Message-Id: <20241214190413.25587-2-m.shachnai@gmail.com>
Date: Sat, 14 Dec 2024 14:04:10 -0500
From: Matan Shachnai <m.shachnai@...il.com>
To: ast@...nel.org
Cc: harishankar.vishwanathan@...il.com,
	srinivas.narayana@...gers.edu,
	santosh.nagarakatte@...gers.edu,
	m.shachnai@...gers.edu,
	Matan Shachnai <m.shachnai@...il.com>,
	Daniel Borkmann <daniel@...earbox.net>,
	John Fastabend <john.fastabend@...il.com>,
	Andrii Nakryiko <andrii@...nel.org>,
	Martin KaFai Lau <martin.lau@...ux.dev>,
	Eduard Zingerman <eddyz87@...il.com>,
	Song Liu <song@...nel.org>,
	Yonghong Song <yonghong.song@...ux.dev>,
	KP Singh <kpsingh@...nel.org>,
	Stanislav Fomichev <sdf@...ichev.me>,
	Hao Luo <haoluo@...gle.com>,
	Jiri Olsa <jolsa@...nel.org>,
	Mykola Lysenko <mykolal@...com>,
	Shuah Khan <shuah@...nel.org>,
	Cupertino Miranda <cupertino.miranda@...cle.com>,
	Menglong Dong <menglong8.dong@...il.com>,
	bpf@...r.kernel.org,
	linux-kernel@...r.kernel.org,
	linux-kselftest@...r.kernel.org
Subject: [PATCH bpf-next v3 1/2] bpf, verifier: Improve precision of BPF_MUL

This patch improves (or maintains) the precision of register value tracking
in BPF_MUL across all possible inputs. It also simplifies
scalar32_min_max_mul() and scalar_min_max_mul().

As it stands, BPF_MUL is composed of three functions:

case BPF_MUL:
  tnum_mul();
  scalar32_min_max_mul();
  scalar_min_max_mul();

The current implementation of scalar_min_max_mul() restricts the u64 input
ranges of dst_reg and src_reg to be within [0, U32_MAX]:

    /* Both values are positive, so we can work with unsigned and
     * copy the result to signed (unless it exceeds S64_MAX).
     */
    if (umax_val > U32_MAX || dst_reg->umax_value > U32_MAX) {
        /* Potential overflow, we know nothing */
        __mark_reg64_unbounded(dst_reg);
        return;
    }

This restriction is done to avoid unsigned overflow, which could otherwise
wrap the result around 0, and leave an unsound output where umin > umax. We
also observe that limiting these u64 input ranges to [0, U32_MAX] leads to
a loss of precision. Consider the case where the u64 bounds of dst_reg are
[0, 2^34] and the u64 bounds of src_reg are [0, 2^2]. While the
multiplication of these two bounds doesn't overflow and is sound [0, 2^36],
the current scalar_min_max_mul() would set the entire register state to
unbounded.

Importantly, we update BPF_MUL to allow signed bound multiplication
(i.e. multiplying negative bounds) as well as allow u64 inputs to take on
values from [0, U64_MAX]. We perform signed multiplication on two bounds
[a,b] and [c,d] by multiplying every combination of the bounds
(i.e. a*c, a*d, b*c, and b*d) and checking for overflow of each product. If
there is an overflow, we mark the signed bounds unbounded [S64_MIN, S64_MAX].
In the case of no overflow, we take the minimum of these products to
be the resulting smin, and the maximum to be the resulting smax.

The key idea here is that if there’s no possibility of overflow, either
when multiplying signed bounds or unsigned bounds, we can safely multiply the
respective bounds; otherwise, we set the bounds that exhibit overflow
(during multiplication) to unbounded.

if (check_mul_overflow(*dst_umax, src_reg->umax_value, dst_umax) ||
       (check_mul_overflow(*dst_umin, src_reg->umin_value, dst_umin))) {
        /* Overflow possible, we know nothing */
        dst_reg->umin_value = 0;
        dst_reg->umax_value = U64_MAX;
    }
  ...

Below, we provide an example BPF program (below) that exhibits the
imprecision in the current BPF_MUL, where the outputs are all unbounded. In
contrast, the updated BPF_MUL produces a bounded register state:

BPF_LD_IMM64(BPF_REG_1, 11),
BPF_LD_IMM64(BPF_REG_2, 4503599627370624),
BPF_ALU64_IMM(BPF_NEG, BPF_REG_2, 0),
BPF_ALU64_IMM(BPF_NEG, BPF_REG_2, 0),
BPF_ALU64_REG(BPF_AND, BPF_REG_1, BPF_REG_2),
BPF_LD_IMM64(BPF_REG_3, 809591906117232263),
BPF_ALU64_REG(BPF_MUL, BPF_REG_3, BPF_REG_1),
BPF_MOV64_IMM(BPF_REG_0, 1),
BPF_EXIT_INSN(),

