CVE-2024-1544

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.