CVE-2024-1544: ECDSA nonce bias caused by truncation

Severity: medium (CVSS 4.9 v3.1)
Exploited in the wild: not listed in CISA KEV
EPSS: 0.3% probability of exploitation in the next 30 days
Public exploit or detection template: none known
Published: 2024-08-27 · updated 2026-06-17
Weakness: CWE-203

Description

Generating the ECDSA nonce k samples a random number r and then truncates this randomness with a modular reduction mod n where n is the order of the elliptic curve. Meaning k = r mod n. The division used during the reduction estimates a factor q_e by dividing the upper two digits (a digit having e.g. a size of 8 byte) of r by the upper digit of n and then decrements q_e in a loop until it has the correct size. Observing the number of times q_e is decremented through a control-flow revealing side-channel reveals a bias in the most significant bits of k. Depending on the curve this is either a negligible bias or a significant bias large enough to reconstruct k with lattice reduction methods. For SECP160R1, e.g., we find a bias of 15 bits.

Affected products

wolfSSL: before 5.7.2 — fixed in 5.7.2

How to fix

Upgrade to a fixed version: wolfSSL 5.7.2. Check the vendor advisory for mitigations.

References

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