diff --git a/grep-3.4-rss-regression-fix.patch b/grep-3.4-rss-regression-fix.patch
new file mode 100644
index 0000000..f8f3daf
--- /dev/null
+++ b/grep-3.4-rss-regression-fix.patch
@@ -0,0 +1,173 @@
+diff --git a/lib/dfa.c b/lib/dfa.c
+index 96ae560..3cb64bc 100644
+--- a/lib/dfa.c
++++ b/lib/dfa.c
+@@ -3597,7 +3597,7 @@ free_mbdata (struct dfa *d)
+ }
+ 
+ /* Return true if every construct in D is supported by this DFA matcher.  */
+-static bool _GL_ATTRIBUTE_PURE
++bool
+ dfa_supported (struct dfa const *d)
+ {
+   for (idx_t i = 0; i < d->tindex; i++)
+diff --git a/lib/dfa.h b/lib/dfa.h
+index c5bff89..fddce39 100644
+--- a/lib/dfa.h
++++ b/lib/dfa.h
+@@ -113,6 +113,9 @@ extern struct dfa *dfasuperset (struct dfa const *d) _GL_ATTRIBUTE_PURE;
+ /* The DFA is likely to be fast.  */
+ extern bool dfaisfast (struct dfa const *) _GL_ATTRIBUTE_PURE;
+ 
++/* Return true if every construct in D is supported by this DFA matcher.  */
++extern bool dfa_supported (struct dfa const *) _GL_ATTRIBUTE_PURE;
++
+ /* Free the storage held by the components of a struct dfa. */
+ extern void dfafree (struct dfa *);
+ 
+diff --git a/src/dfasearch.c b/src/dfasearch.c
+index 337345f..ff7d7ad 100644
+--- a/src/dfasearch.c
++++ b/src/dfasearch.c
+@@ -175,7 +175,7 @@ regex_compile (struct dfa_comp *dc, char const *p, ptrdiff_t len,
+ }
+ 
+ void *
+-GEAcompile (char *pattern, size_t size, reg_syntax_t syntax_bits)
++GEAcompile (char *pattern, size_t size, reg_syntax_t syntax_bits, bool exact)
+ {
+   char *motif;
+   struct dfa_comp *dc = xcalloc (1, sizeof (*dc));
+@@ -277,18 +277,6 @@ GEAcompile (char *pattern, size_t size, reg_syntax_t syntax_bits)
+         }
+     }
+ 
+-  if (buf != NULL)
+-    {
+-      dc->patterns--;
+-      dc->pcount++;
+-
+-      if (!regex_compile (dc, buf, buflen, 0, -1, false))
+-        abort ();
+-
+-      if (buf != pattern)
+-        free (buf);
+-    }
+-
+   /* In the match_words and match_lines cases, we use a different pattern
+      for the DFA matcher that will quickly throw out cases that won't work.
+      Then if DFA succeeds we do some hairy stuff using the regex matcher
+@@ -324,6 +312,21 @@ GEAcompile (char *pattern, size_t size, reg_syntax_t syntax_bits)
+   kwsmusts (dc);
+   dfacomp (NULL, 0, dc->dfa, 1);
+ 
++  if (buf != NULL)
++    {
++      if (exact || !dfa_supported (dc->dfa))
++        {
++          dc->patterns--;
++          dc->pcount++;
++
++          if (!regex_compile (dc, buf, buflen, 0, -1, false))
++            abort ();
++        }
++
++      if (buf != pattern)
++        free (buf);
++    }
++
+   free (motif);
+ 
+   return dc;
+diff --git a/src/grep.c b/src/grep.c
+index 929a37c..a96a869 100644
+--- a/src/grep.c
++++ b/src/grep.c
+@@ -571,7 +571,7 @@ static bool seek_failed;
+ static bool seek_data_failed;
+ 
+ /* Functions we'll use to search. */
+-typedef void *(*compile_fp_t) (char *, size_t, reg_syntax_t);
++typedef void *(*compile_fp_t) (char *, size_t, reg_syntax_t, bool);
+ typedef size_t (*execute_fp_t) (void *, char const *, size_t, size_t *,
+                                 char const *);
+ static execute_fp_t execute;
+@@ -2900,8 +2900,9 @@ main (int argc, char **argv)
+     matcher = try_fgrep_pattern (matcher, keys, &keycc);
+ 
+   execute = matchers[matcher].execute;
+-  compiled_pattern = matchers[matcher].compile (keys, keycc,
+-                                                matchers[matcher].syntax);
++  compiled_pattern =
++    matchers[matcher].compile (keys, keycc, matchers[matcher].syntax,
++                               only_matching | color_option);
+   /* We need one byte prior and one after.  */
+   char eolbytes[3] = { 0, eolbyte, 0 };
+   size_t match_size;
+diff --git a/src/kwsearch.c b/src/kwsearch.c
+index 6f6d4d0..808d3b6 100644
+--- a/src/kwsearch.c
++++ b/src/kwsearch.c
+@@ -47,7 +47,7 @@ struct kwsearch
+    description of the compiled pattern.  */
+ 
+ void *
+-Fcompile (char *pattern, size_t size, reg_syntax_t ignored)
++Fcompile (char *pattern, size_t size, reg_syntax_t ignored, bool exact)
+ {
+   kwset_t kwset;
+   ptrdiff_t total = size;
+@@ -190,7 +190,7 @@ Fexecute (void *vcp, char const *buf, size_t size, size_t *match_size,
+             {
+               fgrep_to_grep_pattern (&kwsearch->pattern, &kwsearch->size);
+               kwsearch->re = GEAcompile (kwsearch->pattern, kwsearch->size,
+-                                         RE_SYNTAX_GREP);
++                                         RE_SYNTAX_GREP, !!start_ptr);
+             }
+           return EGexecute (kwsearch->re, buf, size, match_size, start_ptr);
+         }
+@@ -257,7 +257,7 @@ Fexecute (void *vcp, char const *buf, size_t size, size_t *match_size,
+                     fgrep_to_grep_pattern (&kwsearch->pattern, &kwsearch->size);
+                     kwsearch->re = GEAcompile (kwsearch->pattern,
+                                                kwsearch->size,
+-                                               RE_SYNTAX_GREP);
++                                               RE_SYNTAX_GREP, !!start_ptr);
+                   }
+                 end = memchr (beg + len, eol, (buf + size) - (beg + len));
+                 end = end ? end + 1 : buf + size;
+diff --git a/src/pcresearch.c b/src/pcresearch.c
+index 15a6a59..0e2d4e4 100644
+--- a/src/pcresearch.c
++++ b/src/pcresearch.c
+@@ -108,7 +108,7 @@ jit_exec (struct pcre_comp *pc, char const *subject, int search_bytes,
+ }
+ 
+ void *
+-Pcompile (char *pattern, size_t size, reg_syntax_t ignored)
++Pcompile (char *pattern, size_t size, reg_syntax_t ignored, bool exact)
+ {
+   int e;
+   char const *ep;
+diff --git a/src/search.h b/src/search.h
+index 1d85a7e..af81dcb 100644
+--- a/src/search.h
++++ b/src/search.h
+@@ -56,15 +56,15 @@ extern ptrdiff_t mb_goback (char const **, size_t *, char const *,
+                             char const *);
+ 
+ /* dfasearch.c */
+-extern void *GEAcompile (char *, size_t, reg_syntax_t);
++extern void *GEAcompile (char *, size_t, reg_syntax_t, bool);
+ extern size_t EGexecute (void *, char const *, size_t, size_t *, char const *);
+ 
+ /* kwsearch.c */
+-extern void *Fcompile (char *, size_t, reg_syntax_t);
++extern void *Fcompile (char *, size_t, reg_syntax_t, bool);
+ extern size_t Fexecute (void *, char const *, size_t, size_t *, char const *);
+ 
+ /* pcresearch.c */
+-extern void *Pcompile (char *, size_t, reg_syntax_t);
++extern void *Pcompile (char *, size_t, reg_syntax_t, bool);
+ extern size_t Pexecute (void *, char const *, size_t, size_t *, char const *);
+ 
+ /* grep.c */
diff --git a/grep.spec b/grep.spec
index 0298049..7470e3d 100644
--- a/grep.spec
+++ b/grep.spec
@@ -1,7 +1,7 @@
 Summary: Pattern matching utilities
 Name: grep
 Version: 3.4
-Release: 5%{?dist}
+Release: 6%{?dist}
 License: GPLv3+
 URL: http://www.gnu.org/software/grep/
 
