Misc BN fixes

Never output -0; make "negative zero" an impossibility.
Do better checking on BN_rand top/bottom requirements and #bits.
Update doc.
Ignoring trailing garbage in BN_asc2bn.

Port this commit from boringSSL: https://boringssl.googlesource.com/boringssl/+/899b9b19a4cd3fe526aaf5047ab9234cdca19f7d%5E!/
        Ensure |BN_div| never gives negative zero in the no_branch code.

        Have |bn_correct_top| fix |bn->neg| if the input is zero so that we
        don't have negative zeros lying around.

        Thanks to Brian Smith for noticing.

Reviewed-by: Richard Levitte <levitte@openssl.org>
(cherry picked from commit 01c09f9fde)
(Some manual work required)

crypto/bn/bn.h

@@ -842,6 +842,8 @@ int RAND_pseudo_bytes(unsigned char *buf, int num);
                         if (*(ftl--)) break; \
                 (a)->top = tmp_top; \
                 } \
+        if ((a)->top == 0) \
+            (a)->neg = 0; \
         bn_pollute(a); \
         }
 

crypto/bn/bn_print.c

@@ -72,12 +72,9 @@ char *BN_bn2hex(const BIGNUM *a)
     char *buf;
     char *p;
 
-    if (a->neg && BN_is_zero(a)) {
-        /* "-0" == 3 bytes including NULL terminator */
-        buf = OPENSSL_malloc(3);
-    } else {
+    if (BN_is_zero(a))
+        return OPENSSL_strdup("0");
     buf = OPENSSL_malloc(a->top * BN_BYTES * 2 + 2);
-    }
     if (buf == NULL) {
         BNerr(BN_F_BN_BN2HEX, ERR_R_MALLOC_FAILURE);
         goto err;
@@ -244,10 +241,12 @@ int BN_hex2bn(BIGNUM **bn, const char *a)
     }
     ret->top = h;
     bn_correct_top(ret);
-    ret->neg = neg;
 
     *bn = ret;
     bn_check_top(ret);
+    /* Don't set the negative flag if it's zero. */
+    if (ret->top != 0)
+        ret->neg = neg;
     return (num);
  err:
     if (*bn == NULL)
@@ -299,7 +298,7 @@ int BN_dec2bn(BIGNUM **bn, const char *a)
     if (j == BN_DEC_NUM)
         j = 0;
     l = 0;
-    while (*a) {
+    while (--i >= 0) {
         l *= 10;
         l += *a - '0';
         a++;
@@ -310,11 +309,13 @@ int BN_dec2bn(BIGNUM **bn, const char *a)
             j = 0;
         }
     }
-    ret->neg = neg;
 
     bn_correct_top(ret);
     *bn = ret;
     bn_check_top(ret);
+    /* Don't set the negative flag if it's zero. */
+    if (ret->top != 0)
+        ret->neg = neg;
     return (num);
  err:
     if (*bn == NULL)
@@ -325,6 +326,7 @@ int BN_dec2bn(BIGNUM **bn, const char *a)
 int BN_asc2bn(BIGNUM **bn, const char *a)
 {
     const char *p = a;
+
     if (*p == '-')
         p++;
 
@@ -335,7 +337,8 @@ int BN_asc2bn(BIGNUM **bn, const char *a)
         if (!BN_dec2bn(bn, p))
             return 0;
     }
-    if (*a == '-')
+    /* Don't set the negative flag if it's zero. */
+    if (*a == '-' && (*bn)->top != 0)
         (*bn)->neg = 1;
     return 1;
 }

crypto/bn/bn_rand.c

@@ -121,15 +121,14 @@ static int bnrand(int pseudorand, BIGNUM *rnd, int bits, int top, int bottom)
     int ret = 0, bit, bytes, mask;
     time_t tim;
 
-    if (bits < 0 || (bits == 1 && top > 0)) {
-        BNerr(BN_F_BNRAND, BN_R_BITS_TOO_SMALL);
-        return 0;
-    }
-
     if (bits == 0) {
+        if (top != -1 || bottom != 0)
+            goto toosmall;
         BN_zero(rnd);
         return 1;
     }
+    if (bits < 0 || (bits == 1 && top > 0))
+        goto toosmall;
 
     bytes = (bits + 7) / 8;
     bit = (bits - 1) % 8;
@@ -195,6 +194,10 @@ static int bnrand(int pseudorand, BIGNUM *rnd, int bits, int top, int bottom)
     }
     bn_check_top(rnd);
     return (ret);
+
+toosmall:
+    BNerr(BN_F_BNRAND, BN_R_BITS_TOO_SMALL);
+    return 0;
 }
 
 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom)

doc/crypto/BN_bn2bin.pod

@@ -42,7 +42,9 @@ BN_hex2bn() converts the string B<str> containing a hexadecimal number
 to a B<BIGNUM> and stores it in **B<bn>. If *B<bn> is NULL, a new
 B<BIGNUM> is created. If B<bn> is NULL, it only computes the number's
 length in hexadecimal digits. If the string starts with '-', the
-number is negative. BN_dec2bn() is the same using the decimal system.
+number is negative.
+A "negative zero" is converted to zero.
+BN_dec2bn() is the same using the decimal system.
 
 BN_print() and BN_print_fp() write the hexadecimal encoding of B<a>,
 with a leading '-' for negative numbers, to the B<BIO> or B<FILE>

doc/crypto/BN_rand.pod

@@ -19,7 +19,11 @@ BN_rand, BN_pseudo_rand, BN_rand_range, BN_pseudo_rand_range - generate pseudo-r
 =head1 DESCRIPTION
 
 BN_rand() generates a cryptographically strong pseudo-random number of
-B<bits> in length and stores it in B<rnd>. If B<top> is -1, the
+B<bits> in length and stores it in B<rnd>.
+If B<bits> is less than zero, or too small to
+accomodate the requirements specified by the B<top> and B<bottom>
+parameters, an error is returned.
+If B<top> is -1, the
 most significant bit of the random number can be zero. If B<top> is 0,
 it is set to 1, and if B<top> is 1, the two most significant bits of
 the number will be set to 1, so that the product of two such random