This is about What Could Go Wrong with the "Rainhill 3" immutable file caps: ​http://jacaranda.org/tahoe/immutable-rainhill-3.svg

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#	what bad thing could happen	how	who could do it	what could they target	what crypto property prevents it	how expensive to brute force [footnote 6]
1	shape-shifter immutable file [footnote 1]	collide read-cap (R,T)	creator of a file	their own file	the hash function's and cap format's collision resistance on the read-cap (R,T). This also depends on the hashes and PRP being correctly implemented, and on the suitability of hash_k as a KDF (key derivation function).	approx sqrt(2.p).2(r+t)/2 [footnotes 4,5]
2	unauthorized read	attack the encryption of K_R with R	anyone	any one file	the security of the PRP, the secrecy of the read-key R, and the suitability of hash_r as a KDF.	p.2min(r,k) / m
3	forgery of immutable file	generate a matching read-cap (R,T) for someone else's file	anyone	any one file	the hash function's and cap format's second-preimage resistance on (R,T). This also depends on the hashes and PRP being correctly implemented, and on the suitability of hash_k and hash_r as a KDF.	p.2r+t / m [footnotes 3,5]
4	unauthorized read	attack the encryption of the plaintext with K1	anyone	any one file	the security of the encryption scheme used for the plaintext, and the secrecy of the encryption key K1. The latter also depends on the security and seeding of the RNG that generated it, and on resistance to attack #2.	p.2k / m
5	unauthorized read	figure out the input to the hash function that generates S and/or V	anyone	any one file	the hash function's onewayness for R -> V or V -> S	brute force on R is #2
6	accidental collision	storage indices (S1,T1) and (S2,T2) collide accidentally	not applicable	any two files	approximately random distribution of hash function outputs	[footnote 2]
7	denial of service	prevent access to servers holding sufficient shares (by controlling some of them, or by attacking them or the network)	anyone	any file	not prevented by crypto	not applicable
8	cause invalid share to verify	generate (EncK_R,EncK_V,Q) that hashes to someone else's T, and copy their S	anyone	any one file	the hash function's second-preimage resistance on T	p.2t / m [footnote 3]

where k = bitlength(K_*), r = bitlength(R), s = bitlength(S) = bitlength(V), t = bitlength(T).

p is the success probability of an attack (0 < p <= 1). m is the number of targets for preimage attacks; this assumes that the attacker has stored the relevant hashes for m files and is content with finding a preimage for any of them. Note that since the attacker must also expend work to obtain each target hash, the cost of brute force cannot be reduced below a "square root" attack. For example, the work to forge an immutable file (attack #3) by brute force cannot be reduced to less than sqrt(p).2^(r+t)/2 (roughly the same work as a collision attack), no matter how many targets are available.

1. shape-shifter immutable file: creator creates more than one file matching the immutable file readcap

2. See the probability table at ​http://en.wikipedia.org/wiki/Birthday_Attack . The effective hash length is approximately r+t bits.

3. On Merkle-Damgård hashes with an internal state that is the same size as the hash output (like SHA-256), there are better second-preimage attacks than brute force. See ​http://www.schneier.com/paper-preimages.pdf . The doubled "SHA-256d" construction used by Tahoe does not help here. This is not significant for roadblock/speedbump attacks because the internal state will be much larger than t bits, but it is significant for the other second-preimage attacks.

4. The formula given in the Wikipedia Birthday Attack page is sqrt(2.ln(1/(1-p))).2^(r+t)/2, but the approximation given here is very accurate for small p, and can only underestimate the cost. For p = 1/2 it underestimates by only a factor of 1.18. For p near 1 it underestimates severely; it is very hard for an attacker to be certain to find a collision.

5. In order for the combined hash with output (R,T) to have the strength against collision and preimage attacks given here, there must not be multicollision attacks against the hash truncated to r bits or to t bits, that would yield an easier attack on the combined hash. See ​http://allmydata.org/pipermail/tahoe-dev/2009-October/003006.html .

6. The estimates given here are in terms of work factor, i.e. they are products of machine size and attack time. See ​this paper by Dan Bernstein for discussion of parallel brute-force attacks, including attacks against multiple keys at once.