CVE-2024-1544

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

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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.

CVSS 4.1 · Средний · EPSS 0,3% · Есть исправление

Опубликовано

2024-08-27T18:44:52.770Z

Обновлено

2026-01-27T21:58:42.146Z

Стек: system

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