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.
Weakness
The product behaves differently or sends different responses under different circumstances in a way that is observable to an unauthorized actor, which exposes security-relevant information about the state of the product, such as whether a particular operation was successful or not.
Potential Mitigations
- Compartmentalize the system to have “safe” areas where trust boundaries can be unambiguously drawn. Do not allow sensitive data to go outside of the trust boundary and always be careful when interfacing with a compartment outside of the safe area.
- Ensure that appropriate compartmentalization is built into the system design, and the compartmentalization allows for and reinforces privilege separation functionality. Architects and designers should rely on the principle of least privilege to decide the appropriate time to use privileges and the time to drop privileges.
- Ensure that error messages only contain minimal details that are useful to the intended audience and no one else. The messages need to strike the balance between being too cryptic (which can confuse users) or being too detailed (which may reveal more than intended). The messages should not reveal the methods that were used to determine the error. Attackers can use detailed information to refine or optimize their original attack, thereby increasing their chances of success.
- If errors must be captured in some detail, record them in log messages, but consider what could occur if the log messages can be viewed by attackers. Highly sensitive information such as passwords should never be saved to log files.
- Avoid inconsistent messaging that might accidentally tip off an attacker about internal state, such as whether a user account exists or not.
References