SERVING THE QUANTITATIVE FINANCE COMMUNITY

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### sha1

Hypotheses:H1) Do different implementations of SHA1 pad short strings differently?H2) 8-bit ASCII "a" vs. 16-bit unicode "a"? (i.e., 0x61 vs. 0x0061)H3) SHA1 vs.SHA1.00001?H4) The IETF wants to see if anyone is paying attention?H5) A self referential inside joke: SHA1("SHA1 of 'a'") is 34 AA 97 3C D4 C4 DA A4 F6 1E EB 2B DB AD 27 31 65 34 01 6F?
Last edited by Traden4Alpha on April 25th, 2014, 10:00 pm, edited 1 time in total.

Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### sha1

Cuchulainn
Posts: 62608
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### sha1

QuoteOriginally posted by: Traden4AlphaInteresting! Might SHA1 have multiple fixed points? Imagine looking at an encrypted password file and discovering that the SHA1 of your password is your password!And what about N-cycles.It's to be expected.Maybe you can prove the finite-dimensional (generalisation) version of the Banach fixed pont theorem (and with a bit of mazel you can compute it as well). One issue is in deciding what a good metric is. You also probably need conditions on the space to produce a mapping _not_ to have a fixed point. http://en.wikipedia.org/wiki/Banach_fix ... alizations // If T^n x = y exists then Ty = y (for a Hausdorff topological space) QuotePreimage-resistance: If an attacker only knows the output it should be unfeasible to calculate an input i.e. given an output h it should be unfeasible to calculate an input m such that hash(m)=h.Not my area, but it seems if you can find a fixed point, then you might be able to find out more nice stuff.
Last edited by Cuchulainn on April 26th, 2014, 10:00 pm, edited 1 time in total.
Step over the gap, not into it. Watch the space between platform and train.
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Posts: 23951
Joined: September 20th, 2002, 8:30 pm

### sha1

Doesn't XOR have a fixed point because XOR(x,x) = 0? And if you do x[n] = XOR(x[n-1],y), doesn't it drop into a 2-cycle, in general, and a fixed point for some bit patterns?For x[0] = 0011, y = 1010, the sequence is 1001, 0011, 1001

rmax
Posts: 6080
Joined: December 8th, 2005, 9:31 am

### sha1

QuoteOriginally posted by: Traden4AlphaInteresting! Might SHA1 have multiple fixed points? Imagine looking at an encrypted password file and discovering that the SHA1 of your password is your password!One of the assumptions that Turing used when decoding the Engima. He worked out that that Engima machine never encoded the letter to itself. It drastically reduced the problems space.

rmax
Posts: 6080
Joined: December 8th, 2005, 9:31 am

### sha1

It was electromechanical and worked on a set of rotors that rotated once each time a key was hit. There was also a "plug board" for additional configuration operations. Turing realised that he could subtract the operations of the plugboard by reflecting the signals back through the plugboard configuration, thus cancelling out their effect. This meant that Bletchley Park only had to workout the combination of the rotors (initially 3 but this was increased to 5 later in the war). Turing is always hailed (rightly) as the genius behind enigma, but there were some other brilliant minds that were excellent at lateral thinking.

katastrofa
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Location: Alpha Centauri

### sha1

Don't use SHA1, it's been broken a long time ago.https://www.schneier.com/blog/archives/ ... roken.html

Cuchulainn
Posts: 62608
Joined: July 16th, 2004, 7:38 am
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### sha1

QuoteOriginally posted by: rmaxQuoteOriginally posted by: Traden4AlphaInteresting! Might SHA1 have multiple fixed points? Imagine looking at an encrypted password file and discovering that the SHA1 of your password is your password!One of the assumptions that Turing used when decoding the Engima. He worked out that that Engima machine never encoded the letter to itself. It drastically reduced the problems space.True.And I suppose we can include Uncle Joe in this pantheon.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
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