CVE-2024-1544

ECDSA nonce bias caused by truncation

Published Aug 27, 2024 CVSS 3.1 · 4.1 Medium EPSS < 1% KEV · Not listed
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.

Remediation

No solution or workaround provided in the CVE record

Tracking

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Advisories

Source ID Title
EUVD EUVD EUVD-2024-17291 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.
History
Type Values Removed Values Added
First Time appeared Wolfssl
Wolfssl wolfssl
CPEs cpe:2.3:a:wolfssl:wolfssl:*:*:*:*:*:*:*:*
Vendors & Products Wolfssl
Wolfssl wolfssl
Type Values Removed Values Added
Metrics ssvc

{'options': {'Automatable': 'no', 'Exploitation': 'none', 'Technical Impact': 'partial'}, 'version': '2.0.3'}

Type Values Removed Values Added
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.
Title ECDSA nonce bias caused by truncation
Weaknesses CWE-203
References
Metrics cvssV3_1

{'score': 4.1, 'vector': 'CVSS:3.1/AV:L/AC:H/PR:H/UI:N/S:U/C:H/I:N/A:N'}

Weaknesses

Sources

Status
PUBLISHED
Assigner
wolfSSL
Published
Updated
Jan 27, 2026, 9:58 PM
Reserved
Feb 15, 2024, 5:38 PM
Status
Modified
Published
Aug 27, 2024, 7:15 PM
Modified
Jun 17, 2026, 7:04 AM