CVE-2024-1544
ECDSA nonce bias caused by truncation
- Published
- Updated
- Reserved
- Assigned by
- wolfSSL
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.
Timeline
ID reserved
By wolfSSL
- 6 months later
· 6 months later
Published
- 17 months later
· 17 months later
Record updated
Changes after publication (a new score, a public exploit, EPSS crossing 1, 10 or 50 %, leaving KEV) are kept since November 2026; earlier ones are not known.
Scores
| Scored by | CVSS | Score | Vector |
|---|---|---|---|
| wolfSSLCNA (assigner) | 3.1 | Medium4.1 | CVSS:3.1/AV:L/AC:H/PR:H/UI:N/S:U/C:H/I:N/A:N |
| NVDNVD · Modified | 3.1 | Medium4.9 | CVSS:3.1/AV:N/AC:L/PR:H/UI:N/S:U/C:H/I:N/A:N |
- EPSS (exploitation in 30 days)
- 0.35% · top 71% of all CVEs (7 Nov 2026)
- CISA SSVC
- Exploitation: none · Automatable: no · Technical impact: partial
The list uses the assigner's score when there is one, then CISA's, then NVD's: Medium 4.1.
Weakness
Affected products
References (2)
Sources
The same CVE in the primary databases and aggregators, to check against.
- CVE.org record (opens in a new tab)
- CVE List JSON (GitHub) (opens in a new tab)
- NVD (opens in a new tab)
- FIRST EPSS (opens in a new tab)
- OSV.dev (opens in a new tab)
- GitHub Advisories (opens in a new tab)
- CIRCL Vulnerability-Lookup (opens in a new tab)
Badge for a README or a ticket
[](https://trackcve.app/cve/CVE-2024-1544)Record last updated .