[tor-bugs] #4862 [Tor Hidden Services]: Tor Hidden Service IP replacing numerology

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#4862: Tor Hidden Service IP replacing numerology
---------------------------------+------------------------------------------
 Reporter:  hellais              |          Owner:     
     Type:  enhancement          |         Status:  new
 Priority:  normal               |      Milestone:     
Component:  Tor Hidden Services  |        Version:     
 Keywords:                       |         Parent:     
   Points:                       |   Actualpoints:     
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Description changed by hellais:

Old description:

> In #3825 rransom proposed to tune the number of IP to rebuilt once one
> expires based on the history of the Tor HS usage. I believe these numbers
> are not optimal and there should be a better way to do this.
>
> These are the first numbers that I will try to estimate:
> I = number of intro points
> C = Connections made to an IP in it's lifetime
> T = Total number of connections made to the HS in 24 hours
>
> What we are interested in estimating is the value of NUM_INTRO_POINTS_MAX
> and this is based on the estimation of C. To determine this we will
> consider this equation:
>
> `I = T/C`
> I believe it is reasonable to suppose that a very busy HS will at most
> have 1M connections in 24 hours. This means that:
>
> `I = 1'000'000/C`
> Currently C is set to 16384. I am not sure why this number was chosen,
> but if this number is good we would need to set the value of I to 61.
>
> Lets take for granted that 61 is a good value for NUM_INTRO_POINTS_MAX,
> this means that the number of active IP at a given time should be in the
> range of 3-61.
>
> For this reason I believe it would be good to have the number of IP to
> recreate to be in the range of 1-20 dependent on the history of a Tor HS.
>
> The basic thing we can do is use a linear function to determine this
> number x. We want a linear function that has these properties:
>
> `f(0) = 1``f(4/3) = NUM_INTRO_POINTS_MAX ``(supposing that for lifetime
> of IP tends to end the fraction
> (time_since_publishing/IP_MIN_LT)*(accepted_ip_connection)/(IP_CON_LT) ->
> 4/3)`
> This leads us to this:
>
> `x = (1 -
> NUM_INTRO_POINTS_MAX)*((time_since_publishing/IP_MIN_LT)*(accepted_ip_connection)/(IP_CON_LT))
> + 1`
> in the case of NUM_INTRO_POINTS_MAX = 20 this means:
>
> `x = 25.3333333 *
> (time_since_publishing/IP_MIN_LT)*(accepted_ip_connection)/(IP_CON_LT) +
> 1`
> A better way to do this is have an exponential function that converges
> asymptotically to 20.
>
> Does this seem sane?

New description:

 In #3825 rransom proposed to tune the number of IP to rebuilt once one
 expires based on the history of the Tor HS usage. I believe these numbers
 are not optimal and there should be a better way to do this.

 These are the first numbers that I will try to estimate:
 I = number of intro points
 C = Connections made to an IP in it's lifetime
 T = Total number of connections made to the HS in 24 hours

 What we are interested in estimating is the value of NUM_INTRO_POINTS_MAX
 and this is based on the estimation of C. To determine this we will
 consider this equation:

 `I = T/C`


 I believe it is reasonable to suppose that a very busy HS will at most
 have 1M connections in 24 hours. This means that:

 `I = 1'000'000/C`


 Currently C is set to 16384. I am not sure why this number was chosen, but
 if this number is good we would need to set the value of I to 61.

 Lets take for granted that 61 is a good value for NUM_INTRO_POINTS_MAX,
 this means that the number of active IP at a given time should be in the
 range of 3-61.

 For this reason I believe it would be good to have the number of IP to
 recreate to be in the range of 1-20 dependent on the history of a Tor HS.

 The basic thing we can do is use a linear function to determine this
 number x. We want a linear function that has these properties:

 `f(0) = 1``f(4/3) = NUM_INTRO_POINTS_MAX ``(supposing that for lifetime of
 IP tends to end the fraction
 (time_since_publishing/IP_MIN_LT)*(accepted_ip_connection)/(IP_CON_LT) ->
 4/3)`
 This leads us to this:

 `x = (1 -
 NUM_INTRO_POINTS_MAX)*((time_since_publishing/IP_MIN_LT)*(accepted_ip_connection)/(IP_CON_LT))
 + 1`


 in the case of NUM_INTRO_POINTS_MAX = 20 this means:

 `x = 25.3333333 *
 (time_since_publishing/IP_MIN_LT)*(accepted_ip_connection)/(IP_CON_LT) +
 1`


 A better way to do this is have an exponential function that converges
 asymptotically to 20.

 Does this seem sane?

--

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Ticket URL: <https://trac.torproject.org/projects/tor/ticket/4862#comment:2>
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