This is about What Could Go Wrong with the "Elk Point 2" immutable file caps: http://zooko.com/immutable-elkpoint-2.svg
(http://zooko.com/immutable-elkpoint-2.png if your browser does not correctly handle SVG.)

||#||''what bad thing could happen''||''how''||''who could do it''||''what could they target''||''what crypto property prevents it''||''how expensive to brute force''||
||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 encryption of ''K1'' being deterministic and correct.||approx sqrt(2.''p'').2^(''r''+''t'')/2^ [footnote 7]||
||2||unauthorized read||attack the encryption of ''K1'' with ''R''||anyone||any one file||the security of the encryption scheme used for ''K1'', and the secrecy of the read-key ''R''||''p''.2^min(''r'',''k'')^||
||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 encryption of ''K1'' being deterministic and correct.||''p''/''N''.2^''r''+''t''^ [footnote 5]||
||4||roadblock or speedbump [footnote 2]||generate (''K1enc'',''Dhash'',''V'') that hash to someone else's ''T'', and copy their ''S''||anyone [footnote 6]||any one file||the hash function's and cap format's second-preimage resistance on ''T''||''p''/''N''.2^''t''^||
||5||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.||''p''.2^''k''^||
||6||unauthorized read||figure out the input to the hash function that generates ''S''||anyone||any one file||the hash function's onewayness for (''R'',''T'') -> ''S''||brute force on ''R'' is !#2||
||7||unauthorized deletion||figure out a working destroy-key ''KD'' for a given ''Dhash''||anyone||any one file||the hash function's preimage resistance on ''Dhash'' and the secrecy of ''KD''||''p''/''N''.2^min(''d'',''dh'')^||
||8||accidental collision||storage indices (''S1'',''T1'') and (''S2'',''T2'') collide accidentally||not applicable||any two files||approximately random distribution of hash function outputs||[footnote 4]||
||9||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||
||10||cause invalid share to verify||generate (''K1enc'',''Dhash'',''V'') that hash to someone else's (''T'',''U''), and copy their ''S''||anyone||any one file||the hash function's second-preimage resistance on (''T'',''U'')||''p''/''N''.2^''t''+''u''^ [footnote 5]||
||11||undeletion [footnote 3]||restore a deleted file's shares by controlling the relevant servers||anyone||any one file||not prevented by crypto||not applicable||
||12||undeletion [footnote 3]||generate matching (''R'',''T'',''U'') for a deleted file||anyone||any one file||the hash function's and cap format's second-preimage resistance on (''R'',''T'',''U'')||higher cost than !#3||

where ''k'' = bitlength(''K1''), ''r'' = bitlength(''R''), ''s'' = bitlength(''S''), ''t'' = bitlength(''T''), ''u'' = bitlength(''U''), ''d'' = bitlength(''KD''), ''dh'' = bitlength(''Dhash'').

(The notes to the diagram assume ''k'' == ''r''.)

''p'' is the success probability of an attack (0 < ''p'' <= 1), and ''c''(''p'') = sqrt(2.ln(1/(1-''p''))). (For example, ''c''(1/2) = 1.18 and ''c''(2^-40) = . For small ''p'', ln(1/(1-''p'')) approx= ''p''.)

''N'' is the number of targets for preimage attacks; this assumes that the attacker has stored the relevant hashes for ''N'' files and is content with finding a preimage for any of them.


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

2. ''roadblock'': attacker prevents uploader (including repairer) from being able to write a real share into the right storage index; ''speedbump'': attacker adds his bogus share into the list of shares stored under the storage index by the same method; downloader has to download, examine, and discard the bogus (''K1enc'',''Dhash'',''V'')'s until it finds the real one. Also see http://allmydata.org/pipermail/tahoe-dev/2009-October/002959.html

3. ''undeletion'': attacker makes a deleted file (for which it need not have had a read cap) accessible at its previous storage index, and readable by previous read caps

4. See the probability table at http://en.wikipedia.org/wiki/Birthday_Attack . The effective hash length is approximately min(''s'',''r'')+''t'' bits.

5. 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.

6. ''roadblock''/''speedbump'' attacks could be restricted to holders of a read cap by use of an extra signature, as in the Elk Point 3 design (diagram at http://jacaranda.org/tahoe/mutable-addonly-elkpoint-3.svg for mutable files).

7. 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.