OK, now I’ve got a chance to test on an ARM appliance (similar in power to a 
2-3 year old phone, I think.

Again these are single-core results, but there’s an extra bit of badness here 
in that this is a C implementation of SHA256. We could probably gain around 2 
extra bits with an assembly-language implementation. As it is, it’s about 4 
bits behind the Intel i5.

Yoav

Attachment: data64.xlsx
Description: MS-Excel 2007 spreadsheet

> On Feb 2, 2015, at 8:31 AM, Yoav Nir <ynir.i...@gmail.com> wrote:
> 
> The three-sigma rule applies even with a non-normal distribution.
> 
> Anyway, I tried the 64-key sample. Results are slightly better.
> 
> Yoav
> <data64.xlsx>
>> On Feb 1, 2015, at 7:36 PM, Yaron Sheffer <yaronf.i...@gmail.com> wrote:
>> 
>> Hi Yoav,
>> 
>> This is good, but I'm not sure if it's good enough. The ratio between min 
>> and max (which I trust more than the "mean +/- 3s" rule, because this is not 
>> a normal distribution) is consistently around 4. So if you have to design 
>> your timeouts on a particular machine, you would still have a lot of 
>> uncertainty. For comparison, could you try again with 64 replacing the 16 
>> tries, and with lower bit lengths?
>> 
>> Thanks,
>>      Yaron
>> 
>> On 02/01/2015 11:46 AM, Yoav Nir wrote:
>>> And now it’s really attached.
>>> 
>>> 
>>> 
>>> 
>>>> On Feb 1, 2015, at 11:45 AM, Yoav Nir <ynir.i...@gmail.com> wrote:
>>>> 
>>>> 
>>>>> On Jan 31, 2015, at 12:35 AM, Yoav Nir <ynir.i...@gmail.com> wrote:
>>>>> 
>>>>> 
>>>>>> On Jan 30, 2015, at 3:37 PM, Yaron Sheffer <yaronf.i...@gmail.com> wrote:
>>>>>> 
>>>>>> What I would suggest is: we give the client a single puzzle, and ask it 
>>>>>> to return 16 different solutions. Indeed each puzzle then should be 16X 
>>>>>> easier. The nice thing is, the server should only check *one* of them, 
>>>>>> at random. The client would still need to solve all of them because it 
>>>>>> doesn't want to risk the exchange being rejected because some solutions 
>>>>>> are invalid (the game theory is probably more complex than that, but I 
>>>>>> think what I'm saying is still close to the truth).
>>>>>> 
>>>>>> So: the client does the same amount of work, the server does the same 
>>>>>> amount of work, but the client run-time is still much more deterministic.
>>>> 
>>>> <snip />
>>>> 
>>>>> Note that these are still single core results, and most laptops can do 
>>>>> twice or four times as much. Now, I know that what I SHOULD be doing is 
>>>>> to randomly generate 100 “cookies” and then calculate the times for 
>>>>> different bit lengths for each of them, and then calculate mean and 
>>>>> standard deviation. But just by looking, it looks like it’s much closer 
>>>>> to what we want. 16 bits would be a fine puzzle level for my laptop. No 
>>>>> idea about a phone, although I could try to compile this and run it on an 
>>>>> ARM-based appliance, which should match phones.
>>>> 
>>>> OK. Now I have done it right. See attached. The data suggests that 15 or 
>>>> 16 bits is the level of puzzle that for this kind of hardware is 
>>>> challenging but not too onerous. Add another bit if we assume (probably 
>>>> correctly) that the vast majority of laptops have dual cores at least.
>>>> 
>>>> I would like to run a similar test on an ARM processor, though. The 
>>>> capabilities of phones and tablets are all over the place, what with 
>>>> different versions of ARM processors and devices having anything from dual 
>>>> to octo-core, but it would be nice to get ballpark figures.
>>>> 
>>>> Yoav
>>>> 
>>> 
> 

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