variable signing precompute table

Author: djb

src/ecmult_gen.h

@@ -10,20 +10,27 @@
 #include "scalar.h"
 #include "group.h"
 
+#ifndef ECMULT_GEN_PREC_BITS
+#define ECMULT_GEN_PREC_BITS 4/* 4 bits: 64kB table, fastest; 2 bits: 32kB table, ~75% speed */
+#endif
+#define ECMULT_GEN_PREC_B ECMULT_GEN_PREC_BITS
+#define ECMULT_GEN_PREC_G (1 << ECMULT_GEN_PREC_B)
+#define ECMULT_GEN_PREC_N (256 / ECMULT_GEN_PREC_B)
+
 typedef struct {
     /* For accelerating the computation of a*G:
      * To harden against timing attacks, use the following mechanism:
-     * * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
-     * * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
-     *   * U_i = U * 2^i (for i=0..62)
-     *   * U_i = U * (1-2^63) (for i=63)
-     *   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
-     * For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
-     * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
+     * * Break up the multiplicand into groups of PREC_B bits, called n_0, n_1, n_2, ..., n_(PREC_N-1).
+     * * Compute sum(n_i * (PREC_G)^i * G + U_i, i=0 ... PREC_N-1), where:
+     *   * U_i = U * 2^i, for i=0 ... PREC_N-2
+     *   * U_i = U * (1-2^(PREC_N-1)), for i=PREC_N-1
+     *   where U is a point with no known corresponding scalar. Note that sum(U_i, i=0 ... PREC_N-1) = 0.
+     * For each i, and each of the PREC_G possible values of n_i, (n_i * (PREC_G)^i * G + U_i) is
+     * precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0 ... PREC_N-1).
      * None of the resulting prec group elements have a known scalar, and neither do any of
      * the intermediate sums while computing a*G.
      */
-    secp256k1_ge_storage (*prec)[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
+    secp256k1_ge_storage (*prec)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G]; /* prec[j][i] = (PREC_G)^j * i * G + U_i */
     secp256k1_scalar blind;
     secp256k1_gej initial;
 } secp256k1_ecmult_gen_context;

src/ecmult_gen_impl.h

@@ -28,7 +28,7 @@ static void secp256k1_ecmult_gen_context_init(secp256k1_ecmult_gen_context *ctx)
 
 static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, void **prealloc) {
 #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
-    secp256k1_ge prec[1024];
+    secp256k1_ge prec[ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G];
     secp256k1_gej gj;
     secp256k1_gej nums_gej;
     int i, j;
@@ -40,7 +40,7 @@ static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx
         return;
     }
 #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
-    ctx->prec = (secp256k1_ge_storage (*)[64][16])manual_alloc(prealloc, prealloc_size, base, prealloc_size);
+    ctx->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])manual_alloc(prealloc, prealloc_size, base, prealloc_size);
 
     /* get the generator */
     secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
@@ -64,39 +64,39 @@ static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx
 