Verifier log using the old BPF_MUL:

func#0 @0
0: R1=ctx() R10=fp0
0: (18) r1 = 0xb                      ; R1_w=11
2: (18) r2 = 0x10000000000080         ; R2_w=0x10000000000080
4: (87) r2 = -r2                      ; R2_w=scalar()
5: (87) r2 = -r2                      ; R2_w=scalar()
6: (5f) r1 &= r2                      ; R1_w=scalar(smin=smin32=0,smax=umax=smax32=umax32=11,var_off=(0x0; 0xb)) R2_w=scalar()
7: (18) r3 = 0xb3c3f8c99262687        ; R3_w=0xb3c3f8c99262687
9: (2f) r3 *= r1                      ; R1_w=scalar(smin=smin32=0,smax=umax=smax32=umax32=11,var_off=(0x0; 0xb)) R3_w=scalar()
...

Verifier using the new updated BPF_MUL (more precise bounds at label 9)

func#0 @0
0: R1=ctx() R10=fp0
0: (18) r1 = 0xb                      ; R1_w=11
2: (18) r2 = 0x10000000000080         ; R2_w=0x10000000000080
4: (87) r2 = -r2                      ; R2_w=scalar()
5: (87) r2 = -r2                      ; R2_w=scalar()
6: (5f) r1 &= r2                      ; R1_w=scalar(smin=smin32=0,smax=umax=smax32=umax32=11,var_off=(0x0; 0xb)) R2_w=scalar()
7: (18) r3 = 0xb3c3f8c99262687        ; R3_w=0xb3c3f8c99262687
9: (2f) r3 *= r1                      ; R1_w=scalar(smin=smin32=0,smax=umax=smax32=umax32=11,var_off=(0x0; 0xb)) R3_w=scalar(smin=0,smax=umax=0x7b96bb0a94a3a7cd,var_off=(0x0; 0x7fffffffffffffff))
...

Finally, we proved the soundness of the new scalar_min_max_mul() and
scalar32_min_max_mul() functions. Typically, multiplication operations are
expensive to check with bitvector-based solvers. We were able to prove the
soundness of these functions using Non-Linear Integer Arithmetic (NIA)
theory. Additionally, using Agni [2,3], we obtained the encodings for
scalar32_min_max_mul() and scalar_min_max_mul() in bitvector theory, and
were able to prove their soundness using 8-bit bitvectors (instead of
64-bit bitvectors that the functions actually use).

In conclusion, with this patch,

1. We were able to show that we can improve the overall precision of
   BPF_MUL. We proved (using an SMT solver) that this new version of
   BPF_MUL is at least as precise as the current version for all inputs
   and more precise for some inputs.

2. We are able to prove the soundness of the new scalar_min_max_mul() and
   scalar32_min_max_mul(). By leveraging the existing proof of tnum_mul
   [1], we can say that the composition of these three functions within
   BPF_MUL is sound.

[1] https://ieeexplore.ieee.org/abstract/document/9741267
[2] https://link.springer.com/chapter/10.1007/978-3-031-37709-9_12
[3] https://people.cs.rutgers.edu/~sn349/papers/sas24-preprint.pdf

Co-developed-by: Harishankar Vishwanathan <harishankar.vishwanathan@...il.com>
Signed-off-by: Harishankar Vishwanathan <harishankar.vishwanathan@...il.com>
Co-developed-by: Srinivas Narayana <srinivas.narayana@...gers.edu>
Signed-off-by: Srinivas Narayana <srinivas.narayana@...gers.edu>
Co-developed-by: Santosh Nagarakatte <santosh.nagarakatte@...gers.edu>
Signed-off-by: Santosh Nagarakatte <santosh.nagarakatte@...gers.edu>
Signed-off-by: Matan Shachnai <m.shachnai@...il.com>
---
 kernel/bpf/verifier.c | 72 +++++++++++++++++++------------------------
 1 file changed, 32 insertions(+), 40 deletions(-)

diff --git a/kernel/bpf/verifier.c b/kernel/bpf/verifier.c
index c855e7905c35..5b0f83cc7f4d 100644
--- a/kernel/bpf/verifier.c
+++ b/kernel/bpf/verifier.c
@@ -14118,64 +14118,56 @@ static void scalar_min_max_sub(struct bpf_reg_state *dst_reg,
 static void scalar32_min_max_mul(struct bpf_reg_state *dst_reg,
 				 struct bpf_reg_state *src_reg)
 {
-	s32 smin_val = src_reg->s32_min_value;
-	u32 umin_val = src_reg->u32_min_value;
-	u32 umax_val = src_reg->u32_max_value;
+	s32 *dst_smin = &dst_reg->s32_min_value;
+	s32 *dst_smax = &dst_reg->s32_max_value;
+	u32 *dst_umin = &dst_reg->u32_min_value;
+	u32 *dst_umax = &dst_reg->u32_max_value;
+	s32 tmp_prod[4];
 
