diff --git a/include/linux/bpf_verifier.h b/include/linux/bpf_verifier.h
index 73a98f6240fd..042b76fe8e29 100644
--- a/include/linux/bpf_verifier.h
+++ b/include/linux/bpf_verifier.h
@@ -313,11 +313,6 @@ struct bpf_idx_pair {
 	u32 idx;
 };
 
-struct bpf_id_pair {
-	u32 old;
-	u32 cur;
-};
-
 #define MAX_CALL_FRAMES 8
 /* Maximum number of register states that can exist at once */
 #define BPF_ID_MAP_SIZE ((MAX_BPF_REG + MAX_BPF_STACK / BPF_REG_SIZE) * MAX_CALL_FRAMES)
@@ -559,6 +554,16 @@ struct backtrack_state {
 	u64 stack_masks[MAX_CALL_FRAMES];
 };
 
+struct bpf_id_pair {
+	u32 old;
+	u32 cur;
+};
+
+struct bpf_idmap {
+	u32 tmp_id_gen;
+	struct bpf_id_pair map[BPF_ID_MAP_SIZE];
+};
+
 struct bpf_idset {
 	u32 count;
 	u32 ids[BPF_ID_MAP_SIZE];
@@ -596,7 +601,7 @@ struct bpf_verifier_env {
 	struct bpf_verifier_log log;
 	struct bpf_subprog_info subprog_info[BPF_MAX_SUBPROGS + 1];
 	union {
-		struct bpf_id_pair idmap_scratch[BPF_ID_MAP_SIZE];
+		struct bpf_idmap idmap_scratch;
 		struct bpf_idset idset_scratch;
 	};
 	struct {
diff --git a/kernel/bpf/verifier.c b/kernel/bpf/verifier.c
index 747d69b2eaa5..3d4be26b046f 100644
--- a/kernel/bpf/verifier.c
+++ b/kernel/bpf/verifier.c
@@ -12942,12 +12942,14 @@ static int check_alu_op(struct bpf_verifier_env *env, struct bpf_insn *insn)
 		if (BPF_SRC(insn->code) == BPF_X) {
 			struct bpf_reg_state *src_reg = regs + insn->src_reg;
 			struct bpf_reg_state *dst_reg = regs + insn->dst_reg;
+			bool need_id = src_reg->type == SCALAR_VALUE && !src_reg->id &&
+				       !tnum_is_const(src_reg->var_off);
 
 			if (BPF_CLASS(insn->code) == BPF_ALU64) {
 				/* case: R1 = R2
 				 * copy register state to dest reg
 				 */
-				if (src_reg->type == SCALAR_VALUE && !src_reg->id)
+				if (need_id)
 					/* Assign src and dst registers the same ID
 					 * that will be used by find_equal_scalars()
 					 * to propagate min/max range.
@@ -12966,7 +12968,7 @@ static int check_alu_op(struct bpf_verifier_env *env, struct bpf_insn *insn)
 				} else if (src_reg->type == SCALAR_VALUE) {
 					bool is_src_reg_u32 = src_reg->umax_value <= U32_MAX;
 
-					if (is_src_reg_u32 && !src_reg->id)
+					if (is_src_reg_u32 && need_id)
 						src_reg->id = ++env->id_gen;
 					copy_register_state(dst_reg, src_reg);
 					/* Make sure ID is cleared if src_reg is not in u32 range otherwise
@@ -15122,8 +15124,9 @@ static bool range_within(struct bpf_reg_state *old,
  * So we look through our idmap to see if this old id has been seen before.  If
  * so, we require the new id to match; otherwise, we add the id pair to the map.
  */
-static bool check_ids(u32 old_id, u32 cur_id, struct bpf_id_pair *idmap)
+static bool check_ids(u32 old_id, u32 cur_id, struct bpf_idmap *idmap)
 {
+	struct bpf_id_pair *map = idmap->map;
 	unsigned int i;
 
 	/* either both IDs should be set or both should be zero */
@@ -15134,20 +15137,34 @@ static bool check_ids(u32 old_id, u32 cur_id, struct bpf_id_pair *idmap)
 		return true;
 
 	for (i = 0; i < BPF_ID_MAP_SIZE; i++) {
-		if (!idmap[i].old) {
+		if (!map[i].old) {
 			/* Reached an empty slot; haven't seen this id before */
-			idmap[i].old = old_id;
-			idmap[i].cur = cur_id;
+			map[i].old = old_id;
+			map[i].cur = cur_id;
 			return true;
 		}
-		if (idmap[i].old == old_id)
-			return idmap[i].cur == cur_id;
+		if (map[i].old == old_id)
+			return map[i].cur == cur_id;
+		if (map[i].cur == cur_id)
+			return false;
 	}
 	/* We ran out of idmap slots, which should be impossible */
 	WARN_ON_ONCE(1);
 	return false;
 }
 
+/* Similar to check_ids(), but allocate a unique temporary ID
+ * for 'old_id' or 'cur_id' of zero.
+ * This makes pairs like '0 vs unique ID', 'unique ID vs 0' valid.
+ */
+static bool check_scalar_ids(u32 old_id, u32 cur_id, struct bpf_idmap *idmap)
+{
+	old_id = old_id ? old_id : ++idmap->tmp_id_gen;
+	cur_id = cur_id ? cur_id : ++idmap->tmp_id_gen;
+
+	return check_ids(old_id, cur_id, idmap);
+}
+
 static void clean_func_state(struct bpf_verifier_env *env,
 			     struct bpf_func_state *st)
 {
@@ -15246,7 +15263,7 @@ static void clean_live_states(struct bpf_verifier_env *env, int insn,
 
 static bool regs_exact(const struct bpf_reg_state *rold,
 		       const struct bpf_reg_state *rcur,
-		       struct bpf_id_pair *idmap)
+		       struct bpf_idmap *idmap)
 {
 	return memcmp(rold, rcur, offsetof(struct bpf_reg_state, id)) == 0 &&
 	       check_ids(rold->id, rcur->id, idmap) &&
@@ -15255,7 +15272,7 @@ static bool regs_exact(const struct bpf_reg_state *rold,
 
