ECDSA nonce bias caused by truncation
Summary
ECDSA nonce bias caused by truncation
Original description
The description as published by the source.
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.
Fix status by distribution
Fixed packages published by each distribution for this CVE
- Debian DEBIAN-CVE-2024-1544 wolfssl
- Ubuntu UBUNTU-CVE-2024-1544 wolfssl
References
- advisory github.com
- advisory nvd.nist.gov
- patch github.com
- web github.com