4 ms·
As a historical note, the first time I recall seeing the anti-censorship use case was in “Telex” [1] which uses it to steganographically embed a ciphertext into
by matthewdgreen 2y ago
As a historical note, the first time I recall seeing the anti-censorship use case was in “Telex” [1] which uses it to steganographically embed a ciphertext into a TLS random nonce, so that a router in the middle can detect whether the connection should go to its terminus or be routed somewhere else. However the authors of that paper didn’t have a standard primitive for doing this and so they had to make their own approach. Ironically, an even older use of the general approach is the NSA’s Dual EC DRBG generator [2], which has to encode elliptic curve points into random-looking bit sequences as part of its design as a PRNG. They ended up homebrewing that using standard curves by dropping several bits of each X coordinate, which in theory is all they need because there’s no need to go in the inverse direction. However the conjecture is that Dual EC is backdoored, and the backdoor requires an inverse mapping from bitstrings back to points; this has to be achieved by brute-forcing every possible point and testing.
None of this has anything to do with your comment but I love the history of these steganographic tricks.
[1] https://www.usenix.org/conference/usenix-security-11/telex-anticensorship-network-infrastructure https://www.usenix.org/conference/usenix-security-11/telex-a...
[2] https://en.m.wikipedia.org/wiki/Dual_EC_DRBG https://en.m.wikipedia.org/wiki/Dual_EC_DRBG
- pbsd 2y agoKoblitz in "Elliptic Curve Cryptosystems" [1] dedicated section 3 to how to embed binary strings into points and back, which is of course necessary for elliptic curve ElGamal. [1] https://doi.org/10.1090/S0025-5718-1987-0866109-5 https://doi.org/10.1090/S0025-5718-1987-0866109-5