     /* compute prec. */
     {
-        secp256k1_gej precj[1024]; /* Jacobian versions of prec. */
+        secp256k1_gej precj[ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G]; /* Jacobian versions of prec. */
         secp256k1_gej gbase;
         secp256k1_gej numsbase;
-        gbase = gj; /* 16^j * G */
+        gbase = gj; /* PREC_G^j * G */
         numsbase = nums_gej; /* 2^j * nums. */
-        for (j = 0; j < 64; j++) {
-            /* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
-            precj[j*16] = numsbase;
-            for (i = 1; i < 16; i++) {
-                secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase, NULL);
+        for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
+            /* Set precj[j*PREC_G .. j*PREC_G+(PREC_G-1)] to (numsbase, numsbase + gbase, ..., numsbase + (PREC_G-1)*gbase). */
+            precj[j*ECMULT_GEN_PREC_G] = numsbase;
+            for (i = 1; i < ECMULT_GEN_PREC_G; i++) {
+                secp256k1_gej_add_var(&precj[j*ECMULT_GEN_PREC_G + i], &precj[j*ECMULT_GEN_PREC_G + i - 1], &gbase, NULL);
             }
-            /* Multiply gbase by 16. */
-            for (i = 0; i < 4; i++) {
+            /* Multiply gbase by PREC_G. */
+            for (i = 0; i < ECMULT_GEN_PREC_B; i++) {
                 secp256k1_gej_double_var(&gbase, &gbase, NULL);
             }
             /* Multiply numbase by 2. */
             secp256k1_gej_double_var(&numsbase, &numsbase, NULL);
-            if (j == 62) {
+            if (j == ECMULT_GEN_PREC_N - 2) {
                 /* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
                 secp256k1_gej_neg(&numsbase, &numsbase);
                 secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej, NULL);
             }
         }
-        secp256k1_ge_set_all_gej_var(prec, precj, 1024);
+        secp256k1_ge_set_all_gej_var(prec, precj, ECMULT_GEN_PREC_N * ECMULT_GEN_PREC_G);
     }
-    for (j = 0; j < 64; j++) {
-        for (i = 0; i < 16; i++) {
-            secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*16 + i]);
+    for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
+        for (i = 0; i < ECMULT_GEN_PREC_G; i++) {
+            secp256k1_ge_to_storage(&(*ctx->prec)[j][i], &prec[j*ECMULT_GEN_PREC_G + i]);
         }
     }
 #else
     (void)prealloc;
-    ctx->prec = (secp256k1_ge_storage (*)[64][16])secp256k1_ecmult_static_context;
+    ctx->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])secp256k1_ecmult_static_context;
 #endif
     secp256k1_ecmult_gen_blind(ctx, NULL);
 }
@@ -109,7 +109,7 @@ static void secp256k1_ecmult_gen_context_finalize_memcpy(secp256k1_ecmult_gen_co
 #ifndef USE_ECMULT_STATIC_PRECOMPUTATION
     if (src->prec != NULL) {
         /* We cast to void* first to suppress a -Wcast-align warning. */
-        dst->prec = (secp256k1_ge_storage (*)[64][16])(void*)((unsigned char*)dst + ((unsigned char*)src->prec - (unsigned char*)src));
+        dst->prec = (secp256k1_ge_storage (*)[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G])(void*)((unsigned char*)dst + ((unsigned char*)src->prec - (unsigned char*)src));
     }
 #else
     (void)dst, (void)src;
@@ -133,9 +133,9 @@ static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp25
     /* Blind scalar/point multiplication by computing (n-b)G + bG instead of nG. */
     secp256k1_scalar_add(&gnb, gn, &ctx->blind);
     add.infinity = 0;
-    for (j = 0; j < 64; j++) {
-        bits = secp256k1_scalar_get_bits(&gnb, j * 4, 4);
-        for (i = 0; i < 16; i++) {
+    for (j = 0; j < ECMULT_GEN_PREC_N; j++) {
+        bits = secp256k1_scalar_get_bits(&gnb, j * ECMULT_GEN_PREC_B, ECMULT_GEN_PREC_B);
+        for (i = 0; i < ECMULT_GEN_PREC_G; i++) {
             /** This uses a conditional move to avoid any secret data in array indexes.
              *   _Any_ use of secret indexes has been demonstrated to result in timing
              *   sidechannels, even when the cache-line access patterns are uniform.

src/gen_context.c

@@ -45,23 +45,23 @@ int main(int argc, char **argv) {
     fprintf(fp, "#define _SECP256K1_ECMULT_STATIC_CONTEXT_\n");
     fprintf(fp, "#include \"src/group.h\"\n");
     fprintf(fp, "#define SC SECP256K1_GE_STORAGE_CONST\n");
-    fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_static_context[64][16] = {\n");
+    fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_static_context[ECMULT_GEN_PREC_N][ECMULT_GEN_PREC_G] = {\n");
 
     base = checked_malloc(&default_error_callback, SECP256K1_ECMULT_GEN_CONTEXT_PREALLOCATED_SIZE);
     prealloc = base;
     secp256k1_ecmult_gen_context_init(&ctx);
     secp256k1_ecmult_gen_context_build(&ctx, &prealloc);
-    for(outer = 0; outer != 64; outer++) {
+    for(outer = 0; outer != ECMULT_GEN_PREC_N; outer++) {
         fprintf(fp,"{\n");
-        for(inner = 0; inner != 16; inner++) {
+        for(inner = 0; inner != ECMULT_GEN_PREC_G; inner++) {
             fprintf(fp,"    SC(%uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu, %uu)", SECP256K1_GE_STORAGE_CONST_GET((*ctx.prec)[outer][inner]));
-            if (inner != 15) {
+            if (inner != ECMULT_GEN_PREC_G - 1) {
                 fprintf(fp,",\n");
             } else {
                 fprintf(fp,"\n");
             }
         }
-        if (outer != 63) {
+        if (outer != ECMULT_GEN_PREC_N - 1) {
             fprintf(fp,"},\n");
         } else {
             fprintf(fp,"}\n");