Merge bitcoin#337: variable sized precomputed table for signing

dcb2e3b variable signing precompute table (djb)

Pull request description:

  This pull request gives an option to reduce the precomputed table size for the signing context (`ctx`) by setting `#define ECMULT_GEN_PREC_BITS [N_BITS]`.

  Motivation: Per bitcoin#251 and bitcoin#254, the static table can be reduced to 64kB. However, this is still too big for some of my embedded applications. Setting `#define ECMULT_GEN_PREC_BITS 2` produces a 32kB table at a tradeoff of about 75% of the signing speed. Not defining this value will default to the existing implementation of 4 bits. Statistics:

  ```
  ECMULT_GEN_PREC_BITS = 1
  Precomputed table size: 32kB
  ./bench_sign
  ecdsa_sign: min 195us / avg 200us / max 212us

  ECMULT_GEN_PREC_BITS = 2
  Precomputed table size: 32kB
  ./bench_sign
  ecdsa_sign: min 119us / avg 126us / max 134us

  ECMULT_GEN_PREC_BITS = 4 (default)
  Precomputed table size: 64kB
  ./bench_sign
  ecdsa_sign: min 83.5us / avg 89.6us / max 95.3us

  ECMULT_GEN_PREC_BITS = 8
  Precomputed table size: 512kB
  ./bench_sign
  ecdsa_sign: min 96.4us / avg 99.4us / max 104us
  ```

  Only values of 2 and 4 make sense. 8 bits causes a larger table size with no increase in speed. 1 bit runs, actually, but does not reduce table size and is slower than 2 bits.

ACKs for top commit:
  real-or-random:
    ACK dcb2e3b verified that all changes to the previous ACKed 1d26b27ac90092306bfbc9cdd5123e8a5035202a were due to the rebase
  jonasnick:
    ACK dcb2e3b read the code and tested various configurations with valgrind

Tree-SHA512: ed6f68ca23ffdc4b59d51525336b34b25521233537edbc74d32dfb3eafd8196419be17f01cbf10bd8d87ce745ce143085abc6034727f742163f7e5f13f26f56e

.travis.yml

@@ -11,7 +11,7 @@ cache:
   - src/java/guava/
 env:
   global:
-    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  RECOVERY=no  EXPERIMENTAL=no  JNI=no
+    - FIELD=auto  BIGNUM=auto  SCALAR=auto  ENDOMORPHISM=no  STATICPRECOMPUTATION=yes  ECMULTGENPRECISION=auto  ASM=no  BUILD=check  EXTRAFLAGS=  HOST=  ECDH=no  RECOVERY=no  EXPERIMENTAL=no  JNI=no
     - GUAVA_URL=https://search.maven.org/remotecontent?filepath=com/google/guava/guava/18.0/guava-18.0.jar GUAVA_JAR=src/java/guava/guava-18.0.jar
   matrix:
     - SCALAR=32bit    RECOVERY=yes
@@ -30,6 +30,8 @@ env:
     - EXTRAFLAGS=CPPFLAGS=-DDETERMINISTIC
     - EXTRAFLAGS=CFLAGS=-O0
     - BUILD=check-java JNI=yes ECDH=yes EXPERIMENTAL=yes
+    - ECMULTGENPRECISION=2
+    - ECMULTGENPRECISION=8
 matrix:
   fast_finish: true
   include:
@@ -65,4 +67,4 @@ before_script: ./autogen.sh
 script:
  - if [ -n "$HOST" ]; then export USE_HOST="--host=$HOST"; fi
  - if [ "x$HOST" = "xi686-linux-gnu" ]; then export CC="$CC -m32"; fi
- - ./configure --enable-experimental=$EXPERIMENTAL --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --enable-module-ecdh=$ECDH --enable-module-recovery=$RECOVERY --enable-jni=$JNI $EXTRAFLAGS $USE_HOST && make -j2 $BUILD
+ - ./configure --enable-experimental=$EXPERIMENTAL --enable-endomorphism=$ENDOMORPHISM --with-field=$FIELD --with-bignum=$BIGNUM --with-scalar=$SCALAR --enable-ecmult-static-precomputation=$STATICPRECOMPUTATION --with-ecmult-gen-precision=$ECMULTGENPRECISION --enable-module-ecdh=$ECDH --enable-module-recovery=$RECOVERY --enable-jni=$JNI $EXTRAFLAGS $USE_HOST && make -j2 $BUILD

Makefile.am

@@ -151,11 +151,11 @@ endif
 endif
 
 if USE_ECMULT_STATIC_PRECOMPUTATION
-CPPFLAGS_FOR_BUILD +=-I$(top_srcdir)
+CPPFLAGS_FOR_BUILD +=-I$(top_srcdir) -I$(builddir)/src
 
 gen_context_OBJECTS = gen_context.o
 gen_context_BIN = gen_context$(BUILD_EXEEXT)
-gen_%.o: src/gen_%.c
+gen_%.o: src/gen_%.c src/libsecp256k1-config.h
 	$(CC_FOR_BUILD) $(CPPFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) -c $< -o $@
 
