  void polyt1_unpack(poly *r, const uint8_t *a) {
      for (size_t i = 0; i < N / 8; ++i) {
          r->coeffs[8 * i + 0] = ((a[9 * i + 0]     ) | ((uint32_t) a[9 * i + 1] << 8)) & 0x1FF;
          r->coeffs[8 * i + 1] = ((a[9 * i + 1] >> 1) | ((uint32_t) a[9 * i + 2] << 7)) & 0x1FF;
          r->coeffs[8 * i + 2] = ((a[9 * i + 2] >> 2) | ((uint32_t) a[9 * i + 3] << 6)) & 0x1FF;
          r->coeffs[8 * i + 3] = ((a[9 * i + 3] >> 3) | ((uint32_t) a[9 * i + 4] << 5)) & 0x1FF;
          r->coeffs[8 * i + 4] = ((a[9 * i + 4] >> 4) | ((uint32_t) a[9 * i + 5] << 4)) & 0x1FF;
          r->coeffs[8 * i + 5] = ((a[9 * i + 5] >> 5) | ((uint32_t) a[9 * i + 6] << 3)) & 0x1FF;
          r->coeffs[8 * i + 6] = ((a[9 * i + 6] >> 6) | ((uint32_t) a[9 * i + 7] << 2)) & 0x1FF;
          r->coeffs[8 * i + 7] = ((a[9 * i + 7] >> 7) | ((uint32_t) a[9 * i + 8] << 1)) & 0x1FF;
      }
  }
  
  /*************************************************
  * Name:        polyt0_pack
  *
  * Description: Bit-pack polynomial t0 with coefficients in ]-2^{D-1}, 2^{D-1}].
  *              Input coefficients are assumed to lie in ]Q-2^{D-1}, Q+2^{D-1}].
  *
  * Arguments:   - uint8_t *r: pointer to output byte array with at least
  *                                  POLT0_SIZE_PACKED bytes
  *              - const poly *a: pointer to input polynomial
  **************************************************/
  void polyt0_pack(uint8_t *r, const poly *a) {
      uint32_t t[4];
  
      for (size_t i = 0; i < N / 4; ++i) {
          t[0] = Q + (1u << (D - 1)) - a->coeffs[4 * i + 0];
          t[1] = Q + (1u << (D - 1)) - a->coeffs[4 * i + 1];
          t[2] = Q + (1u << (D - 1)) - a->coeffs[4 * i + 2];
          t[3] = Q + (1u << (D - 1)) - a->coeffs[4 * i + 3];
  
          r[7 * i + 0] =  (uint8_t)(t[0]);
          r[7 * i + 1] =  (uint8_t)(t[0] >> 8);
          r[7 * i + 1] |= (uint8_t)(t[1] << 6);
          r[7 * i + 2] =  (uint8_t)(t[1] >> 2);
          r[7 * i + 3] =  (uint8_t)(t[1] >> 10);
          r[7 * i + 3] |= (uint8_t)(t[2] << 4);
          r[7 * i + 4] =  (uint8_t)(t[2] >> 4);
          r[7 * i + 5] =  (uint8_t)(t[2] >> 12);
          r[7 * i + 5] |= (uint8_t)(t[3] << 2);
          r[7 * i + 6] =  (uint8_t)(t[3] >> 6);
      }
  }
  
  /*************************************************
  * Name:        polyt0_unpack
  *
  * Description: Unpack polynomial t0 with coefficients in ]-2^{D-1}, 2^{D-1}].
  *              Output coefficients lie in ]Q-2^{D-1},Q+2^{D-1}].
  *
  * Arguments:   - poly *r: pointer to output polynomial
  *              - const uint8_t *a: byte array with bit-packed polynomial
  **************************************************/
  void polyt0_unpack(poly *r, const uint8_t *a) {
  
      for (size_t i = 0; i < N / 4; ++i) {
          r->coeffs[4 * i + 0] = a[7 * i + 0];
          r->coeffs[4 * i + 0] |= (uint32_t) (a[7 * i + 1] & 0x3F) << 8;
  
          r->coeffs[4 * i + 1] = a[7 * i + 1] >> 6;
          r->coeffs[4 * i + 1] |= (uint32_t) a[7 * i + 2] << 2;
          r->coeffs[4 * i + 1] |= (uint32_t) (a[7 * i + 3] & 0x0F) << 10;
  
          r->coeffs[4 * i + 2] = a[7 * i + 3] >> 4;
          r->coeffs[4 * i + 2] |= (uint32_t) a[7 * i + 4] << 4;
          r->coeffs[4 * i + 2] |= (uint32_t) (a[7 * i + 5] & 0x03) << 12;
  
