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.
| Métrique | Valeur | Interprétation |
|---|---|---|
|
AV (Vecteur d'Attaque)
Attack Vector
|
Local (L)
|
Exploit nécessite un accès local au système |
|
AC (Complexité d'Attaque)
Attack Complexity
|
High (H)
|
Conditions spécifiques doivent être réunies pour exploiter |
|
PR (Privilèges Requis)
Privileges Required
|
High (H)
|
Authentifié avec privilèges administratifs |
|
UI (Interaction Utilisateur)
User Interaction
|
None (N)
|
Aucune interaction utilisateur nécessaire |
|
S (Périmètre)
Scope
|
Unchanged (U)
|
Impact reste dans le périmètre du composant compromis |
|
C (Impact Confidentialité)
Confidentiality Impact
|
High (H)
|
Divulgation totale d'informations |
|
I (Impact Intégrité)
Integrity Impact
|
None (N)
|
Aucune modification de données possible |
|
A (Impact Disponibilité)
Availability Impact
|
None (N)
|
Aucune interruption de service |
ECDSA nonce bias caused by truncation