diff --git a/crypto/bn/bn_test.cc b/crypto/bn/bn_test.cc
index 1ad5c479..8c41e48e 100644
--- a/crypto/bn/bn_test.cc
+++ b/crypto/bn/bn_test.cc
@@ -99,7 +99,6 @@ static const int num0 = 100; // number of tests
 static const int num1 = 50;  // additional tests for some functions
 static const int num2 = 5;   // number of tests for slow functions
 
-static bool test_mul(FILE *fp);
 static bool test_div(FILE *fp, BN_CTX *ctx);
 static int rand_neg();
 
@@ -122,6 +121,7 @@ static bool test_asc2bn(BN_CTX *ctx);
 static bool test_mpi();
 static bool test_rand();
 static bool test_asn1();
+static bool TestNegativeZero();
 static bool RunTest(FileTest *t, void *arg);
 
 // A wrapper around puts that takes its arguments in the same order as our *_fp
@@ -180,12 +180,6 @@ int main(int argc, char *argv[]) {
                          "| grep -v 0 */\n");
   puts_fp(bc_file.get(), "obase=16\nibase=16\n");
 
-  message(bc_file.get(), "BN_mul");
-  if (!test_mul(bc_file.get())) {
-    return 1;
-  }
-  flush_fp(bc_file.get());
-
   message(bc_file.get(), "BN_div");
   if (!test_div(bc_file.get(), ctx.get())) {
     return 1;
@@ -260,7 +254,8 @@ int main(int argc, char *argv[]) {
       !test_asc2bn(ctx.get()) ||
       !test_mpi() ||
       !test_rand() ||
-      !test_asn1()) {
+      !test_asn1() ||
+      !TestNegativeZero()) {
     return 1;
   }
 
@@ -463,6 +458,33 @@ static bool TestSquare(FileTest *t, BN_CTX *ctx) {
   return true;
 }
 
+static bool TestProduct(FileTest *t, BN_CTX *ctx) {
+  ScopedBIGNUM a = GetBIGNUM(t, "A");
+  ScopedBIGNUM b = GetBIGNUM(t, "B");
+  ScopedBIGNUM product = GetBIGNUM(t, "Product");
+  ScopedBIGNUM zero(BN_new());
+  if (!a || !b || !product || !zero) {
+    return false;
+  }
+
+  BN_zero(zero.get());
+
+  ScopedBIGNUM ret(BN_new()), remainder(BN_new());
+  if (!ret || !remainder ||
+      !BN_mul(ret.get(), a.get(), b.get(), ctx) ||
+      !ExpectBIGNUMsEqual(t, "A * B", product.get(), ret.get()) ||
+      !BN_div(ret.get(), remainder.get(), product.get(), a.get(), ctx) ||
+      !ExpectBIGNUMsEqual(t, "Product / A", b.get(), ret.get()) ||
+      !ExpectBIGNUMsEqual(t, "Product % A", zero.get(), remainder.get()) ||
+      !BN_div(ret.get(), remainder.get(), product.get(), b.get(), ctx) ||
+      !ExpectBIGNUMsEqual(t, "Product / B", a.get(), ret.get()) ||
+      !ExpectBIGNUMsEqual(t, "Product % B", zero.get(), remainder.get())) {
+    return false;
+  }
+
+  return true;
+}
+
 struct Test {
   const char *name;
   bool (*func)(FileTest *t, BN_CTX *ctx);
@@ -474,6 +496,7 @@ static const Test kTests[] = {
     {"LShift", TestLShift},
     {"RShift", TestRShift},
     {"Square", TestSquare},
+    {"Product", TestProduct},
 };
 
 static bool RunTest(FileTest *t, void *arg) {
@@ -579,66 +602,6 @@ static bool test_div(FILE *fp, BN_CTX *ctx) {
   return true;
 }
 