-	if (smin_val < 0 || dst_reg->s32_min_value < 0) {
-		/* Ain't nobody got time to multiply that sign */
-		__mark_reg32_unbounded(dst_reg);
-		return;
-	}
-	/* Both values are positive, so we can work with unsigned and
-	 * copy the result to signed (unless it exceeds S32_MAX).
-	 */
-	if (umax_val > U16_MAX || dst_reg->u32_max_value > U16_MAX) {
-		/* Potential overflow, we know nothing */
-		__mark_reg32_unbounded(dst_reg);
-		return;
+	if (check_mul_overflow(*dst_umax, src_reg->u32_max_value, dst_umax) ||
+	    check_mul_overflow(*dst_umin, src_reg->u32_min_value, dst_umin)) {
+		/* Overflow possible, we know nothing */
+		dst_reg->u32_min_value = 0;
+		dst_reg->u32_max_value = U32_MAX;
 	}
-	dst_reg->u32_min_value *= umin_val;
-	dst_reg->u32_max_value *= umax_val;
-	if (dst_reg->u32_max_value > S32_MAX) {
+	if (check_mul_overflow(*dst_smin, src_reg->s32_min_value, &tmp_prod[0]) ||
+	    check_mul_overflow(*dst_smin, src_reg->s32_max_value, &tmp_prod[1]) ||
+	    check_mul_overflow(*dst_smax, src_reg->s32_min_value, &tmp_prod[2]) ||
+	    check_mul_overflow(*dst_smax, src_reg->s32_max_value, &tmp_prod[3])) {
 		/* Overflow possible, we know nothing */
 		dst_reg->s32_min_value = S32_MIN;
 		dst_reg->s32_max_value = S32_MAX;
 	} else {
-		dst_reg->s32_min_value = dst_reg->u32_min_value;
-		dst_reg->s32_max_value = dst_reg->u32_max_value;
+		dst_reg->s32_min_value = min_array(tmp_prod, 4);
+		dst_reg->s32_max_value = max_array(tmp_prod, 4);
 	}
 }
 
 static void scalar_min_max_mul(struct bpf_reg_state *dst_reg,
 			       struct bpf_reg_state *src_reg)
 {
-	s64 smin_val = src_reg->smin_value;
-	u64 umin_val = src_reg->umin_value;
-	u64 umax_val = src_reg->umax_value;
+	s64 *dst_smin = &dst_reg->smin_value;
+	s64 *dst_smax = &dst_reg->smax_value;
+	u64 *dst_umin = &dst_reg->umin_value;
+	u64 *dst_umax = &dst_reg->umax_value;
+	s64 tmp_prod[4];
 
-	if (smin_val < 0 || dst_reg->smin_value < 0) {
-		/* Ain't nobody got time to multiply that sign */
-		__mark_reg64_unbounded(dst_reg);
-		return;
-	}
-	/* Both values are positive, so we can work with unsigned and
-	 * copy the result to signed (unless it exceeds S64_MAX).
-	 */
-	if (umax_val > U32_MAX || dst_reg->umax_value > U32_MAX) {
-		/* Potential overflow, we know nothing */
-		__mark_reg64_unbounded(dst_reg);
-		return;
+	if (check_mul_overflow(*dst_umax, src_reg->umax_value, dst_umax) ||
+	    check_mul_overflow(*dst_umin, src_reg->umin_value, dst_umin)) {
+		/* Overflow possible, we know nothing */
+		dst_reg->umin_value = 0;
+		dst_reg->umax_value = U64_MAX;
 	}
-	dst_reg->umin_value *= umin_val;
-	dst_reg->umax_value *= umax_val;
-	if (dst_reg->umax_value > S64_MAX) {
+	if (check_mul_overflow(*dst_smin, src_reg->smin_value, &tmp_prod[0]) ||
+	    check_mul_overflow(*dst_smin, src_reg->smax_value, &tmp_prod[1]) ||
+	    check_mul_overflow(*dst_smax, src_reg->smin_value, &tmp_prod[2]) ||
+	    check_mul_overflow(*dst_smax, src_reg->smax_value, &tmp_prod[3])) {
 		/* Overflow possible, we know nothing */
 		dst_reg->smin_value = S64_MIN;
 		dst_reg->smax_value = S64_MAX;
 	} else {
-		dst_reg->smin_value = dst_reg->umin_value;
-		dst_reg->smax_value = dst_reg->umax_value;
+		dst_reg->smin_value = min_array(tmp_prod, 4);
+		dst_reg->smax_value = max_array(tmp_prod, 4);
 	}
 }
 
-- 
2.25.1

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