54 lines
1.8 KiB
Plaintext
54 lines
1.8 KiB
Plaintext
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We should try to be rigorous about this, which seemingly shows an
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issue.
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There is a call to GNUNET_CRYPTO_kdf in
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bkey = rsa_blinding_key_derive (len, bks);
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that gives exactly len bits where
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len = GNUNET_CRYPTO_rsa_public_key_len (pkey);
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Now r = 2^(len-1)/pkey.n is the probability that a set high bit being
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okay, meaning bkey < pkey.n. It follows that (1-r)/2 of the time bkey >
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pkey.n making the effective bkey be
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bkey mod pkey.n = bkey - pkey.n
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so the effective bkey has its high bit set with probability r/2.
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We expect r to be close to 1/2 if the exchange is honest, but the
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exchange can choose r otherwise.
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In blind signing, the exchange sees
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B = bkey * S mod pkey.n
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On deposit, the exchange sees S so they can compute bkey' = B/S mod
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pkey.n for all B they recorded to see if bkey' has it's high bit set.
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Also, note the exchange can compute 1/S efficiently since they know the
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factors of pkey.n.
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I suppose that happens with probability r/(1+r) if its the wrong B, not
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completely sure. If otoh we've the right B, then we've the probability
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r/2 of a set high bit in the effective bkey.
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Interestingly, r^2-r has a maximum at the default r=1/2 anyways, giving
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the wrong and right probabilities 1/3 and 1/4, respectively.
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I fear this gives the exchange a meaningful fraction of a bit of
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information per coin involved in the transaction. It sounds damaging if
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numerous coins were involved. And it could run across transactions in
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some scenarios.
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I suspect we need a more uniform deterministic pseudo-random number
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generator for blinding factors. Just fyi, our old call to
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gcry_mpi_randomize had this same problem.
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As I said before, I do not believe this to be a problem for the full
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domain hash, but maybe my setting that second to high bit makes it worse
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or something, not sure.
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It's late, maybe I've worked out some probabilities wrong, but looks
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right.
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