 $(gen_context_BIN): $(gen_context_OBJECTS)

README.md

@@ -61,3 +61,12 @@ libsecp256k1 is built using autotools:
     $ make
     $ make check
     $ sudo make install  # optional
+
+Exhaustive tests
+-----------
+
+    $ ./exhaustive_tests
+
+With valgrind, you might need to increase the max stack size:
+
+    $ valgrind --max-stackframe=2500000 ./exhaustive_tests

configure.ac

@@ -165,6 +165,14 @@ AC_ARG_WITH([ecmult-window], [AS_HELP_STRING([--with-ecmult-window=SIZE|auto],
 )],
 [req_ecmult_window=$withval], [req_ecmult_window=auto])
 
+AC_ARG_WITH([ecmult-gen-precision], [AS_HELP_STRING([--with-ecmult-gen-precision=2|4|8|auto],
+[Precision bits to tune the precomputed table size for signing.]
+[The size of the table is 32kB for 2 bits, 64kB for 4 bits, 512kB for 8 bits of precision.]
+[A larger table size usually results in possible faster signing.]
+["auto" is a reasonable setting for desktop machines (currently 4). [default=auto]]
+)],
+[req_ecmult_gen_precision=$withval], [req_ecmult_gen_precision=auto])
+
 AC_CHECK_TYPES([__int128])
 
 if test x"$enable_coverage" = x"yes"; then
@@ -423,6 +431,22 @@ case $set_ecmult_window in
   ;;
 esac
 
+#set ecmult gen precision
+if test x"$req_ecmult_gen_precision" = x"auto"; then
+  set_ecmult_gen_precision=4
+else
+  set_ecmult_gen_precision=$req_ecmult_gen_precision
+fi
+
+case $set_ecmult_gen_precision in
+2|4|8)
+  AC_DEFINE_UNQUOTED(ECMULT_GEN_PREC_BITS, $set_ecmult_gen_precision, [Set ecmult gen precision bits])
+  ;;
+*)
+  AC_MSG_ERROR(['ecmult gen precision not 2, 4, 8 or "auto"'])
+  ;;
+esac
+
 if test x"$use_tests" = x"yes"; then
   SECP_OPENSSL_CHECK
   if test x"$has_openssl_ec" = x"yes"; then
@@ -558,6 +582,7 @@ echo "  bignum                  = $set_bignum"
 echo "  field                   = $set_field"
 echo "  scalar                  = $set_scalar"
 echo "  ecmult window size      = $set_ecmult_window"
+echo "  ecmult gen prec. bits   = $set_ecmult_gen_precision"
 echo
 echo "  CC                      = $CC"
 echo "  CFLAGS                  = $CFLAGS"

src/basic-config.h

@@ -24,6 +24,7 @@
 #undef USE_SCALAR_8X32
 #undef USE_SCALAR_INV_BUILTIN
 #undef USE_SCALAR_INV_NUM
+#undef ECMULT_WINDOW_SIZE
 
 #define USE_NUM_NONE 1
 #define USE_FIELD_INV_BUILTIN 1

src/ecmult_gen.h

@@ -10,20 +10,27 @@
 #include "scalar.h"
 #include "group.h"
 
+#if ECMULT_GEN_PREC_BITS != 2 && ECMULT_GEN_PREC_BITS != 4 && ECMULT_GEN_PREC_BITS != 8
+#  error "Set ECMULT_GEN_PREC_BITS to 2, 4 or 8."
+#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

@@ -4,9 +4,14 @@
  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
  **********************************************************************/
 
+// Autotools creates libsecp256k1-config.h, of which ECMULT_GEN_PREC_BITS is needed.
+// ifndef guard so downstream users can define their own if they do not use autotools.
+#if !defined(ECMULT_GEN_PREC_BITS)
+#include "libsecp256k1-config.h"
+#endif
 #define USE_BASIC_CONFIG 1
-
 #include "basic-config.h"
+
 #include "include/secp256k1.h"
 #include "util.h"
 #include "field_impl.h"
@@ -45,23 +50,26 @@ 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, "#if ECMULT_GEN_PREC_N != %d || ECMULT_GEN_PREC_G != %d\n", ECMULT_GEN_PREC_N, ECMULT_GEN_PREC_G);
+    fprintf(fp, "   #error configuration mismatch, invalid ECMULT_GEN_PREC_N, ECMULT_GEN_PREC_G. Try deleting ecmult_static_context.h before the build.\n");
+    fprintf(fp, "#endif\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");