CVE-2025-30147 – The curious case of subgroup check on Besu

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3 months ago

Due to Marius Van Der Wijden for creating the check case and statetest, and for serving to the Besu staff verify the difficulty. Additionally, kudos to the Besu staff, the EF safety staff, and Kevaundray Wedderburn. Moreover, due to Justin Traglia, Marius Van Der Wijden, Benedikt Wagner, and Kevaundray Wedderburn for proofreading. When you’ve got every other questions/feedback, discover me on twitter at @asanso

tl;dr: Besu Ethereum execution client model 25.2.2 suffered from a consensus difficulty associated to the EIP-196/EIP-197 precompiled contract dealing with for the elliptic curve alt_bn128 (a.ok.a. bn254). The problem was mounted in launch 25.3.0.
Here is the complete CVE report.

N.B.: A part of this put up requires some information about elliptic curves (cryptography).

Introduction

The bn254 curve (also called alt_bn128) is an elliptic curve utilized in Ethereum for cryptographic operations. It helps operations resembling elliptic curve cryptography, making it essential for varied Ethereum options. Previous to EIP-2537 and the current Pectra launch, bn254 was the one pairing curve supported by the Ethereum Digital Machine (EVM). EIP-196 and EIP-197 outline precompiled contracts for environment friendly computation on this curve. For extra particulars about bn254, you’ll be able to learn here.

A major safety vulnerability in elliptic curve cryptography is the invalid curve assault, first launched within the paper “Differential fault attacks on elliptic curve cryptosystems”. This assault targets using factors that don’t lie on the right elliptic curve, resulting in potential safety points in cryptographic protocols. For non-prime order curves (like these showing in pairing-based cryptography and in $G_2$ for bn254), it’s particularly necessary that the purpose is within the appropriate subgroup. If the purpose doesn’t belong to the right subgroup, the cryptographic operation might be manipulated, doubtlessly compromising the safety of methods counting on elliptic curve cryptography.

To test if some extent P is legitimate in elliptic curve cryptography, it should be verified that the purpose lies on the curve and belongs to the right subgroup. That is particularly important when the purpose P comes from an untrusted or doubtlessly malicious supply, as invalid or specifically crafted factors can result in safety vulnerabilities. Beneath is pseudocode demonstrating this course of:

# Pseudocode for checking if level P is legitimate
def is_valid_point(P):
    if not is_on_curve(P):    
        return False
    if not is_in_subgroup(P):
        return False
    return True

Subgroup membership checks

As talked about above, when working with any level of unknown origin, it’s essential to confirm that it belongs to the right subgroup, along with confirming that the purpose lies on the right curve. For bn254, that is solely needed for $G_2$ , as a result of $G_1$ is of prime order. An easy technique to check membership in $G$ is to multiply some extent by $r$ , the place $r$ is the cofactor of the curve, which is the ratio between the order of the curve and the order of the bottom level.

Nevertheless, this technique might be expensive in follow as a result of giant dimension of the prime $r$ , particularly for $G_2$ . In 2021, Scott proposed a sooner technique for subgroup membership testing on BLS12 curves utilizing an simply computable endomorphism, making the method 2×, 4×, and 4× faster for various teams (this method is the one laid out in EIP-2537 for quick subgroup checks, as detailed in this document).
Later, Dai et al. generalized Scott’s technique to work for a broader vary of curves, together with BN curves, lowering the variety of operations required for subgroup membership checks. In some instances, the method might be almost free. Koshelev additionally launched a technique for non-pairing-friendly curves using the Tate pairing, which was finally additional generalized to pairing-friendly curves.

The Actual Slim Shady

As you’ll be able to see from the timeline on the finish of this put up, we acquired a report a couple of bug affecting Pectra EIP-2537 on Besu, submitted by way of the Pectra Audit Competition. We’re solely calmly pertaining to that difficulty right here, in case the unique reporter desires to cowl it in additional element. This put up focuses particularly on the BN254 EIP-196/EIP-197 vulnerability.

