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Why is SHA1 preimage-resistant? The best reference that I can find is Rogaway & Shrimpton's 2009 paper, and I'll use their definitions. The kind of preimage resistance that is wanted is aPre. There is a provisional (but strong enough, since the compression function goes from 512 to 160 bits) implication of aSec->aPre. But there is no implication from Coll->aSec (or from anything else ->aSec, for that matter), and most of the published work concentrates on Coll. So, perhaps I should ask: why is SHA1 second-preimage-resistant?

We know that the RSA public-key cryptosystem is based on the inherent difficulty of factoring large primes. Is there a similar intractable problem that lies behind second-preimage resistance?

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the generalizations on key recovery from block ciphers using differential or linear analysis is what you should be looking at, since the message is treated as the key to a block cipher in SHA –  Richie Frame Dec 9 at 11:20

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