Allele Security Alert
Platform DH key recovery via invalid curve attack
AMD EPYC server platforms
AMD EPYC server platforms (codename “Naples”) running SEV firmware version 0.17 build 11 and below are affected
AMD EPYC server platforms (codename “Naples”) running SEV firmware version 0.17 build 22
Proof of concept
The SEV elliptic-curve (ECC) implementation was found to be vulnerable to an invalid curve attack. At launch-start command, an attacker can send small order ECC points not on the official NIST curves, and force the SEV firmware to multiply a small order point by the firmware’s private DH scalar.
By collecting enough modular residues, an attacker can recover the complete PDH private key. With the PDH, an attacker can recover the session key and the VM’s launch secret. This breaks the confidentiality guarantees offered by SEV.
Key exchange during VM launch
1. The PSP publishes its PDH public key through SEV_PDH_CERT_EXPORT command. This key is computed by multiplying the ECC generator (NIST P256/P384 curves are supported) by the PDH private key: A<-G*k, where k, the private key, is randomly generated in the range (1, order(G)).
2. The client generates its private DH key, s, and computes the shared key C<-A*s=G*k*s. C is the shared point on the curve. Its x-coordinate is hashed and used as the master shared secret. Two keys KEK/KIK are derived from the master secret, and used to protect (encryption+integrity) the session keys.
3. The client computes its public key B<-G*s and sends it to the PSP through the SEV_LAUNCH_START command.
4. The PSP computes the shared key C by multiplying the client’s public key by its PDH private scalar: C<-B*k=G*s*k. Like the client, the PSP takes C’s x coordinate, computes the master shared secret and derives the KEK/KIK. These are used to unwrap the session keys. See API specification  for details.
ECDH security relies on the generator point, G, having a large order and on the discrete logarithm problem being hard for the curve.
Note that in step 4, the PSP performs a computation with its private key on user supplied data – the client’s public point.
Invalid curve attack
ECC point multiplication relies on a point addition primitive. There are different implementations for ECC point addition. A common one is based on the short Weierstrass ECC form, as described in . Note that the curve’s “b” equation parameter is never used.
An invalid curve attack is where the ECDH point multiplication is done on a different curve – different (a,b) parameters. This becomes possible in the short Weierstrass point addition function since the “b” parameter is not used. On this curve, the point has a small prime order. By trying all possible values for the small order point, an attacker can recover the private scalar bits (modulo the order). The modular residues are assembled offline using the Chinese Remainder Theorem, leading to a full key recovery. See the original paper  on invalid curve attacks, or a more recent paper  on the topic.
Cfir Cohen (Google Cloud Security Team)
AMD-SEV: Platform DH key recovery via invalid curve attack (CVE-2019-9836)
AMD Product Security | AMD
Secure Encrypted Virtualization API Version 0.17
Short Weierstrass curves
Differential Fault Attacks on Elliptic Curve Cryptosystems (Extended Abstract)
Breaking the Bluetooth Pairing – Fixed Coordinate Invalid Curve Attack
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Last modified: September 2, 2019