/*

* Montgomery Reduction

* (C) 1999-2011 Jack Lloyd

*     2006 Luca Piccarreta

*     2016 Matthias Gierlings

*

* Botan is released under the Simplified BSD License (see license.txt)

*/

#include <botan/internal/mp_core.h>

#include <botan/assert.h>

#include <botan/exceptn.h>

#include <botan/mem_ops.h>

#include <botan/internal/ct_utils.h>

namespace Botan {

/*

* Montgomery reduction - product scanning form

*

* Algorithm 5 from "Energy-Efficient Software Implementation of Long

* Integer Modular Arithmetic"

* (https://www.iacr.org/archive/ches2005/006.pdf)

*

* See also

*

* https://eprint.iacr.org/2013/882.pdf

* https://www.microsoft.com/en-us/research/wp-content/uploads/1996/01/j37acmon.pdf

*/

void bigint_monty_redc_generic(

   word r[], const word z[], size_t z_size, const word p[], size_t p_size, word p_dash, word ws[]) {

   BOTAN_ARG_CHECK(z_size >= 2 * p_size && p_size > 0, "Invalid sizes for bigint_monty_redc_generic");

   word3<word> accum;

   accum.add(z[0]);

   ws[0] = accum.monty_step(p[0], p_dash);

   for(size_t i = 1; i != p_size; ++i) {

      for(size_t j = 0; j < i; ++j) {

         accum.mul(ws[j], p[i - j]);

      }

      accum.add(z[i]);

      ws[i] = accum.monty_step(p[0], p_dash);

   }

   for(size_t i = 0; i != p_size - 1; ++i) {

      for(size_t j = i + 1; j != p_size; ++j) {

         accum.mul(ws[j], p[p_size + i - j]);

      }

      accum.add(z[p_size + i]);

      ws[i] = accum.extract();

   }

   accum.add(z[2 * p_size - 1]);

   ws[p_size - 1] = accum.extract();

   // w1 is the final part, which is not stored in the workspace

   const word w1 = accum.extract();

   /*

   * The result might need to be reduced mod p. To avoid a timing

   * channel, always perform the subtraction. If in the compution

   * of x - p a borrow is required then x was already < p.

   *

   * x starts at ws[0] and is p_size bytes long plus a possible high

   * digit left over in w1.

   *

   * x - p starts at z[0] and is also p_size bytes long

   *

   * If borrow was set after the subtraction, then x was already less

   * than p and the subtraction was not needed. In that case overwrite

   * z[0:p_size] with the original x in ws[0:p_size].

   *

   * We only copy out p_size in the final step because we know

   * the Montgomery result is < P

   */

   bigint_monty_maybe_sub(p_size, r, w1, ws, p);

}

}  // namespace Botan