Precomputation will not necessarily be LIm-Lee precomputation.
[openssl.git] / crypto / ec / ec_mult.c
index d43bdc2..651de97 100644 (file)
@@ -1,4 +1,3 @@
-/* TODO */
 /* crypto/ec/ec_mult.c */
 /* ====================================================================
  * Copyright (c) 1998-2001 The OpenSSL Project.  All rights reserved.
  *
  */
 
+#include <openssl/err.h>
+
 #include "ec_lcl.h"
+
+
+/* TODO: width-m NAFs */
+
+/* TODO: optional precomputation of multiples of the generator */
+
+
+#define EC_window_bits_for_scalar_size(b) \
+               ((b) >= 2000 ? 6 : \
+                (b) >=  800 ? 5 : \
+                (b) >=  300 ? 4 : \
+                (b) >=   70 ? 3 : \
+                (b) >=   20 ? 2 : \
+                 1)
+/* For window size 'w' (w >= 2), we compute the odd multiples
+ *      1*P .. (2^w-1)*P.
+ * This accounts for  2^(w-1)  point additions (neglecting constants),
+ * each of which requires 16 field multiplications (4 squarings
+ * and 12 general multiplications) in the case of curves defined
+ * over GF(p), which are the only curves we have so far.
+ *
+ * Converting these precomputed points into affine form takes
+ * three field multiplications for inverting Z and one squaring
+ * and three multiplications for adjusting X and Y, i.e.
+ * 7 multiplications in total (1 squaring and 6 general multiplications),
+ * again except for constants.
+ *
+ * The average number of windows for a 'b' bit scalar is roughly
+ *          b/(w+1).
+ * Each of these windows (except possibly for the first one, but
+ * we are ignoring constants anyway) requires one point addition.
+ * As the precomputed table stores points in affine form, these
+ * additions take only 11 field multiplications each (3 squarings
+ * and 8 general multiplications).
+ *
+ * So the total workload, except for constants, is
+ *
+ *        2^(w-1)*[5 squarings + 18 multiplications]
+ *      + (b/(w+1))*[3 squarings + 8 multiplications]
+ *
+ * If we assume that 10 squarings are as costly as 9 multiplications,
+ * our task is to find the 'w' that, given 'b', minimizes
+ *
+ *        2^(w-1)*(5*9 + 18*10) + (b/(w+1))*(3*9 + 8*10)
+ *      = 2^(w-1)*225 +           (b/(w+1))*107.
+ *
+ * Thus optimal window sizes should be roughly as follows:
+ *
+ *    w >= 6  if         b >= 1414
+ *     w = 5  if 1413 >= b >=  505
+ *     w = 4  if  504 >= b >=  169
+ *     w = 3  if  168 >= b >=   51
+ *     w = 2  if   50 >= b >=   13
+ *     w = 1  if   12 >= b
+ *
+ * If we assume instead that squarings are exactly as costly as
+ * multiplications, we have to minimize
+ *      2^(w-1)*23 + (b/(w+1))*11.
