4.1 MEDIUM
- CVSS version: 3.1
- Attack vector (AV): LOCAL
- Attack complexity (AC): HIGH
- Privileges required (PR): HIGH
- User interaction (UI): NONE
- Scope (S): UNCHANGED
- Confidentiality impact (C): HIGH
- Integrity impact (I): NONE
- Availability impact (A): NONE
ECDSA nonce bias caused by truncation
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.
References
Affected products
- =<5.6.4
Package maintainers
-
@vifino Adrian Pistol <vifino@tty.sh>
-
@fabaff Fabian Affolter <mail@fabian-affolter.ch>