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Why is Lamport-Diffie secure? I note that there is a demonstration based on onewayness (in the book postquantum cryptography). But a one way function is not sufficient to ensure that it can not infer some bits or any feature of the key signature.

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As far as we know, there there are collision resistant hashes (if necessary we can even weaken that to random prefix collision resistance) which resist quantum computers with slightly larger security parameter. –  CodesInChaos Nov 30 '13 at 14:34
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