-static bool test_mul(FILE *fp) {
-  ScopedBN_CTX ctx(BN_CTX_new());
-  ScopedBIGNUM a(BN_new());
-  ScopedBIGNUM b(BN_new());
-  ScopedBIGNUM c(BN_new());
-  ScopedBIGNUM d(BN_new());
-  ScopedBIGNUM e(BN_new());
-  if (!ctx || !a || !b || !c || !d || !e) {
-    return false;
-  }
-
-  for (int i = 0; i < num0 + num1; i++) {
-    if (i <= num1) {
-      if (!BN_rand(a.get(), 100, 0, 0) ||
-          !BN_rand(b.get(), 100, 0, 0)) {
-        return false;
-      }
-    } else if (!BN_rand(b.get(), i - num1, 0, 0)) {
-      return false;
-    }
-    a->neg = rand_neg();
-    b->neg = rand_neg();
-    if (!BN_mul(c.get(), a.get(), b.get(), ctx.get())) {
-      return false;
-    }
-    if (fp != NULL) {
-      BN_print_fp(fp, a.get());
-      puts_fp(fp, " * ");
-      BN_print_fp(fp, b.get());
-      puts_fp(fp, " - ");
-      BN_print_fp(fp, c.get());
-      puts_fp(fp, "\n");
-    }
-    if (!BN_div(d.get(), e.get(), c.get(), a.get(), ctx.get()) ||
-        !BN_sub(d.get(), d.get(), b.get())) {
-      return false;
-    }
-    if (!BN_is_zero(d.get()) || !BN_is_zero(e.get())) {
-      fprintf(stderr, "Multiplication test failed!\n");
-      return false;
-    }
-  }
-
-  // Test that BN_mul never gives negative zero.
-  if (!BN_set_word(a.get(), 1)) {
-    return false;
-  }
-  BN_set_negative(a.get(), 1);
-  BN_zero(b.get());
-  if (!BN_mul(c.get(), a.get(), b.get(), ctx.get())) {
-    return false;
-  }
-  if (!BN_is_zero(c.get()) || BN_is_negative(c.get())) {
-    fprintf(stderr, "Multiplication test failed!\n");
-    return false;
-  }
-
-  return true;
-}
-
 static int rand_neg() {
   static unsigned int neg = 0;
   static const int sign[8] = {0, 0, 0, 1, 1, 0, 1, 1};
@@ -1760,3 +1723,29 @@ static bool test_asn1() {
 
   return true;
 }
+
+static bool TestNegativeZero() {
+  ScopedBN_CTX ctx(BN_CTX_new());
+  ScopedBIGNUM a(BN_new());
+  ScopedBIGNUM b(BN_new());
+  ScopedBIGNUM c(BN_new());
+  if (!ctx || !a || !b || !c) {
+    return false;
+  }
+
+  // Test that BN_mul never gives negative zero.
+  if (!BN_set_word(a.get(), 1)) {
+    return false;
+  }
+  BN_set_negative(a.get(), 1);
+  BN_zero(b.get());
+  if (!BN_mul(c.get(), a.get(), b.get(), ctx.get())) {
+    return false;
+  }
+  if (!BN_is_zero(c.get()) || BN_is_negative(c.get())) {
+    fprintf(stderr, "Multiplication test failed!\n");
+    return false;
+  }
+
+  return true;
+}
diff --git a/crypto/bn/bn_tests.txt b/crypto/bn/bn_tests.txt
index db6245b4..1d91bccf 100644
--- a/crypto/bn/bn_tests.txt
+++ b/crypto/bn/bn_tests.txt
@@ -5348,3 +5348,608 @@ A = -e53ad05c88568f09f616797f0b7f2756fb543d691ec2a5b645c1e5892a247302826419a35b1
 
