CRYPTO_ELLIGATOR_MAP(3MONOCYPHER) | 3MONOCYPHER | CRYPTO_ELLIGATOR_MAP(3MONOCYPHER) |
crypto_elligator_map
,
crypto_elligator_rev
,
crypto_elligator_key_pair
—
hiding of X25519 public keys
#include
<monocypher.h>
void
crypto_elligator_map
(uint8_t
curve[32], const uint8_t hidden[32]);
int
crypto_elligator_rev
(uint8_t
hidden[32], const uint8_t curve[32],
uint8_t tweak);
void
crypto_elligator_key_pair
(uint8_t
hidden[32], uint8_t secret_key[32],
uint8_t seed[32]);
These functions allow obfuscating X25519 public keys by making them appear effectively indistinguishable from random noise. This is of interest for key exchange protocols that require indistinguishability from randomness, such as padded uniform random blobs (PURBs). They are intended for ephemeral (short-lived, possibly just one-time) X25519 keys, not for long-term public keys. After an initial key exchange involving hidden keys, subsequent key exchange messages should be encrypted instead; see, for example, the Noise Protocol Framework. This is an advanced feature. Unless you are implementing an protocol that requires indistinguishability of all communications from random noise, consider crypto_x25519(3monocypher) instead. Both this family of functions and crypto_x25519(3monocypher) should be used as a building block to implement a key exchange protocol.
For understanding what these functions do, it is important to note that a “public key” in this context refers to a point on Curve25519. This also means that these functions are not compatible with crypto_eddsa_sign(3monocypher) and related functions.
crypto_elligator_rev
()
takes a public key curve and a
tweak, hiding the public key so that it is effectively
indistinguishable from random noise. Note that only
crypto_x25519_dirty_fast(3monocypher)
or
crypto_x25519_dirty_small(3monocypher)
can generate a suitable public key; the
crypto_x25519(3monocypher)
function is insufficient. The tweak must be chosen at
random. Even then, this operation
may fail
because not all curve points are capable of being hidden. In this case,
crypto_elligator_rev
() must be tried again with a
new key pair, though tweak does not need to be
changed. On average, two attempts are needed. Once a suitable public key has
been found, crypto_elligator_rev
() always succeeds
for it. Given the same values for tweak and
curve, crypto_elligator_rev
()
yields the same output value hidden.
crypto_elligator_map
()
performs the inverse operation: It decodes a hidden point to a curve point
on Curve25519.
crypto_elligator_key_pair
()
is a convenience function that generates a secret key and its corresponding
public key, which is effectively indistinguishable from random noise, from a
random seed. The
execution time of this function is unpredictable because it may take
many failures until a key pair could be generated successfully.
crypto_elligator_key_pair
() uses
crypto_x25519_dirty_fast(3monocypher)
internally; if code size is an important concern, its functionality can be
replicated with
crypto_x25519_dirty_small(3monocypher)
instead.
The arguments are:
crypto_elligator_rev
().The hidden and curve arguments may overlap or point at the same buffer.
crypto_elligator_rev
() returns 0 on
success and -1 if the given curve argument is
unsuitable for hiding.
crypto_elligator_map
() and
crypto_elligator_key_pair
() return nothing. They
cannot fail.
Generate a key pair manually using crypto_x25519_dirty_small(3monocypher) instead of its fast variant:
uint8_t sk [32]; /* Secret key output */ uint8_t pk [32]; /* Hidden public key output */ uint8_t tweak; /* Random tweak input */ arc4random_buf(&tweak, 1); for (;;) { arc4random_buf(sk, 32); crypto_x25519_dirty_small(pk, sk); if (crypto_elligator_rev(pk, pk, tweak) == 0) break; } /* Now save the secret key and send the hidden public key. */
Performing a key exchange with the other party's public key having been hidden:
uint8_t hidden_pk [32]; /* Their hidden public key */ uint8_t their_pk [32]; /* Their unhidden public key */ uint8_t your_sk [32]; /* Your secret key */ uint8_t shared_key[32]; /* Shared session key */ crypto_elligator_map(their_pk, hidden_pk); crypto_x25519(shared_key, your_sk, their_pk); /* Wipe secrets if they are no longer needed */ crypto_wipe(your_sk, 32);
crypto_x25519(3monocypher), crypto_x25519_dirty_small(3monocypher), intro(3monocypher)
These functions implement the Elligator 2 mapping for Curve25519. This mapping is incompatible with both the hash-to-curve Internet draft and the implementation of Elligator 2 in libsodium. Elligator 2 was described in: Daniel J. Bernstein, Mike Hamburg, Anna Krasnova, and Tanja Lange, Elligator: Elliptic-curve points indistinguishable from uniform random strings, Association for Computing Machinery, CCS '13: Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security, pp. 967–980, 2013.
The crypto_curve_to_hidden
(),
crypto_hidden_to_curve
(), and
crypto_hidden_key_pair
() functions first appeared in
Monocypher 3.1.0. In Monocypher 4.1.0, they were renamed
crypto_elligator_rev
(),
crypto_elligator_map
(), and
crypto_elligator_key_pair
() respectively.
Monocypher does not perform any input validation. Any deviation from the specified input and output length ranges results in undefined behaviour. Make sure your inputs are correct.
The secret keys for the public keys fed into
crypto_elligator_rev
()
must be chosen
randomly rather than deterministically. Otherwise, the timing
information given by the required number of retries also leaks information
on the secret keys.
These functions help build highly difficult-to-analyse protocols but are insufficient by themselves: Other metadata, such as the number of bytes sent in a packet or the size of the 32-byte random looking string that represents the curve point itself, can be very strong indicators of the use of cryptography. Consider using appropriate padding algorithms, such as PADME, and obscure other metadata as much as possible.
January 26, 2023 | Debian |