I think Jim McCoy and Jack Lloyd are talking past one another because  
you're thinking of different "secure hash" properties.

On Apr 28, 2008, at 4:03 PM, Jim McCoy wrote:

> [Perhaps I am just misunderstanding your construction, but MD4(x) ||
> SHA-256(x) is only as strong as MD4, not stronger than SHA-256  
> alone...]

It depends on what properties you are talking about.  Such a  
combination is at least as strong as the strongest hash for collision- 
resistance, but probably at least as weak as the weakest one for pre- 
image resistance.

Consider SHAstupid = SHA-256(x) || first_256_bits_of_(x)

This has collision resistance even better than SHA-256 has, but its  
preimage resistance is terrible.

Regards,

Zooko

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