  `Val Henson  wrote:>On Thu, Aug 14, 2003 at 07:40:25PM +0000, David Wagner wrote:>> I don't see where you are getting this from.  Define>>   F(x) = first80bits(SHA(x))>>   G(x) = first80bits(SHA(x)) xor last80bits(SHA(x)).>> What makes you think that F is a better (or worse) hash function than G?>>See Matt Mackall's earlier post on correlation, excerpted at the end>of this message.  Basically, with two strings x and y, the entropy of>x alone or y alone is always greater than or equal to the entropy of x>xored with y.>>entropy(x) >= entropy(x xor y)>entropy(y) >= entropy(x xor y)Sorry; that's not accurate.  Here's a counterexample.  Let x and y betwo 80-bit strings.  Assume that x is either 0 or 1 (equal probabilityfor both possibilities).  Assume y is either 0 or 2 (equal probabilityfor both possibilities), and is independent of x.  Then  entropy(x) = 1 bit  entropy(y) = 1 bit  entropy(x xor y) = 2 bitsThe difference between F and G is very small, and there is not muchbasis for choosing one over the other.-To unsubscribe from this list: send the line "unsubscribe linux-kernel" inthe body of a message to majordomo@vger.kernel.orgMore majordomo info at  http://vger.kernel.org/majordomo-info.htmlPlease read the FAQ at  http://www.tux.org/lkml/`   