          r->coeffs[4 * i + 3] = a[7 * i + 5] >> 2;
          r->coeffs[4 * i + 3] |= (uint32_t) a[7 * i + 6] << 6;
  
          r->coeffs[4 * i + 0] = Q + (1U << (D - 1)) - r->coeffs[4 * i + 0];
          r->coeffs[4 * i + 1] = Q + (1U << (D - 1)) - r->coeffs[4 * i + 1];
          r->coeffs[4 * i + 2] = Q + (1U << (D - 1)) - r->coeffs[4 * i + 2];
          r->coeffs[4 * i + 3] = Q + (1U << (D - 1)) - r->coeffs[4 * i + 3];
      }
  }
  
  /*************************************************
  * Name:        polyz_pack
  *
  * Description: Bit-pack polynomial z with coefficients
  *              in [-(GAMMA1 - 1), GAMMA1 - 1].
  *              Input coefficients are assumed to be standard representatives.
  *
  * Arguments:   - uint8_t *r: pointer to output byte array with at least
  *                                  POLZ_SIZE_PACKED bytes
  *              - const poly *a: pointer to input polynomial
  **************************************************/
  void polyz_pack(uint8_t *r, const poly *a) {
      uint32_t t[2];
  
      for (size_t i = 0; i < N / 2; ++i) {
          /* Map to {0,...,2*GAMMA1 - 2} */
          t[0] = GAMMA1 - 1 - a->coeffs[2 * i + 0];
          t[0] += ((int32_t)t[0] >> 31) & Q;
          t[1] = GAMMA1 - 1 - a->coeffs[2 * i + 1];
          t[1] += ((int32_t)t[1] >> 31) & Q;
  
          r[5 * i + 0]  = (uint8_t)t[0];
          r[5 * i + 1]  = (uint8_t)(t[0] >>  8);
          r[5 * i + 2]  = (uint8_t)(t[0] >> 16);
          r[5 * i + 2] |= (uint8_t)(t[1] <<  4);
          r[5 * i + 3]  = (uint8_t)(t[1] >>  4);
          r[5 * i + 4]  = (uint8_t)(t[1] >> 12);
      }
  }
  
  /*************************************************
  * Name:        polyz_unpack
  *
  * Description: Unpack polynomial z with coefficients
  *              in [-(GAMMA1 - 1), GAMMA1 - 1].
  *              Output coefficients are standard representatives.
  *
  * Arguments:   - poly *r: pointer to output polynomial
  *              - const uint8_t *a: byte array with bit-packed polynomial
  **************************************************/
  void polyz_unpack(poly *r, const uint8_t *a) {
      for (size_t i = 0; i < N / 2; ++i) {
          r->coeffs[2 * i + 0]  = a[5 * i + 0];
          r->coeffs[2 * i + 0] |= (uint32_t) a[5 * i + 1] << 8;
          r->coeffs[2 * i + 0] |= (uint32_t) (a[5 * i + 2] & 0x0F) << 16;
  
          r->coeffs[2 * i + 1]  = a[5 * i + 2] >> 4;
          r->coeffs[2 * i + 1] |= (uint32_t) a[5 * i + 3] << 4;
          r->coeffs[2 * i + 1] |= (uint32_t) a[5 * i + 4] << 12;
  
          r->coeffs[2 * i + 0]  = GAMMA1 - 1 - r->coeffs[2 * i + 0];
          r->coeffs[2 * i + 0] += ((int32_t)r->coeffs[2 * i + 0] >> 31) & Q;
          r->coeffs[2 * i + 1]  = GAMMA1 - 1 - r->coeffs[2 * i + 1];
          r->coeffs[2 * i + 1] += ((int32_t)r->coeffs[2 * i + 1] >> 31) & Q;
      }
  }
  
  /*************************************************
  * Name:        polyw1_pack
  *
  * Description: Bit-pack polynomial w1 with coefficients in [0, 15].
  *              Input coefficients are assumed to be standard representatives.
  *
  * Arguments:   - uint8_t *r: pointer to output byte array with at least
  *                                  POLW1_SIZE_PACKED bytes
  *              - const poly *a: pointer to input polynomial
  **************************************************/
  void polyw1_pack(uint8_t *r, const poly *a) {
      for (size_t i = 0; i < N / 2; ++i) {
          r[i] = (uint8_t)(a->coeffs[2 * i + 0] | a->coeffs[2 * i + 1] << 4);
      }
  
  }
  