 Square = eea8028b26e0df090504d54da714a6f5f2695202e53cff479c78aedd47a8dc676243ec586740fde53b3eca9ca02b91031ce766242184109503fbe25b1b6d318e3cd5970fabd16dfa22984dd2e9f1e0f14c189170fc69c031d66663703e6235a942d51a4545bd7b0769d01d302ce2b00b83f01568a1e378f61fd0ca6201b0490330580cd9de85719e174a71915d7efbf65cd73d8f4e66f27e0dd3144d58ec09ed0f7ed7d1238ee596922807100fb7a11127944ddcdec6a9ca3bbf6df7301e354f3f049bfb7c275b43c3d8cda5907a932fba507c9145ea3166081c1b48fcc710ee32cd931f936c796b14f8a78a592e67753a7c9e428a01719c8ba82652f3a89fae110
 A = -3dcb44be1e54c5a5d7db48055ca9afa1ebe2ae648aa6e16ac497502a7deee09ffa124720fad0ab163ce8b3ea6a90f110ea52b67dbc424d0cf1e8c9726dfd9e45bebcefaa5cd5706edeed27896525f31c6bbea3d67ee97badefabf3e2532470b66e3ae3100f66ddf50cf02fc3a8e3f44c304251d3b6a7ca3a6e4bd5d16a41bd97a4
+
+
+# Product tests.
+#
+# These test vectors satisfy A * B = Product.
+
+Product = 5befab3320f8f90542f3120235abd926aac3805a19e343f690
+A = b057af553afb120db6b7764f8
+B = 857734c4c27a1d17f7cf59dee
+
+Product = -ab1ce167f4b2945c55ae3f87df50ad07d4be87cf9f8aa07b0c
+A = ae7a6a87ea8981a567d0b3ecc
+B = -fb0fed5f8c737bcacef4d6cb1
+
+Product = -c2606cd48e6b075c8da79eb4668e7157f1f175c2860fd4c475
+A = -c28dc31984d4583e9d45424c3
+B = ffc4581a5c3f885cf42767e67
+
+Product = aa6805b5408aff7f914472756da07830dcad902834dbdd6944
+A = -ffa07ff9f503511954e5dd3f9
+B = -aaa7af472ad8957763f5a7c64
+
+Product = 58ca2569173389df29b5ce4b784086055dee821a7243db7210
+A = af417d936f4690008811a1ae8
+B = 81b26b80b43aa65aa55ded52a
+
+Product = -a043d31dfce8bd01724d31c863d0a64f1bf013509d77737c42
+A = fb5fae5edefb6997d44a1ecd6
+B = -a336e50c6f7845a1686cc88a3
+
+Product = -b5d6a45ffce851b201239d938ba551bab7dcb59fc11fc35fce
+A = -f918faa58bb57a2ffb8b01f05
+B = bae08c3006fade695029a1df6
+
+Product = 6f2fde7d1a18625d727c6345ed85e597d546d9228bf7f0564a
+A = -8d108d7a16f0696d4ceb24445
+B = -c9c764cae465207097ef8d2c2
+
+Product = 93808b1140841dc9735cd61c6f855ddbbb83066689b0d7e1a0
+A = b386d08daf3fa2154e9c768d6
+B = d2557dceb2d02d04d9c578670
+
+Product = -ad04212ca8cadb1f7861c5130ba3a747046a2a7e4a0c72b69a
+A = e4e5f7d1311e0c5f2e404d55b
+B = -c18057a328d8c7375afdfd4ee
+
+Product = -685e75c232f2b4a0e455fe5ee8aea52f292ad8b8178320e692
+A = -a683312f132b2320632e74ef6
+B = a0758f12791453b4af354730b
+
+Product = 6f588c53185c503dc5b0dc3002d3817ca2e7eb2370b3e9a647
+A = -d70c9b93170261091f0c53f27
+B = -848c86c51a186ac4c9080d3e1
+
+Product = 5e3bc5a04e054a9a244bf7c86cae215072fdb70e9199989427
+A = 898b64ef09d7cf63966e1a3b5
+B = af638b12f26aa5d12e97439eb
+
+Product = -8d8372b235b16108285203c03a8aef6fdd3c0e1a9fd31d4f68
+A = f6003dc83818c14fbe36c9998
+B = -9343f6cbcc81fa4c9399dce5f
+
+Product = -5ee6509abeeb7af7fc5caef40d1822ad3150c8d74f522dc7c8
+A = -875ff6f56ca72cbdf614bb9ca
+B = b375a68a21dfb1f159c22fa14
+
+Product = ada25be404a17385af5a330da799e5909da81bfa0715baa6f4
+A = -c9b8df392e76abc3eb7d5ce04
+B = -dc5ab818c70594dd917b4243d
+
+Product = bb24422ee4656ddfcd50ec38201b15baf679d3b75e5cb878ca
+A = f8e12cf4defe388b78510f687
+B = c07ee817b4ae95c2915b88966
+
+Product = -93da296ba164c7220a17330647aef0980c94eddd2cfa2a3b2d
