> The chain merging data is interesting. I see from the data below
> that the percentage of chains merged starts at 5% and then decreases
> linearly with the number of start values. The interesting thing is
> this:
> (vertical axis: % of chains lost, horizontal axis: chains left)
> screenshot of graph
>
> I clearly see two lines. It appears that round functions 10, 14, 17,
> 21, 24, 28 and 31 (+/- 1) generate 0.5% less chain mergers. Do we
> have any clue why? Do they share a common bit value, or have a
> certain number of bits? Could you reconstruct the xor patterns for
> the 32 rounds, Sacha?
advance was 307232, second column is numbits==1 count
the only pattern i see is that the rounds with less chain mergers are
evenly spaced (ignoring round 1 - 10)
The values seem pretty prng to me. Probably just random fluctuation with
some influence on the next few rounds which restore the balance again.
2 26 39894c217a0103d7 (corresponds with the change between line 1 and 2
in the cited mail below)
3 24 e1ba888001e4d846
4 38 cb4caa7fecb9d16e
5 33 4c85f57e646611db
6 27 86011c6836045ef7
7 31 25e5fe857594042d
8 23 e0a1e00c94a39038
9 39 d10cdf47ad3ecdfd
10 23 14419070b2a619c1
11 29 2528cbe0974487a7
12 29 eb4c42d3885e3056
13 27 2c8d032fa00f28d6
14 28 26d0d1081f654d56
15 33 cf051426d32e97de
16 23 268920cf2111848e
17 33 c8bf942585591ef6
18 27 683aa0e50f4dc430
19 29 85cf17a8609bd122
20 23 032700c2533017a9
21 30 d1def48ea02e00d6
22 31 1e840ef31c1df554
23 32 c0137443fae91fe8
24 31 be66851b891dde08
25 28 280809b7bdea8d24
26 32 472733e1083cd3f5
27 29 7ddc0ac425912b1c
28 37 4abb1ad0e4d76bfd
29 36 de5bab07b94ba3ca
30 31 8a74eab16ac4395c
31 37 958b3eb1bad1eb37
32 28 b588a2bb4b1c2861
33 32 d5a9265ccbf8424e
the final chain count is:
32 cannot reconstruct
33 416172330
>
> (equations are:
> y = 4.5613 * 10-9 x + 0.1163
> y = 3.937 * 10-9 x + 0.0581)
>
> And if you could find the time to do it, I would really like to see
> the same table but then for the 100-forward case. I hope to relate
> some real-world data to the statistics derived above.
>
sure. some more debugging and 3 days to build the table.
i hope you do not mean exactly the same table, but the same layout,
different advance, different start values, cause then i would have
to find the seed that mersenne twistered the start values again ;)
>
>
> On 1/12/10 12:58 AM, sascha wrote:
> >For a 32 rounds table with 1024*1024*1024 start values:
> >1 1073741823
> >2 1023438982
> >3 976087268
> >4 932768763
> >5 893795050
> >6 857258423
> >7 824594686
> >8 793842630
> >9 764984529
> >10 742264968
> >11 717542086
> >12 693794500
> >13 671348674
> >14 653519282
> >15 633911863
> >16 615705741
> >17 600811372
> >18 584022929
> >19 567966279
> >20 553038610
> >21 541126688
> >22 527714176
> >23 514813648
> >24 504121909
> >25 492442040
> >26 480922764
> >27 469931269
> >28 461146395
> >29 451036696
> >30 441442433
> >31 433670029
> >32 ?
> >33 ?
> >
> >sum: 20.5 Grounds
> >(instead of 30 Grounds)
> >
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