diff --git a/doc/userguide/rules/payload-keywords.rst b/doc/userguide/rules/payload-keywords.rst
index 6daa0e14f12f..b591d749c041 100644
--- a/doc/userguide/rules/payload-keywords.rst
+++ b/doc/userguide/rules/payload-keywords.rst
@@ -535,6 +535,12 @@ When ``relative`` is included, there must be a previous ``content`` or ``pcre``
 
 Note: if ``oper`` is ``/`` and the divisor is 0, there will never be a match on the ``byte_math`` keyword.
 
+Note: if ``oper`` is ``<<`` or ``>>`` and ``rvalue`` is 64 or greater, the result is 0.
+A rule that gives such an ``rvalue`` as a number still loads, with a warning, unless
+``byte_math`` is passed to ``--strict-rule-keywords``, which makes the rule fail to
+load instead. When ``rvalue`` names a variable the count is only known once the rule
+runs.
+
 The result can be stored in a result variable and referenced by
 other rule options later in the rule.
 
diff --git a/rust/src/detect/byte_math.rs b/rust/src/detect/byte_math.rs
index c7447330fbec..58e44582391f 100644
--- a/rust/src/detect/byte_math.rs
+++ b/rust/src/detect/byte_math.rs
@@ -1,4 +1,4 @@
-/* Copyright (C) 2022 Open Information Security Foundation
+/* Copyright (C) 2022-2026 Open Information Security Foundation
  *
  * You can copy, redistribute or modify this Program under the terms of
  * the GNU General Public License version 2 as published by the Free
@@ -617,6 +617,21 @@ mod tests {
         );
     }
 
+    #[test]
+    // a shift count of 64 or more parses; the rule loads with a warning from
+    // DetectByteMathSetup() and the shift yields 0 at match time
+    fn test_parser_shift_rvalue() {
+        assert!(parse_bytemath("bytes 4, offset 3933, oper >>, rvalue 63, result foo").is_ok());
+        assert!(parse_bytemath("bytes 4, offset 3933, oper <<, rvalue 63, result foo").is_ok());
+        assert!(parse_bytemath("bytes 4, offset 3933, oper >>, rvalue 64, result foo").is_ok());
+        assert!(parse_bytemath("bytes 4, offset 3933, oper <<, rvalue 64, result foo").is_ok());
+        assert!(parse_bytemath("bytes 4, offset 3933, oper >>, rvalue 100, result foo").is_ok());
+        assert!(parse_bytemath("bytes 4, offset 3933, oper +, rvalue 100, result foo").is_ok());
+        assert!(
+            parse_bytemath("bytes 4, offset 3933, oper >>, rvalue myrvalue, result foo").is_ok()
+        );
+    }
+
     #[test]
     fn test_parser_bitmask_invalid() {
         assert!(parse_bytemath(
diff --git a/src/detect-bytemath.c b/src/detect-bytemath.c
index fe88d69e4aef..5a00c3332c77 100644
--- a/src/detect-bytemath.c
+++ b/src/detect-bytemath.c
@@ -1,4 +1,4 @@
-/* Copyright (C) 2020-2022 Open Information Security Foundation
+/* Copyright (C) 2020-2026 Open Information Security Foundation
  *
  * You can copy, redistribute or modify this Program under the terms of
  * the GNU General Public License version 2 as published by the Free
@@ -189,7 +189,11 @@ int DetectByteMathDoMatch(DetectEngineThreadCtx *det_ctx, const DetectByteMathDa
             }
             break;
         case RightShift:
-            val >>= rvalue;
+            if (rvalue < 64) {
+                val >>= rvalue;
+            } else {
+                val = 0;
+            }
             break;
     }
 
@@ -293,6 +297,31 @@ static int DetectByteMathSetup(DetectEngineCtx *de_ctx, Signature *s, const char
     if (data == NULL)
         goto error;
 