+A = bc5dc74ddf7a1363d1c2b1f25
+B = -c8f069bad7f93cbfe6df51169
+
+Product = -6b2e1d132c4e0b0dc9b7e7de7d424fda5180480cb5ff47c755
+A = -a8048acb66a8bb88df39266e7
+B = a34e0b265d71435ae8c92a463
+
+Product = 6ccb2cd93783576a8602ae43f41c786008b6623a4cca0a010a
+A = -b071f1f54790c951c1dd2a1cf
+B = -9dd89bb4d9b546207e282e2d6
+
+Product = 5c742ba47d0d64bd97509927ce957deedb855766cc24c60016
+A = b44f3f252c368096fa62747f2
+B = 83439b97dbac579fa4f7b7d23
+
+Product = -7347ba65691c913286c2fb55e45b177f031c1d86ae0e9f654f
+A = 937cf0643ffa53cdea24d642f
+B = -c81881f78243dd5737a7d28e1
+
+Product = -9bc0649a703674e59f83ff9b8a560e5cbf51f65ca310f80f95
+A = -b536f8d9769be6f62da941ae5
+B = dc0746fb101881ae0cacde6f1
+
+Product = bf4992fc3a124de350f9fb90ea825cf663b1fa051282ef22e2
+A = -ff7eacc7de1bb01d668c693aa
+B = -bfaa6627f9fc7ba68ae41bb2d
+
+Product = 7c8992d34cc0b63f1c953f68d4e12a99d3f3a34d16bd76caa9
+A = 9e0d5a850d078890a983c0ec9
+B = c9b72c118b3e1f1023a696ce1
+
+Product = -a75840c95082b9a0ae0d6e0a4eb5e09288e4e2a66e9697d9cd
+A = b2b042a21045a74ef1a5091d9
+B = -efbf8b120b384e869692a1b15
+
+Product = -a510b333bdb4ed7479c142e8fbe2b12f7671a42acbe16c0998
+A = -e7fd5e0bb5496b9d876c27f65
+B = b6262653b2be44501af1d85b8
+
+Product = a1c1e90afc4684754155526e307fc6ed798746f347bae2c880
+A = -b84674832b26ded0a690a8ff0
+B = -e0b7bdf2fd05a038ed3640b78
+
+Product = 5588e0c33bffbefcc5695ca0615abd383343f21a8a0d22b222
+A = 80cad81ad9a66ab6a1c2e5669
+B = aa0453a77c8af1584f54750d2
+
+Product = -6460c2fcd6cf3304ab163ea883ac48e2031cd10f2e9014c0ab
+A = c49ad3d7c8848d4fbf913b10b
+B = -82b3dedbe3cc7cd532ad632e1
+
+Product = -a18717330b711669e85abde8c4dce426529aa621ba3da2a477
+A = -cab4a9c0a331a5a5e826dda1f
+B = cbfee5041c13075dfe3399aa9
+
+Product = 8ab6282ee892b53c083d319a9dcab48af97a1ac8493c0bfcad
+A = -f7d13e47f9aaac8c25f9bf75b
+B = -8f4aa95231c1e2336aa092297
+
+Product = 8f2d1c23c78777ed371f13155445ca3c88cbc0a9b299bdf9d3
+A = 9d8248d00defce1ad081337c3
+B = e8b479295ecd9cef7301f24b1
+
+Product = -86d5e0c5b581fe59819730b4b71e33d1f85f9ab504c7dbe2d6
+A = b21b45e88acff48562a19729a
+B = -c1cdfebccc763beeac394b997
+
+Product = -484ca05aefa113bdfcb1bc623f730c9f9555b462a8ab4c9606
+A = -8c12b406c02c4417163c0956b
+B = 8422b15c80c1c087b17eedd92
+
+Product = 614c3c91f60050c785fd229a3ad74674577a90cacb654e0a5c
+A = -93d45bce155a23a397506d96a
+B = -a87e339c3fd5aebede5fb1b36
+
+Product = 9683285f194a7e4feeab196a36bdfc4f828035fd184b9cc692
+A = f196d8fe760fdcae7eb60e2f7
+B = 9f7d88a2163ad818bf3a6377e
+
+Product = -988a64599c19cc64f3cadc1a83fea6550185f6cc3ab82af822
+A = d0584b2a306671e4d2c9d0c7b
+B = -bb6e7559df199c68d6df3a3c6
+
+Product = -68456814cb0edd951196d04c853172afdd5787a5bd69a57876
+A = -cefce1b0a1fb22862418bb597
+B = 80f614139947aea5e76cd55fa
+
+Product = b4b1cbf5d6566e7a57aee0cc5c9c8ec4ad885e8766aa7662a4
+A = -d68ed1bea046c6cad057e21db
+B = -d7988b9be54f6e332d019032c
+
+Product = 6b09212675ff5257a1384371e17b37dcc268bbb141577902e4
+A = a8208053adc20a609d5d01404
+B = a2fa927c5458c4fe662d7a3b9
+
+Product = -8361bc26f9bcf55f677e047d822d3004027da0d0455b244d10
+A = e82b6410b29020c2d6810a977
