## Message Posted: Thu, 27 Apr 2006 @ 10:11:23 GMT

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 Subj: Re: Index Mechanism? From: Victor Sokovin

Christian,

 I think the given formula is just an an example. It should somehow show, that only commutative operators ( *, + ) are used.

 It could also be

```          > PI( A, B, C ) = PI( A, C, B ) = PI( B, A, C ) = PI( C, A, B )
> = PI( C, B, A)
```

I think this could still be called commutativity for an operator with 3 arguments. I assume it is commutative for any n. This is good to know because this property does not follow from anything. This is just how it has been implemented and it is good to know this. So far so good.

 With the formula:

```          > H(A)*H(B)+H(A)*H(C)+H(B)*H(C)+H(A)*H(B)*H(C)+H(A)+H(B)+H(C) =
> H(A)*H(C)+H(A)*H(B)+H(C)*H(B)+H(A)*H(C)*H(B)+H(A)+H(C)+H(B) =
```

Here I am lost. If * and + are just addition and multiplication for hex numbers then such a formula always holds true because it holds true for integers (either hex or decimal or whatever).

So, my problem is that I don't understand how this formula helps me understand hashing, and composite PI in particular.

Perhaps * and + stand for other operations in this context? If so, which operations?

Is there any formula / relationship which would, say, calculate PI(A,B,C) in terms of PI(A,B), PI(A,C) and PI(B,C)? Perhaps the formula above is trying to say something about such a calculation?

I hope I have made my questions more precise.

Regards,

Victor

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