From e1e8ffbd9b87a479e8663b1eb0630bce4a7f663f Mon Sep 17 00:00:00 2001 From: Matan Shachnai Date: Tue, 26 Nov 2024 12:38:43 -0500 Subject: [PATCH] bpf, verifier: Improve precision of BPF_MUL MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 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. The key idea of our patch is that if there’s no possibility of overflow, we can multiply the unsigned bounds; otherwise, we set the 64-bit bounds to [0, U64_MAX], marking them as 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; } ... Now, to update the signed bounds based on the unsigned bounds, we need to ensure that the unsigned bounds don't cross the signed boundary (i.e., if ((s64)reg->umin_value <= (s64)reg->umax_value)). We observe that this is done anyway by __reg_deduce_bounds later, so we can just set signed bounds to unbounded [S64_MIN, S64_MAX]. Deferring the assignment of s64 bounds to reg_bounds_sync removes the current redundancy in scalar_min_max_mul(), which currently sets the s64 bounds based on the u64 bounds only in the case where umin <= umax <= 2^(63)-1. 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 16-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. 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 Signed-off-by: Harishankar Vishwanathan Co-developed-by: Srinivas Narayana Signed-off-by: Srinivas Narayana Co-developed-by: Santosh Nagarakatte Signed-off-by: Santosh Nagarakatte Signed-off-by: Matan Shachnai --- kernel/bpf/verifier.c | 72 +++++++++++++++---------------------------- 1 file changed, 24 insertions(+), 48 deletions(-) diff --git a/kernel/bpf/verifier.c b/kernel/bpf/verifier.c index 1c4ebb326785d..172816e8f1a48 100644 --- a/kernel/bpf/verifier.c +++ b/kernel/bpf/verifier.c @@ -13827,65 +13827,41 @@ 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; + u32 *dst_umin = &dst_reg->u32_min_value; + u32 *dst_umax = &dst_reg->u32_max_value; - 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; - } - 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_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->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->u32_min_value = 0; + dst_reg->u32_max_value = U32_MAX; } + + /* Set signed bounds to unbounded and improve precision in + * reg_bounds_sync() + */ + dst_reg->smin_value = S32_MIN; + dst_reg->smax_value = S32_MAX; } 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; + u64 *dst_umin = &dst_reg->umin_value; + u64 *dst_umax = &dst_reg->umax_value; - 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; - } - dst_reg->umin_value *= umin_val; - dst_reg->umax_value *= umax_val; - if (dst_reg->umax_value > S64_MAX) { + 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->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->umin_value = 0; + dst_reg->umax_value = U64_MAX; } + + /* Set signed bounds to unbounded and improve precision in + * reg_bounds_sync() + */ + dst_reg->smin_value = S64_MIN; + dst_reg->smax_value = S64_MAX; } static void scalar32_min_max_and(struct bpf_reg_state *dst_reg,