+    /* A shift of 64 or more clears the 64 bit value being shifted, so the
+     * result is 0 for every packet. Only a literal rvalue can be checked
+     * here; a variable one is read from the payload at match time. */
+    if ((data->oper == LeftShift || data->oper == RightShift) &&
+            !(data->flags & DETECT_BYTEMATH_FLAG_RVALUE_VAR) && data->rvalue >= 64) {
+        if (SigMatchStrictEnabled(DETECT_BYTEMATH)) {
+            SCLogError("byte_math rvalue %u is 64 or more, so \"%s\" always gives 0", data->rvalue,
+                    data->oper == LeftShift ? "<<" : ">>");
+            goto error;
+        }
+        if (s->id > 0) {
+            SCLogWarning("signature sid:%u: byte_math rvalue %u is 64 or more, so \"%s\" "
+                         "always gives 0",
+                    s->id, data->rvalue, data->oper == LeftShift ? "<<" : ">>");
+        } else if (de_ctx != NULL && de_ctx->rule_file != NULL) {
+            SCLogWarning("signature at %s:%u: byte_math rvalue %u is 64 or more, so \"%s\" "
+                         "always gives 0",
+                    de_ctx->rule_file, de_ctx->rule_line, data->rvalue,
+                    data->oper == LeftShift ? "<<" : ">>");
+        } else {
+            SCLogWarning("byte_math rvalue %u is 64 or more, so \"%s\" always gives 0",
+                    data->rvalue, data->oper == LeftShift ? "<<" : ">>");
+        }
+    }
+
     int sm_list;
     if (s->init_data->list != DETECT_SM_LIST_NOTSET) {
         if (DetectBufferGetActiveList(de_ctx, s) == -1)
@@ -376,6 +405,8 @@ static int DetectByteMathSetup(DetectEngineCtx *de_ctx, Signature *s, const char
             SCLogError("unknown byte_ keyword var seen in byte_math - %s", rvalue);
             goto error;
         }
+        /* rvalue becomes a byte_values[] index here, so a check on the
+         * literal count has to run above this point. */
         data->rvalue = index;
         data->flags |= DETECT_BYTEMATH_FLAG_RVALUE_VAR;
         SCFree(rvalue);
@@ -1001,6 +1032,59 @@ static int DetectByteMathPacket02(void)
     PASS;
 }
 
+/**
+ * \test A payload-supplied shift count of 64 or more yields 0 instead of
+ *       shifting a uint64_t by its own width.
+ */
+static int DetectByteMathPacket03(void)
+{
+    /* byte 0 is the shift count (64), byte 1 the value shifted, byte 2 the
+     * expected result */
+    uint8_t buf[] = { 0x40, 0xff, 0x00 };
+
+    Packet *p = UTHBuildPacket(buf, sizeof(buf), IPPROTO_UDP);
+    FAIL_IF_NULL(p);
+
+    /* 0xff >> 64 is 0 */
+    FAIL_IF_NOT(UTHPacketMatchSig(p, "alert udp any any -> any any "
+                                     "(byte_extract: 1, 0, shift;"
+                                     "byte_math: bytes 1, offset 1, oper >>, rvalue shift, result "
+                                     "var;"
+                                     "byte_test: 1, =, var, 2;"
+                                     "sid:1;)"));
+    UTHFreePacket(p);
+
+    PASS;
+}
+
+/**
+ * \test A literal shift count of 64 or more parses and keeps its value, so
+ *       DetectByteMathSetup() can warn about it.
+ */
+static int DetectByteMathParseTest17(void)
+{
+    DetectByteMathData *bmd = DetectByteMathParse(
+            NULL, "bytes 4, offset 2, oper >>, rvalue 64, result foo", NULL, NULL);
+    FAIL_IF_NULL(bmd);
+    FAIL_IF_NOT(bmd->oper == RightShift);
+    FAIL_IF_NOT(bmd->rvalue == 64);
+    DetectByteMathFree(NULL, bmd);
+
+    bmd = DetectByteMathParse(
+            NULL, "bytes 4, offset 2, oper <<, rvalue 100, result foo", NULL, NULL);
+    FAIL_IF_NULL(bmd);
+    FAIL_IF_NOT(bmd->oper == LeftShift);
+    FAIL_IF_NOT(bmd->rvalue == 100);
+    DetectByteMathFree(NULL, bmd);
+
+    bmd = DetectByteMathParse(
+            NULL, "bytes 4, offset 2, oper >>, rvalue 63, result foo", NULL, NULL);
+    FAIL_IF_NULL(bmd);
+    DetectByteMathFree(NULL, bmd);
+
+    PASS;
+}
+
 static int DetectByteMathContext01(void)
 {
     DetectEngineCtx *de_ctx = NULL;
@@ -1071,8 +1155,10 @@ static void DetectByteMathRegisterTests(void)
     UtRegisterTest("DetectByteMathParseTest14", DetectByteMathParseTest14);
     UtRegisterTest("DetectByteMathParseTest15", DetectByteMathParseTest15);
     UtRegisterTest("DetectByteMathParseTest16", DetectByteMathParseTest16);
+    UtRegisterTest("DetectByteMathParseTest17", DetectByteMathParseTest17);
     UtRegisterTest("DetectByteMathPacket01", DetectByteMathPacket01);
     UtRegisterTest("DetectByteMathPacket02", DetectByteMathPacket02);
+    UtRegisterTest("DetectByteMathPacket03", DetectByteMathPacket03);
     UtRegisterTest("DetectByteMathContext01", DetectByteMathContext01);
 }
 #endif /* UNITTESTS */