Breaking ECDSA with Two Affinely Related Nonces

The security of the Elliptic Curve Digital Signature Algorithm ECDSA depends on the uniqueness and secrecy of the nonce, which is used in each signature. While it is well understood that nonce $k$ reuse across two distinct messages can leak the private key, we show that even if a distinct value i...

UBUNTU-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 qe by dividing the upper two digits a digit having e....

CVE-2024-1544 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 qe by dividing the upper two digits a digit having e....

CVE-2024-1544 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 qe by dividing the upper two digits a digit having e....