[qrmn]

Of course, the Elligator and related mappings allow for (a subset of) valid curve points to be mapped to indistinguishable bit strings, which is very handy in some protocols. A backdoor merchant using Elligator 2, or Elligator Squared, in this particular setup wouldn't be detectable.

[adg001]

Exactly. I attack and repair the Curve25519 backdoor using Elligator in illusoryTLS, a talk delivered at HITB SecConf (and other conferences) based on my entry to the first Underhanded Crypto Contest http://illusoryTLS.com/

Code at https://github.com/secYOUre/rsaelligatorbd

[makomk]

I don't think you even need anything that fancy - pretty sure just encrypting the leak again with a fixed AES key would do the job well enough. If someone manages to get hold of the AES key they could use it distinguish backdoored keys from random, but at that point you've been caught anyway.

[adg001]

There are a number of properties that a carefully designed asymmetric backdoor is expected to have. NOBUS (Nobody But Us) and forward-secrecy are among them. With a forward-secret backdoor, if a reverse­-engineer breaches the key-generator, then the previously stolen information remains confidential.

If the key-generator embeds a secret key (for seed exfiltration), the backdoor design will never be robust against reverse engineering. In fact, exposure of the embedded key gives to the attacker the ability to retroactively factor with ease the moduli of public-keys generated in the past, and recover the private-keys.

The designs of Curve25519 and illusoryTLS embed only an elliptic-curve public-key. Therefore, the exploitation requires access to the associated private-key /i.e., NOBUS property).

For the longer story about the sorrow state of the Web PKI and the nitty gritty details on this cryptographic backdoor, you may want to review the illusoryTLS whitepaper http://conference.hitb.org/hitbsecconf2015ams/wp-content/upl...