diff --git a/crypto/o_str.c b/crypto/o_str.c
index 29c324f474..beabec0ddc 100644
--- a/crypto/o_str.c
+++ b/crypto/o_str.c
@@ -198,7 +198,12 @@ char *OPENSSL_buf2hexstr(const unsigned char *buffer, long len)
     const unsigned char *p;
     int i;
 
-    if ((tmp = OPENSSL_malloc(len * 3 + 1)) == NULL) {
+    if (len == 0)
+    {
+        return OPENSSL_zalloc(1);
+    }
+
+    if ((tmp = OPENSSL_malloc(len * 3)) == NULL) {
         CRYPTOerr(CRYPTO_F_OPENSSL_BUF2HEXSTR, ERR_R_MALLOC_FAILURE);
         return NULL;
     }
diff --git a/doc/crypto/OPENSSL_malloc.pod b/doc/crypto/OPENSSL_malloc.pod
index ba50221f1c..5d254f7b90 100644
--- a/doc/crypto/OPENSSL_malloc.pod
+++ b/doc/crypto/OPENSSL_malloc.pod
@@ -124,7 +124,7 @@ An odd number of hex digits is an error.
 
 OPENSSL_buf2hexstr() takes the specified buffer and length, and returns
 a hex string for value, or NULL on error.
-B<Buffer> cannot be NULL; if B<len> is NULL an empty string is returned.
+B<Buffer> cannot be NULL; if B<len> is 0 an empty string is returned.
 
 OPENSSL_hexchar2int() converts a character to the hexadecimal equivalent,
 or returns -1 on error.