 /* Returns true if (rold safe implies rcur safe) */
 static bool regsafe(struct bpf_verifier_env *env, struct bpf_reg_state *rold,
-		    struct bpf_reg_state *rcur, struct bpf_id_pair *idmap)
+		    struct bpf_reg_state *rcur, struct bpf_idmap *idmap)
 {
 	if (!(rold->live & REG_LIVE_READ))
 		/* explored state didn't use this */
@@ -15292,15 +15309,42 @@ static bool regsafe(struct bpf_verifier_env *env, struct bpf_reg_state *rold,
 
 	switch (base_type(rold->type)) {
 	case SCALAR_VALUE:
-		if (regs_exact(rold, rcur, idmap))
-			return true;
-		if (env->explore_alu_limits)
-			return false;
+		if (env->explore_alu_limits) {
+			/* explore_alu_limits disables tnum_in() and range_within()
+			 * logic and requires everything to be strict
+			 */
+			return memcmp(rold, rcur, offsetof(struct bpf_reg_state, id)) == 0 &&
+			       check_scalar_ids(rold->id, rcur->id, idmap);
+		}
 		if (!rold->precise)
 			return true;
-		/* new val must satisfy old val knowledge */
+		/* Why check_ids() for scalar registers?
+		 *
+		 * Consider the following BPF code:
+		 *   1: r6 = ... unbound scalar, ID=a ...
+		 *   2: r7 = ... unbound scalar, ID=b ...
+		 *   3: if (r6 > r7) goto +1
+		 *   4: r6 = r7
+		 *   5: if (r6 > X) goto ...
+		 *   6: ... memory operation using r7 ...
+		 *
+		 * First verification path is [1-6]:
+		 * - at (4) same bpf_reg_state::id (b) would be assigned to r6 and r7;
+		 * - at (5) r6 would be marked <= X, find_equal_scalars() would also mark
+		 *   r7 <= X, because r6 and r7 share same id.
+		 * Next verification path is [1-4, 6].
+		 *
+		 * Instruction (6) would be reached in two states:
+		 *   I.  r6{.id=b}, r7{.id=b} via path 1-6;
+		 *   II. r6{.id=a}, r7{.id=b} via path 1-4, 6.
+		 *
+		 * Use check_ids() to distinguish these states.
+		 * ---
+		 * Also verify that new value satisfies old value range knowledge.
+		 */
 		return range_within(rold, rcur) &&
-		       tnum_in(rold->var_off, rcur->var_off);
+		       tnum_in(rold->var_off, rcur->var_off) &&
+		       check_scalar_ids(rold->id, rcur->id, idmap);
 	case PTR_TO_MAP_KEY:
 	case PTR_TO_MAP_VALUE:
 	case PTR_TO_MEM:
@@ -15346,7 +15390,7 @@ static bool regsafe(struct bpf_verifier_env *env, struct bpf_reg_state *rold,
 }
 
 static bool stacksafe(struct bpf_verifier_env *env, struct bpf_func_state *old,
-		      struct bpf_func_state *cur, struct bpf_id_pair *idmap)
+		      struct bpf_func_state *cur, struct bpf_idmap *idmap)
 {
 	int i, spi;
 
@@ -15449,7 +15493,7 @@ static bool stacksafe(struct bpf_verifier_env *env, struct bpf_func_state *old,
 }
 
 static bool refsafe(struct bpf_func_state *old, struct bpf_func_state *cur,
-		    struct bpf_id_pair *idmap)
+		    struct bpf_idmap *idmap)
 {
 	int i;
 
@@ -15497,13 +15541,13 @@ static bool func_states_equal(struct bpf_verifier_env *env, struct bpf_func_stat
 
 	for (i = 0; i < MAX_BPF_REG; i++)
 		if (!regsafe(env, &old->regs[i], &cur->regs[i],
-			     env->idmap_scratch))
+			     &env->idmap_scratch))
 			return false;
 
-	if (!stacksafe(env, old, cur, env->idmap_scratch))
+	if (!stacksafe(env, old, cur, &env->idmap_scratch))
 		return false;
 
-	if (!refsafe(old, cur, env->idmap_scratch))
+	if (!refsafe(old, cur, &env->idmap_scratch))
 		return false;
 
 	return true;
@@ -15518,7 +15562,8 @@ static bool states_equal(struct bpf_verifier_env *env,
 	if (old->curframe != cur->curframe)
 		return false;
 
-	memset(env->idmap_scratch, 0, sizeof(env->idmap_scratch));
+	env->idmap_scratch.tmp_id_gen = env->id_gen;
+	memset(&env->idmap_scratch.map, 0, sizeof(env->idmap_scratch.map));
 
 	/* Verification state from speculative execution simulation
 	 * must never prune a non-speculative execution one.
@@ -15536,7 +15581,7 @@ static bool states_equal(struct bpf_verifier_env *env,
 		return false;
 
 	if (old->active_lock.id &&
-	    !check_ids(old->active_lock.id, cur->active_lock.id, env->idmap_scratch))
+	    !check_ids(old->active_lock.id, cur->active_lock.id, &env->idmap_scratch))
 		return false;
 
 	if (old->active_rcu_lock != cur->active_rcu_lock)