+B = -90ddfe0e7f0d6b9cdc0815f70
+
+Product = -f1b6da00923fd513a83e32040a515649fbd362f69ebc016d9f
+A = -f9b697d9ec774a8d1ee5ea905
+B = f7ccb46a8869cb028492bed53
+
+Product = d06206963f2e150bacdb32c823c3a47f013d5a267c3c0d0c88
+A = -ea8e63afa99c719897ad7f2ab
+B = -e36f11f55b6148d1b4f46e598
+
+Product = af774a5eae6084df5ca499ef005642730adabf6a4f9533e2fd
+A = e4c7af7eea3ec9cc2443b7319
+B = c457bc264c8461789931baf85
+
+Product = -76350f428bfbb95e6c253ec0f457aa84cebe8c7cb1af2a2120
+A = 8fd1ff97465775d44dee58ae0
+B = -d268a7d328f44baf80e35119f
+
+Product = -787ae3f114f9a8dd4d249d5d3f3b0897b02564b9469416cefe
+A = -bc0b398bd0ec045b0cf147b7e
+B = a4050955c234e473257d0c641
+
+Product = 9d6320b3d4aabac097a079b9bd2aca7f1898bcab0f23409fd0
+A = -9d7a4ebac630cc0662b816fb5
+B = -ffda517d3eb3214986b04e290
+
+Product = 80bab8bd800ac8c9dc3bb57dca306f10af6fd88c5d8314833c
+A = 834bc50140d6c6ab938dc58b6
+B = fafee47793cbc533b3c66af3a
+
+Product = -b08920f5922226b1dec87151ae087d8a7e5c1aea8c9be148b6
+A = bfd5b1ad323c79428cb2db36a
+B = -eb956a10edebdd658e6810fcf
+
+Product = -6d428e08e8350bb4b0fae3b662c82df2aef7beadaa17430dbb
+A = -a57da276998c548101f514e9f
+B = a9040c1909712e1149d295765
+
+Product = a57da276998c548101f514e9f
+A = -a57da276998c548101f514e9f
+B = -1
+
+Product = 14afb44ed3318a90203ea29d3e
+A = a57da276998c548101f514e9f
+B = 2
+
+Product = -295f689da6631520407d453a7c
+A = a57da276998c548101f514e9f
+B = -4
+
+Product = -867614005cc204a8d19720fe13
+A = -a57da276998c548101f514e9f
+B = d
+
+Product = 12bf3b676f64e5929d38c35e803
+A = -a57da276998c548101f514e9f
+B = -1d
+
+Product = 24d8f92c68303ed0b96f91a8167
+A = a57da276998c548101f514e9f
+B = 39
+
+Product = -49b1f258d0607da172df23502ce
+A = a57da276998c548101f514e9f
+B = -72
+
+Product = -6fd5e6ca25c3d51b2e529f22173
+A = -a57da276998c548101f514e9f
+B = ad
+
+Product = 1276d4705b81b82da4c7e82559d7
+A = -a57da276998c548101f514e9f
+B = -1c9
+
+Product = 1ddb9abfc5d4017f068a67b5f4fd
+A = a57da276998c548101f514e9f
+B = 2e3
+
+Product = -3a8b41c914b1b4a4e341433601f7
+A = a57da276998c548101f514e9f
+B = -5a9
+
+Product = -97c0f4ba414d6e7d4c8b7ced84d4
+A = -a57da276998c548101f514e9f
+B = eac
+
+Product = 1198739e0c23639c176d46d13f7c8
+A = -a57da276998c548101f514e9f
+B = -1b38
+
+Product = 159150954ee0dedf541e4dbac0ec3
+A = a57da276998c548101f514e9f
+B = 215d
+
+Product = -441d4bc44c86f02ff12c3d91a1562
+A = a57da276998c548101f514e9f
+B = -695e
+
+Product = -64726b76005ebee27592237ba5dde
+A = -a57da276998c548101f514e9f
+B = 9b62
+
+Product = bbe4ec7cf7c5bbd198e0ea86bb658
+A = -a57da276998c548101f514e9f
+B = -122a8
+
+Product = 21f717d05681fd2eb1796776a69ef7
+A = a57da276998c548101f514e9f
+B = 348a9
+
+Product = -396ac788a1748bc6955f99be4d2c64
+A = a57da276998c548101f514e9f
+B = -58d1c
+
+Product = -54a213eb083aed1a04f3d1b2da62e7
+A = -a57da276998c548101f514e9f
+B = 82eb9
+
+Product = 1366fb9c20fb14b8b9a9be4b3e3dde1
+A = -a57da276998c548101f514e9f
+B = -1e037f
+
+Product = 238d65fd26da4733e5d93ab2485d40b
+A = a57da276998c548101f514e9f
+B = 36ff15
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