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

CVE-2024-1544 is fixed in wolfssl on 1 platform by DEBIAN-CVE-2024-1544 (version 5.7.2-0.1), released August 27, 2024. It is not reported as exploited. Patch Radar priority: Routine.

- Web page: https://patchblox.com/security/cve/CVE-2024-1544
- Priority: Routine
- CVSS: 4.9 (Moderate)
- EPSS: 0.0035
- CISA KEV: not listed
- Exploited (vendor report): no
- Publicly disclosed: no
- Published: Aug 27, 2024
- Weakness: Observable Discrepancy
- Vendor advisory: https://msrc.microsoft.com/update-guide/vulnerability/CVE-2024-1544

## 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.

## Where it's fixed

| Platform | Product | Fixed in | Fix | Released |
|---|---|---|---|---|
| Linux | wolfssl Debian 13.5 (trixie) | 5.7.2-0.1 | [DEBIAN-CVE-2024-1544](https://patchblox.com/security/data/fix/linux/debian-cve-2024-1544.md) | Aug 27, 2024 |

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