+ *
+ * This gives us the following (nearly unchanged) table of optimal
+ * windows sizes:
+ *
+ *    w >= 6  if         b >= 1406
+ *     w = 5  if 1405 >= b >=  502
+ *     w = 4  if  501 >= b >=  168
+ *     w = 3  if  167 >= b >=   51
+ *     w = 2  if   50 >= b >=   13
+ *     w = 1  if   12 >= b
+ *
+ * Note that neither table tries to take into account memory usage
+ * (allocation overhead, code locality etc.).  Actual timings with
+ * NIST curves P-192, P-224, and P-256 with scalars of 192, 224,
+ * and 256 bits, respectively, show that  w = 3  (instead of 4) is
+ * preferrable; timings with NIST curve P-384 and 384-bit scalars
+ * confirm that  w = 4  is optimal for this case; and timings with
+ * NIST curve P-521 and 521-bit scalars show that  w = 4  (instead
+ * of 5) is preferrable.  So we generously round up all the
+ * boundaries and use the following table:
+ *
+ *    w >= 6  if         b >= 2000
+ *     w = 5  if 1999 >= b >=  800
+ *     w = 4  if  799 >= b >=  300
+ *     w = 3  if  299 >= b >=   70
+ *     w = 2  if   69 >= b >=   20
+ *     w = 1  if   19 >= b
+ */
+
+
+
+/* Compute
+ *      \sum scalars[i]*points[i]
+ * where
+ *      scalar*generator
+ * is included in the addition if scalar != NULL
+ */
+int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+       size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
+       {
+       BN_CTX *new_ctx = NULL;
+       EC_POINT *generator = NULL;
+       EC_POINT *tmp = NULL;
+       size_t totalnum;
+       size_t i, j;
+       int k, t;
+       int r_is_at_infinity = 1;
+       size_t max_bits = 0;
+       size_t *wsize = NULL; /* individual window sizes */
+       unsigned long *wbits = NULL; /* individual window contents */
+       int *wpos = NULL; /* position of bottom bit of current individual windows
+                          * (wpos[i] is valid if wbits[i] != 0) */
+       size_t num_val;
+       EC_POINT **val = NULL; /* precomputation */
+       EC_POINT **v;
+       EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */
+       int ret = 0;
+       
+       if (scalar != NULL)
+               {
+               generator = EC_GROUP_get0_generator(group);
+               if (generator == NULL)
+                       {
+                       ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
+                       return 0;
+                       }
+               }
+       
+       for (i = 0; i < num; i++)
+               {
+               if (group->meth != points[i]->meth)
+                       {
+                       ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
+                       return 0;
+                       }
+               }
+
+       totalnum = num + (scalar != NULL);
+
+       wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]);
+       wbits = OPENSSL_malloc(totalnum * sizeof wbits[0]);
+       wpos = OPENSSL_malloc(totalnum * sizeof wpos[0]);
+       if (wsize == NULL || wbits == NULL || wpos == NULL) goto err;
+
+       /* num_val := total number of points to precompute */
+       num_val = 0;
+       for (i = 0; i < totalnum; i++)
+               {
+               size_t bits;
+
+               bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar);
+               wsize[i] = EC_window_bits_for_scalar_size(bits);
+               num_val += 1u << (wsize[i] - 1);
+               if (bits > max_bits)
+                       max_bits = bits;
+               wbits[i] = 0;
+               wpos[i] = 0;
+               }
+
+       /* all precomputed points go into a single array 'val',
+        * 'val_sub[i]' is a pointer to the subarray for the i-th point */
+       val = OPENSSL_malloc((num_val + 1) * sizeof val[0]);
+       if (val == NULL) goto err;
+       val[num_val] = NULL; /* pivot element */
+
+       val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]);
+       if (val_sub == NULL) goto err;
+
+       /* allocate points for precomputation */
+       v = val;
+       for (i = 0; i < totalnum; i++)
+               {
+               val_sub[i] = v;
+               for (j = 0; j < (1u << (wsize[i] - 1)); j++)
+                       {
+                       *v = EC_POINT_new(group);
+                       if (*v == NULL) goto err;
+                       v++;
+                       }
+               }
+       if (!(v == val + num_val))
+               {
+               ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR);
+               goto err;
+               }
+
+       if (ctx == NULL)
+               {
+               ctx = new_ctx = BN_CTX_new();
+               if (ctx == NULL)
+                       goto err;
+               }
+       
+       tmp = EC_POINT_new(group);
+       if (tmp == NULL) goto err;
+
+       /* prepare precomputed values:
+        *    val_sub[i][0] :=     points[i]
+        *    val_sub[i][1] := 3 * points[i]
+        *    val_sub[i][2] := 5 * points[i]
+        *    ...
