Are linkable ring signatures available in Ethereum?

Question

Are transactions with ring signatures available in Ethereum? There should be as anonymity/fungibility is important.

Also, I think Vitalk Buterin mentioned it may be possible to implement an EVM operation that allows for less gas usage for ring transactions. Did I get that right? If so, what is the operation and is anyone working on implementing it in the EVM?

Answer 1

In a January 15 2016 blog post, Vitalik mentions:

Ring signatures are more mathematically involved than simple signatures, but they are quite practical to implement; some sample code for ring signatures on top of Ethereum can be found here.

Here is a snippet:

def verify(msgHash:bytes32, x0:uint256, s:uint256[], Ix:uint256, Iy:uint256, pub_xs:uint256[], pub_ys:bytes):
    # Number of pubkeys
    n = len(pub_xs)
    # Decompress the provided I value
    Iy = recover_y(Ix, Iy)
    # Store the list of intermediate values in the "ring"
    e = array(n + 1)
    # Set the first value in the ring to that provided in the signature
    e[0] = [x0, sha3(x0)]
    i = 1
    while i < n + 1:
        prev_i = (i - 1) % n
        # Decompress the public key
        pub_yi = recover_y(pub_xs[i % n], bit(pub_ys, i % n))
        # Create the next values in the ring based on the provided s value
        k1 = ecmul(Gx, Gy, 1, s[prev_i])
        k2 = ecmul(pub_xs[i % n], pub_yi, 1, e[prev_i][1])
        pub1 = decompose(ecsubtract(k1, k2))
        k3 = self.hash_pubkey_to_pubkey([pub_xs[i % n], pub_yi], outitems=2)
        k4 = ecmul(k3[0], k3[1], 1, s[prev_i])
        k5 = ecmul(Ix, Iy, 1, e[prev_i][1])
        pub2 = decompose(ecsubtract(k4, k5))
        left = sha3([msgHash, pub1[0], pub1[1], pub2[0], pub2[1]]:arr)
        right = sha3(left)
        # FOR DEBUGGING
        # if i >= 1:
        #     log(type=PubkeyLogEvent, pub_xs[i], pub_yi)
        #     log(type=PubkeyLogEvent, pub1[0], pub1[1])
        #     log(type=PubkeyLogEvent, pub2[0], pub2[1])
        #     log(type=ValueLogEvent, left)
        #     log(type=ValueLogEvent, right)
        e[i] = [left, right]
        i += 1
    # Check that the ring is consistent
    return((e[n][0] == e[0][0] and e[n][1] == e[0][1]):bool)

Note, the top of the file does say "TOTALLY NOT TESTED AND LIKELY BROKEN AT THIS POINT; AWAITING A TEST SUITE".

EDIT by user @bleepbloop: Vitalik has confirmed that this is a very early PoC and not fully functional at present.

Looking at the code again, I think I = Ix, Iy is the 'tag' that makes this scheme linkable, there just isn't yet a function to store and compare the I values that have been previously seen, which would be needed in order to prevent double spending/double withdrawals.