The unique reporter noticed that in Besu, the is_in_subgroup test was carried out earlier than the is_on_curve test. Here is an instance of what which may appear to be:

# Pseudocode for checking if level P is legitimate
def is_valid_point(P):
    if not is_in_subgroup(P):    
        if not is_on_curve(P):
            return False  
        return False
    return True

Intrigued by the difficulty above on the BLS curve, we determined to check out the Besu code for the BN curve. To my nice shock, we discovered one thing like this:

# Pseudocode for checking if level P is legitimate
def is_valid_point(P):
    if not is_in_subgroup(P):    
        return False
    return True

Wait, what? The place is the is_on_curve test? Precisely—there is not one!!!

Now, to doubtlessly bypass the is_valid_point operate, all you’d must do is present some extent that lies inside the appropriate subgroup however is not truly on the curve.

However wait—is that even attainable?

Properly, sure—however just for specific, well-chosen curves. Particularly, if two curves are isomorphic, they share the identical group construction, which suggests you possibly can craft some extent from the isomorphic curve that passes subgroup checks however would not lie on the meant curve.

Sneaky, proper?

Did you say isomorpshism?

Be at liberty to skip this part in case you’re not within the particulars—we’re about to go a bit deeper into the mathematics.

Let $Fqmathbb{F}_q$ be a finite subject with attribute completely different from 2 and three, that means $q = p^f$ for some prime $p \geq 5$ and integer $f \geq 1$ . We take into account elliptic curves $E$ over $Fqmathbb{F}_q$ given by the brief Weierstraß equation:

y^2 = x^3 + A x + B

the place $A$ and $B$ are constants satisfying $4A3+27B2≠04A^3 + 27B^2 neq 0$ .^[This condition ensures the curve is non-singular; if it were violated, the equation would define a singular point lacking a well-defined tangent, making it impossible to perform meaningful self-addition. In such cases, the object is not technically an elliptic curve.]

Curve Isomorphisms

Two elliptic curves are thought of isomorphic^[To exploit the vulnerabilities described here, we really want isomorphic curves, not just isogenous curves.] if they are often associated by an affine change of variables. Such transformations protect the group construction and be sure that level addition stays constant. It may be proven that the one attainable transformations between two curves briefly Weierstraß type take the form:

(e^2 x, e^3 y)

for some nonzero $mathbb{F}_q$ . Making use of this transformation to the curve equation leads to:

y^2 = x^3 + A e^{4} x + B e^{6}

The $j$ -invariant of a curve is outlined as:

frac{4A^3}{4A^3 + 27B^2}

Each ingredient of $Fqmathbb{F}_q$ could be a attainable $j$ -invariant.^[Both BLS and BN curves have a j-invariant equal to 0, which is really special.] When two elliptic curves share the identical $j$ -invariant, they’re both isomorphic (within the sense described above) or they’re twists of one another.^[We omit the discussion about twists here, as they are not relevant to this case.]

Exploitability

At this level, all that is left is to craft an appropriate level on a fastidiously chosen curve, and voilà—le jeu est fait.

You’ll be able to strive the check vector utilizing this link and benefit from the trip.

Conclusion

On this put up, we explored the vulnerability in Besu’s implementation of elliptic curve checks. This flaw, if exploited, might enable an attacker to craft some extent that passes subgroup membership checks however doesn’t lie on the precise curve. The Besu staff has since addressed this difficulty in launch 25.3.0. Whereas the difficulty was remoted to Besu and didn’t have an effect on different purchasers, discrepancies like this elevate necessary considerations for multi-client ecosystems like Ethereum. A mismatch in cryptographic checks between purchasers may end up in divergent habits—the place one consumer accepts a transaction or block that one other rejects. This type of inconsistency can jeopardize consensus and undermine belief within the community’s uniformity, particularly when refined bugs stay unnoticed throughout implementations. This incident highlights why rigorous testing and strong safety practices are completely important—particularly in blockchain methods, the place even minor cryptographic missteps can ripple out into main systemic vulnerabilities. Initiatives just like the Pectra audit competitors play an important function in proactively surfacing these points earlier than they attain manufacturing. By encouraging numerous eyes to scrutinize the code, such efforts strengthen the general resilience of the ecosystem.

Timeline

15-03-2025 – Bug affecting Pectra EIP-2537 on Besu reported by way of the Pectra Audit Competition.
17-03-2025 – Found and reported the EIP-196/EIP-197 difficulty to the Besu staff.
17-03-2025 – Marius Van Der Wijden created a check case and statetest to breed the difficulty.
17-03-2025 – The Besu staff promptly acknowledged and fixed the difficulty.

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