+        */
+       for (i = 0; i < totalnum; i++)
+               {
+               if (i < num)
+                       {
+                       if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err;
+                       if (scalars[i]->neg)
+                               {
+                               if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err;
+                               }
+                       }
+               else
+                       {
+                       if (!EC_POINT_copy(val_sub[i][0], generator)) goto err;
+                       if (scalar->neg)
+                               {
+                               if (!EC_POINT_invert(group, val_sub[i][0], ctx)) goto err;
+                               }
+                       }
+
+               if (wsize[i] > 1)
+                       {
+                       if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err;
+                       for (j = 1; j < (1u << (wsize[i] - 1)); j++)
+                               {
+                               if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err;
+                               }
+                       }
+               }
+
+#if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */
+       if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err;
+#endif
+
+       r_is_at_infinity = 1;
+
+       for (k = max_bits - 1; k >= 0; k--)
+               {
+               if (!r_is_at_infinity)
+                       {
+                       if (!EC_POINT_dbl(group, r, r, ctx)) goto err;
+                       }
+               
+               for (i = 0; i < totalnum; i++)
+                       {
+                       if (wbits[i] == 0)
+                               {
+                               const BIGNUM *s;
+
+                               s = i < num ? scalars[i] : scalar;
+
+                               if (BN_is_bit_set(s, k))
+                                       {
+                                       /* look at bits  k - wsize[i] + 1 .. k  for this window */
+                                       t = k - wsize[i] + 1;
+                                       while (!BN_is_bit_set(s, t)) /* BN_is_bit_set is false for t < 0 */
+                                               t++;
+                                       wpos[i] = t;
+                                       wbits[i] = 1;
+                                       for (t = k - 1; t >= wpos[i]; t--)
+                                               {
+                                               wbits[i] <<= 1;
+                                               if (BN_is_bit_set(s, t))
+                                                       wbits[i]++;
+                                               }
+                                       /* now wbits[i] is the odd bit pattern at bits wpos[i] .. k */
+                                       }
+                               }
+                       
+                       if ((wbits[i] != 0) && (wpos[i] == k))
+                               {
+                               if (r_is_at_infinity)
+                                       {
+                                       if (!EC_POINT_copy(r, val_sub[i][wbits[i] >> 1])) goto err;
+                                       r_is_at_infinity = 0;
+                                       }
+                               else
+                                       {
+                                       if (!EC_POINT_add(group, r, r, val_sub[i][wbits[i] >> 1], ctx)) goto err;
+                                       }
+                               wbits[i] = 0;
+                               }
+                       }
+               }
+
+       if (r_is_at_infinity)
+               if (!EC_POINT_set_to_infinity(group, r)) goto err;
+       
+       ret = 1;
+
+ err:
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       if (tmp != NULL)
+               EC_POINT_free(tmp);
+       if (wsize != NULL)
+               OPENSSL_free(wsize);
+       if (wbits != NULL)
+               OPENSSL_free(wbits);
+       if (wpos != NULL)
+               OPENSSL_free(wpos);
+       if (val != NULL)
+               {
+               for (v = val; *v != NULL; v++)
+                       EC_POINT_clear_free(*v);
+
+               OPENSSL_free(val);
+               }
+       if (val_sub != NULL)
+               {
+               OPENSSL_free(val_sub);
+               }
+       return ret;
+       }
+
+
+int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx)
+       {
+       const EC_POINT *points[1];
+       const BIGNUM *scalars[1];
+
+       points[0] = point;
+       scalars[0] = p_scalar;
+
+       return EC_POINTs_mul(group, r, g_scalar, (point != NULL && p_scalar != NULL), points, scalars, ctx);
+       }
+
+
+int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
+       {
+       const EC_POINT *generator;
+       BN_CTX *new_ctx = NULL;
+       BIGNUM *order;
+       int ret = 0;
+
+       generator = EC_GROUP_get0_generator(group);
+       if (generator == NULL)
+               {
+               ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNDEFINED_GENERATOR);
+               return 0;
+               }
+
+       if (ctx == NULL)
+               {
+               ctx = new_ctx = BN_CTX_new();
+               if (ctx == NULL)
+                       return 0;
+               }
+       
+       BN_CTX_start(ctx);
+       order = BN_CTX_get(ctx);
+       if (order == NULL) goto err;
+       
+       if (!EC_GROUP_get_order(group, order, ctx)) return 0;
+       if (BN_is_zero(order))
+               {
+               ECerr(EC_F_EC_GROUP_PRECOMPUTE_MULT, EC_R_UNKNOWN_ORDER);
+               goto err;
+               }
+
+       /* TODO */
+
+       ret = 1;
+       
+ err:
+       BN_CTX_end(ctx);
+       if (new_ctx != NULL)
+               BN_CTX_free(new_ctx);
+       return ret;
+       }