@@ -21,6 +21,9 @@ Patch2: 0001-Revert-L-exit-status-change-introduced-in-grep-3.2.patch
 # removes some tests that fail on armv7hl, by Paul Eggert
 # re-diffed to apply to 3.4
 Patch3: 0001-perror-strerror_r-remove-unportable-tests.patch
+# https://bugzilla.redhat.com/show_bug.cgi?id=1967370
+# https://git.savannah.gnu.org/cgit/grep.git/patch/?id=ae65513edc80a1b65f19264b9bed95d870602967
+Patch4: grep-3.4-rss-regression-fix.patch
 
 BuildRequires: gcc
 BuildRequires: pcre-devel >= 3.9-10, texinfo, gettext
@@ -46,6 +49,7 @@ GNU grep is needed by many scripts, so it shall be installed on every system.
 %patch1 -p1 -b .help-align
 %patch2 -p1 -b .zgrep-fix
 %patch3 -p1 -b .remove-broken-tests
+%patch4 -p1 -b .rss-regression-fix
 
 %build
 %global BUILD_FLAGS $RPM_OPT_FLAGS
@@ -88,6 +92,11 @@ make check
 %{_libexecdir}/grepconf.sh
 
 %changelog
+* Tue Jun 15 2021 Jaroslav Škarvada <jskarvad@redhat.com> - 3.4-6
+- Backported upstream fix for many-regexp N^2 RSS regression
+  by rss-regression-fix patch (without test)
+  Resolves: rhbz#1967370
+
 * Wed Aug 26 2020 Adam Williamson <awilliam@redhat.com> - 3.4-5
 - Backport fix for upstream #28105 to fix zgrep
   Resolves: rhbz#1872913