diff --git a/lib/rpmfi.c b/lib/rpmfi.c
index b67680c172..430bf046b6 100644
--- a/lib/rpmfi.c
+++ b/lib/rpmfi.c
@@ -116,7 +116,7 @@ struct rpmfiles_s {
     struct fingerPrint_s * fps;	/*!< File fingerprint(s). */
 
     int digestalgo;		/*!< File digest algorithm */
-    int signaturelength;	/*!< File signature length */
+    uint32_t *signatureoffs;	/*!< File signature offsets */
     int veritysiglength;	/*!< Verity signature length */
     uint16_t verityalgo;	/*!< Verity algorithm */
     unsigned char * digests;	/*!< File digests in binary. */
@@ -578,10 +578,18 @@ const unsigned char * rpmfilesFSignature(rpmfiles fi, int ix, size_t *len)
     const unsigned char *signature = NULL;
 
     if (fi != NULL && ix >= 0 && ix < rpmfilesFC(fi)) {
-	if (fi->signatures != NULL)
-	    signature = fi->signatures + (fi->signaturelength * ix);
-	if (len)
-	    *len = fi->signaturelength;
+	if (fi->signatures != NULL && fi->signatureoffs != NULL) {
+	    uint32_t off = fi->signatureoffs[ix];
+	    size_t slen = 0;
+
+	    if (off != 0) {
+		signature = fi->signatures + off;
+		slen = fi->signatureoffs[ix+1] - off;
+	    }
+
+	    if (len)
+		*len = slen;
+	}
     }
     return signature;
 }
@@ -1277,6 +1285,7 @@ rpmfiles rpmfilesFree(rpmfiles fi)
 	fi->flangs = _free(fi->flangs);
 	fi->digests = _free(fi->digests);
 	fi->signatures = _free(fi->signatures);
+	fi->signatureoffs = _free(fi->signatureoffs);
 	fi->veritysigs = _free(fi->veritysigs);
 	fi->fcaps = _free(fi->fcaps);
 
@@ -1506,6 +1515,49 @@ static void rpmfilesBuildNLink(rpmfiles fi, Header h)
     return;
 }
 
+/*
+ * Convert a tag of variable len hex strings to binary presentation,
+ * accessed via offsets to a contiguous binary blob. Empty strings are
+ * special-cased to a block of zeros at offset 0 which makes them easy
+ * to distinguish elsewhere. The offsets array always has one extra
+ * element to allow calculating the size of the last element.
+ */
+static uint8_t *hex2binv(Header h, rpmTagVal tag, rpm_count_t num,
+			uint32_t **offsetp)
+{
+    struct rpmtd_s td;
+    uint8_t *bin = NULL;
+    uint32_t *offs = NULL;
+    int nzeros = 16;
+
+    if (headerGet(h, tag, &td, HEADERGET_MINMEM) && rpmtdCount(&td) == num) {
+	const char *s;
+	int i = 0;
+	uint8_t *t = bin = xmalloc(((rpmtdSize(&td) / 2) + 1) + nzeros);
+	offs = xmalloc((num + 1) * sizeof(*offs));
+
+	memset(t, 0, nzeros);
+	t += nzeros;
+
+	while ((s = rpmtdNextString(&td))) {
+	    uint32_t len = strlen(s) / 2;
+	    if (len == 0) {
+		offs[i] = 0;
+	    } else {
+		offs[i] = t - bin;
+		for (int j = 0; j < len; j++, t++, s += 2)
+		    *t = (rnibble(s[0]) << 4) | rnibble(s[1]);
+	    }
+	    i++;
+	}
+	offs[i] = t - bin;
+	*offsetp = offs;
+
+	rpmtdFreeData(&td);
+    }
+    return bin;
+}
+
 /* Convert a tag of hex strings to binary presentation */
 static uint8_t *hex2bin(Header h, rpmTagVal tag, rpm_count_t num, size_t len)
 {
@@ -1654,9 +1706,8 @@ static int rpmfilesPopulate(rpmfiles fi, Header h, rpmfiFlags flags)
     fi->signatures = NULL;
     /* grab hex signatures from header and store in binary format */
     if (!(flags & RPMFI_NOFILESIGNATURES)) {
-	fi->signaturelength = headerGetNumber(h, RPMTAG_FILESIGNATURELENGTH);
-	fi->signatures = hex2bin(h, RPMTAG_FILESIGNATURES,
-				 totalfc, fi->signaturelength);
+	fi->signatures = hex2binv(h, RPMTAG_FILESIGNATURES,
+				 totalfc, &fi->signatureoffs);
     }
 
     fi->veritysigs = NULL;
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 60fd7cc269..f78e17c3e9 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -102,6 +102,7 @@ EXTRA_DIST += data/RPMS/hello-2.0-1.i686.rpm
 EXTRA_DIST += data/RPMS/hello-2.0-1.x86_64.rpm
 EXTRA_DIST += data/RPMS/hello-2.0-1.x86_64-signed.rpm
 EXTRA_DIST += data/RPMS/hlinktest-1.0-1.noarch.rpm
+EXTRA_DIST += data/RPMS/imatest-1.0-1.fc34.noarch.rpm
 EXTRA_DIST += data/SRPMS/foo-1.0-1.src.rpm
 EXTRA_DIST += data/SRPMS/hello-1.0-1.src.rpm
 EXTRA_DIST += data/SOURCES/hello.c
diff --git a/tests/data/RPMS/imatest-1.0-1.fc34.noarch.rpm b/tests/data/RPMS/imatest-1.0-1.fc34.noarch.rpm
new file mode 100644
index 0000000000..9b47cf9dd0
Binary files /dev/null and b/tests/data/RPMS/imatest-1.0-1.fc34.noarch.rpm differ
diff --git a/tests/rpmpython.at b/tests/rpmpython.at
index 4b801447cd..8289d84c61 100644
--- a/tests/rpmpython.at
+++ b/tests/rpmpython.at
@@ -624,6 +624,17 @@ for f in fi:
 ],
 [])
 
+RPMPY_TEST([file sets 1],[
+ts = rpm.ts()
+h = ts.hdrFromFdno('${RPMDATA}/RPMS/imatest-1.0-1.fc34.noarch.rpm')
+files = rpm.files(h)
+for f in files:
+   myprint('%s: %s' % (f.name, f.imasig.hex()))
+],
+[/usr/share/example1: 030204a598255400483046022100e5117bdafa73baaeb1f1dc46ecaa46981a62d417745a33532572b63dc6d95d16022100c789107ac5b91e2d915e1df3c7b78414f6b3f50899d44c1de381d0e938dfc82b
+/usr/share/example2: 030204a598255400473045022100c10943795bff5d9c0db53dd4f8e4b845615fd08a2be295c30a80f5bdb4e6a41302203038840cc6abaab92acb56cb3e3ce520b17f22ff7444a8d5d0f703a44d5307a3
+],
+[])
 RPMPY_TEST([string pool 1],[
 p = rpm.strpool()
 for s in ['foo', 'bar', 'foo', 'zoo']: