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RE: [hackers-il] Re: To Hash or not to Hash [was Re: \\\"On Lisp\ \\" now a=

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  • Chen Shapira
    ... Any ideas on how to do this? Or more generally: Suppose I want to create a large amount of random variables, all independent, all with a specific
    Message 1 of 13 , Feb 7, 2002
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      > Perhaps all you want is to distribute a set of values in a
      > uniform fashion.

      Any ideas on how to do this?
      Or more generally: Suppose I want to create a large amount of random
      variables, all independent, all with a specific distribution function
      (either discrete or continuous).
      How do I do something like that? any known algorithms?

      I-want-to-see-the-law-of-large-numbers-ly yours,
      Chen.
    • Nadav Har'El
      ... I may be misunderstanding you, but isn t as psuedo-random-number-generator *exactly* what you are after? I mean, for each key a PRNG generates a sequence
      Message 2 of 13 , Feb 7, 2002
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        On Thu, Feb 07, 2002, Chen Shapira wrote about "RE: [hackers-il] Re: To Hash or not to Hash [was Re: \\\"On Lisp\ \\" now a=":
        >
        > > Perhaps all you want is to distribute a set of values in a
        > > uniform fashion.
        >
        > Any ideas on how to do this?
        > Or more generally: Suppose I want to create a large amount of random
        > variables, all independent, all with a specific distribution function
        > (either discrete or continuous).
        > How do I do something like that? any known algorithms?

        I may be misunderstanding you, but isn't as psuedo-random-number-generator
        *exactly* what you are after?
        I mean, for each key a PRNG generates a sequence of values distributed in a
        given distribution (usually a uniform distribution over, say, [0,1], but it's
        easy to convert it to any distribution you want). For different seeds, an
        ideal PRNG will generate *independent* random sequences (variables).

        PRNG and hash functions have a lot in common - many times you'll see code
        resembling a PRNG inside an hash function, and vice versa - hash functions
        used to "mix" pseudo-random number data in a PRNG. But they are still two
        different concepts.

        --
        Nadav Har'El | Thursday, Feb 7 2002, 26 Shevat 5762
        nyh@... |-----------------------------------------
        Phone: +972-53-245868, ICQ 13349191 |Tea or coffee? Coffee, without cream. It
        http://nadav.harel.org.il |will be without milk, we have no cream.
      • Arik Baratz
        now a=3D?= MIME-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Curiously enough, I have come upon this problem not long ago. What I have
        Message 3 of 13 , Feb 7, 2002
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          \" now a=3D?=
          MIME-Version: 1.0
          Content-Type: text/plain; charset=iso-8859-1


          Curiously enough, I have come upon this problem not long ago. What I have
          contrived was to map a uniform distribution function to another, say, normal
          function.

          Impossible you say? You are correct. But I did an approximation. Still didn\'t
          test it, it\'s all on paper yet.

          -- Arik

          On 07.02.2002 at 21:16:32, Chen Shapira <chen@...> wrote:

          >
          > > Perhaps all you want is to distribute a set of values in a
          > > uniform fashion.
          >
          > Any ideas on how to do this?
          > Or more generally: Suppose I want to create a large amount of random
          > variables, all independent, all with a specific distribution function
          > (either discrete or continuous).
          > How do I do something like that? any known algorithms?
          >
          > I-want-to-see-the-law-of-large-numbers-ly yours,
          > Chen.
          >
          >
          > To unsubscribe from this group, send an email to:
          > hackers-il-unsubscribe@egroups.com
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          >
          >
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          >
          >




          Arik Baratz
          System Engineer
          arikb@...

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        • Shlomi Fish
          ... To quote von-Neumann: Anyone who considers arithmetical methods of producing random numbers is, of course, in a state of sin. Any pseudo-number generation
          Message 4 of 13 , Feb 7, 2002
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            On Thu, 7 Feb 2002, Chen Shapira wrote:

            >
            > > Perhaps all you want is to distribute a set of values in a
            > > uniform fashion.
            >
            > Any ideas on how to do this?
            > Or more generally: Suppose I want to create a large amount of random
            > variables, all independent, all with a specific distribution function
            > (either discrete or continuous).
            > How do I do something like that? any known algorithms?
            >

            To quote von-Neumann:

            Anyone who considers arithmetical methods of producing random numbers is,
            of course, in a state of sin.

            Any pseudo-number generation routine is a heuristic that aims to generate
            numbers that seem random to the above layer. They are not really random.

            The Linux Kernel has a random number device, which uses timings of events
            to generate random numbers, which are more true. I also heard of a device
            that uses small differences in temperature to generate random numbers.

            Sometimes, however, one will prefer to use a pseudo-random number
            generator in order to be able to re-create the behaviour by feeding it
            with the same seed. So, pseudo-random numbers are not necessarily
            inferior, and sometimes even much superior.

            There was a research by a few Finnish workers a few years ago (I read it
            in "Nature") where they showed that several pseudo-random number
            methodologies did not pass several basic randomosity tests. It was quite
            interesting toread.

            > I-want-to-see-the-law-of-large-numbers-ly yours,
            > Chen.
            >

            Then read integers by using /dev/urandom, sum them up in fixed quantities
            (use 64-bit precision), and plot their distribution. You should get a bell
            curve. If not - tell the Linux developers, that it does not work.

            Regards,

            Shlomi Fish

            >
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            > hackers-il-unsubscribe@egroups.com
            >
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            >
            >



            ----------------------------------------------------------------------
            Shlomi Fish shlomif@...
            Home Page: http://t2.technion.ac.il/~shlomif/
            Home E-mail: shlomif@...

            "Let's suppose you have a table with 2^n cups..."
            "Wait a second - is n a natural number?"
          • Nadav Har'El
            ... This is a very narrow-minded view of the state-of-the-art in random number generation and its modern uses. It is possible to generate real random numbers
            Message 5 of 13 , Feb 8, 2002
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              On Fri, Feb 08, 2002, Shlomi Fish wrote about "[hackers-il] RE: Re: To Hash or not to Hash [was Re: \\\"On Lisp\ \\" now a=":
              > To quote von-Neumann:
              >
              > Anyone who considers arithmetical methods of producing random numbers is,
              > of course, in a state of sin.
              >
              > Any pseudo-number generation routine is a heuristic that aims to generate
              > numbers that seem random to the above layer. They are not really random.

              This is a very narrow-minded view of the state-of-the-art in random number
              generation and its modern uses.

              It is possible to generate "real" random numbers from physical processes,
              like Linux's /dev/random does, and like the Intel's newer chips have random
              number generations on them (if you want, I can send you their white-paper,
              it's quite interesting - some of the things they do are actually based on
              Von-Neumann's ideas :) ).
              But typically, these physical processes can generate a limited number of
              quality random numbers per second. Say, 1024 bits a second.

              What do you do if you application needs thousands or millions of quality
              random numbers each second? Consider, for example, an SSL webserver that
              serves 4000 pages a second, or a online-casino server that needs to generate
              many random numbers each second. Both need quality random numbers (meaning
              that the distribution is indeed uniform, with the proper mean, and so on) and
              need secure random numbers (an adversery can't guess the next number in
              the sequence, even if he knows the results of all the previous dice-throws).

              So what you do is to use a cryptographic-quality PRNG based on a truely-
              random (from /dev/random or hardware) seed, and every once in a while (say,
              every second) mix new truely-random data into the seed.

              The numbers you generate this way are "truely random" in every way you can
              think of (except perhaps the philosophical sense). They are correctly
              distributed, pass every randomness tests (unless you have bugs, of course),
              and even given the ENTIRE list of random numbers R1...Rn there is no way
              for the advesary to calculate R(n+1) withing a resonable time.

              Again, read OpenSSL's sslrand(3) for a short discussion of cryptographic
              PRNGs.


              --
              Nadav Har'El | Friday, Feb 8 2002, 26 Shevat 5762
              nyh@... |-----------------------------------------
              Phone: +972-53-245868, ICQ 13349191 |Hi! I'm a signature virus! Copy me into
              http://nadav.harel.org.il |your signature to help me spread!
            • Shlomi Fish
              ... I still insist on calling the numbers between to calls to /dev/random pseudo-random. Maybe they can pass every randomness test I can think of that does not
              Message 6 of 13 , Feb 8, 2002
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                On Fri, 8 Feb 2002, Nadav Har'El wrote:

                > On Fri, Feb 08, 2002, Shlomi Fish wrote about "[hackers-il] RE: Re: To Hash or not to Hash [was Re: \\\"On Lisp\ \\" now a=":
                > > To quote von-Neumann:
                > >
                > > Anyone who considers arithmetical methods of producing random numbers is,
                > > of course, in a state of sin.
                > >
                > > Any pseudo-number generation routine is a heuristic that aims to generate
                > > numbers that seem random to the above layer. They are not really random.
                >
                > This is a very narrow-minded view of the state-of-the-art in random number
                > generation and its modern uses.
                >
                > It is possible to generate "real" random numbers from physical processes,
                > like Linux's /dev/random does, and like the Intel's newer chips have random
                > number generations on them (if you want, I can send you their white-paper,
                > it's quite interesting - some of the things they do are actually based on
                > Von-Neumann's ideas :) ).
                > But typically, these physical processes can generate a limited number of
                > quality random numbers per second. Say, 1024 bits a second.
                >
                > What do you do if you application needs thousands or millions of quality
                > random numbers each second? Consider, for example, an SSL webserver that
                > serves 4000 pages a second, or a online-casino server that needs to generate
                > many random numbers each second. Both need quality random numbers (meaning
                > that the distribution is indeed uniform, with the proper mean, and so on) and
                > need secure random numbers (an adversery can't guess the next number in
                > the sequence, even if he knows the results of all the previous dice-throws).
                >
                > So what you do is to use a cryptographic-quality PRNG based on a truely-
                > random (from /dev/random or hardware) seed, and every once in a while (say,
                > every second) mix new truely-random data into the seed.
                >
                > The numbers you generate this way are "truely random" in every way you can
                > think of (except perhaps the philosophical sense). They are correctly
                > distributed, pass every randomness tests (unless you have bugs, of course),
                > and even given the ENTIRE list of random numbers R1...Rn there is no way
                > for the advesary to calculate R(n+1) withing a resonable time.
                >

                I still insist on calling the numbers between to calls to /dev/random
                pseudo-random. Maybe they can pass every randomness test I can think of
                that does not have a-priori knowledge, but are still generated by a
                deterministic algorithm.

                If you wish to call them "truely random" fine, but I still insist they are
                pseudo-random "limquta'in".

                > Again, read OpenSSL's sslrand(3) for a short discussion of cryptographic
                > PRNGs.
                >

                Maybe I will. I'm not too much into crypto now.

                As a side note I should say, that when I wanted to say that when I wrote
                the first version of Freecell Solver, I generated a list of 1000 boards by
                using a perl script. I called Perl's srand() function but also called it
                for each board, believing I'll get a better randomness. But then it was
                hard to re-create these boards, without copying all of them.

                The re-solution was that I know use the Microsoft Freecell Deals, and to
                lesser extent the PySol deals to test new versions of the solver. This is
                just another example, where pseudo-random numbers actually work to your
                advantage.

                So far my best experience in cryptography was when I implemented RSA
                encryption and decryption in Scheme (for very small keys) for my SICP
                course. It was pretty entertaining but I did not understand too much why
                it should have worked. And I think it is an important factor when giving a
                computer exercise.

                Regards,

                Shlomi Fish

                There is no IGLU Cabal! At least there is not a true IGLU Cabal. But there
                is a pseudo-IGLU Cabal.

                >
                > --
                > Nadav Har'El | Friday, Feb 8 2002, 26 Shevat 5762
                > nyh@... |-----------------------------------------
                > Phone: +972-53-245868, ICQ 13349191 |Hi! I'm a signature virus! Copy me into
                > http://nadav.harel.org.il |your signature to help me spread!
                >
                >
                > To unsubscribe from this group, send an email to:
                > hackers-il-unsubscribe@egroups.com
                >
                >
                >
                > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
                >
                >



                ----------------------------------------------------------------------
                Shlomi Fish shlomif@...
                Home Page: http://t2.technion.ac.il/~shlomif/
                Home E-mail: shlomif@...

                "Let's suppose you have a table with 2^n cups..."
                "Wait a second - is n a natural number?"
              • Oleg Goldshmidt
                ... Well, it is quite possible, of course. For well-behaved distributions (typically those with easily invertable CDF) it is often even efficient. In the
                Message 7 of 13 , Feb 10, 2002
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                  Arik Baratz <arikb@...> writes:

                  > Curiously enough, I have come upon this problem not long ago. What I have
                  > contrived was to map a uniform distribution function to another, say, normal
                  > function.
                  >
                  > Impossible you say? You are correct. But I did an
                  > approximation. Still didn\'t test it, it\'s all on paper yet.

                  Well, it is quite possible, of course. For well-behaved distributions
                  (typically those with easily invertable CDF) it is often even
                  efficient. In the general case the rejection method will work, but
                  might be wasteful. Without even going to my bookshelf I am sure that
                  Knuth has a lot to say about it. The theory part of Numerical Recipes
                  is short but clear (don't touch the implementation though).

                  In fact, a much more fundamental and difficult problem is to find a
                  good and efficient uniform pseudo-random generator. For any serious
                  work one has to be very careful about readily available algorithms and
                  implementations (e.g. see my comment regarding NR above). On the other
                  hand, don't expect to come up with a good RNG yourself. Not that it is
                  impossible, just quite improbable ;-).

                  --
                  Oleg Goldshmidt | ogoldshmidt@...
                  If it aint't broken it hasn't got enough features yet.
                • Oleg Goldshmidt
                  ... This quote precedes just about every RNG publication I have ever seen, of course ;-) ... It is very random (a colleague of mine and I submitted it, among
                  Message 8 of 13 , Feb 10, 2002
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                    Shlomi Fish <shlomif@...> writes:

                    > To quote von-Neumann:
                    >
                    > Anyone who considers arithmetical methods of producing random numbers is,
                    > of course, in a state of sin.

                    This quote precedes just about every RNG publication I have ever seen,
                    of course ;-)

                    > The Linux Kernel has a random number device, which uses timings of events
                    > to generate random numbers, which are more true.

                    It is very random (a colleague of mine and I submitted it, among quite
                    a few others, to a battery of tests), but not very efficient. It might
                    be, incidentally, quite suitable for seeding a PRNG. If you can afford
                    the lack of portability, that is (seeding RNGs randomly is an
                    interesting problem in itself, once you start thinking about the
                    requirements, after discovering that what you thought should be random
                    isn't).

                    > There was a research by a few Finnish workers a few years ago (I read it
                    > in "Nature") where they showed that several pseudo-random number
                    > methodologies did not pass several basic randomosity tests.

                    Can you provide a reference? I have a long-standing interest in the subject.

                    A few years ago I studied the state of the art in some depth. The
                    following is a very brief summary (the full report is, and will
                    remain, property of my employer at the time unless they will grant me
                    a release):

                    http://groups.google.com/groups?selm=m3emyz0xsm.fsf%40NOSPAM.netvision.net.il&output=gplain

                    Just in case it is relevant for understanding the context of this
                    summary, here is my original request for pointers:

                    http://groups.google.com/groups?selm=lvzpj6d5sq.fsf%40NOSPAM.netvision.net.il&output=gplain

                    --
                    Oleg Goldshmidt | ogoldshmidt@...
                    If it aint't broken it hasn't got enough features yet.
                  • Shlomi Fish
                    ... I happen to like this quote very much. Albeit I think that if you know what your application considers as random, you might be able to compose a good
                    Message 9 of 13 , Feb 10, 2002
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                      On 10 Feb 2002, Oleg Goldshmidt wrote:

                      > Shlomi Fish <shlomif@...> writes:
                      >
                      > > To quote von-Neumann:
                      > >
                      > > Anyone who considers arithmetical methods of producing random numbers is,
                      > > of course, in a state of sin.
                      >
                      > This quote precedes just about every RNG publication I have ever seen,
                      > of course ;-)
                      >

                      I happen to like this quote very much. Albeit I think that if you know
                      what your application considers as random, you might be able to compose a
                      good pseudo-random number generator.

                      > > The Linux Kernel has a random number device, which uses timings of events
                      > > to generate random numbers, which are more true.
                      >
                      > It is very random (a colleague of mine and I submitted it, among quite
                      > a few others, to a battery of tests), but not very efficient. It might
                      > be, incidentally, quite suitable for seeding a PRNG. If you can afford
                      > the lack of portability, that is (seeding RNGs randomly is an
                      > interesting problem in itself, once you start thinking about the
                      > requirements, after discovering that what you thought should be random
                      > isn't).
                      >

                      I did not know it was not very fast. That does make it problematic.

                      > > There was a research by a few Finnish workers a few years ago (I read it
                      > > in "Nature") where they showed that several pseudo-random number
                      > > methodologies did not pass several basic randomosity tests.
                      >
                      > Can you provide a reference? I have a long-standing interest in the subject.
                      >

                      Unfortunately, Google returns junk. The article was written in the
                      magazine "Nature" (a very famous British publication - one of the two
                      topmost scientific publications in the world) It was written by its
                      editor. I don't remember the editor's name, etc. but I remember the
                      general wave of the article.

                      I cannot find it in the nature.com/nature search, so I'm sorry I could not
                      be of more assistant. (please reply to me by E-mail if you wish to hear
                      what I can remember of it)

                      > A few years ago I studied the state of the art in some depth. The
                      > following is a very brief summary (the full report is, and will
                      > remain, property of my employer at the time unless they will grant me
                      > a release):
                      >
                      > http://groups.google.com/groups?selm=m3emyz0xsm.fsf%40NOSPAM.netvision.net.il&output=gplain
                      >
                      > Just in case it is relevant for understanding the context of this
                      > summary, here is my original request for pointers:
                      >
                      > http://groups.google.com/groups?selm=lvzpj6d5sq.fsf%40NOSPAM.netvision.net.il&output=gplain
                      >

                      Regards,

                      Shlomi Fish

                      > --
                      > Oleg Goldshmidt | ogoldshmidt@...
                      > If it aint't broken it hasn't got enough features yet.
                      >
                      >
                      > To unsubscribe from this group, send an email to:
                      > hackers-il-unsubscribe@egroups.com
                      >
                      >
                      >
                      > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
                      >
                      >



                      ----------------------------------------------------------------------
                      Shlomi Fish shlomif@...
                      Home Page: http://t2.technion.ac.il/~shlomif/
                      Home E-mail: shlomif@...

                      "Let's suppose you have a table with 2^n cups..."
                      "Wait a second - is n a natural number?"
                    • Nadav Har'El
                      ... /dev/random s not being fast is a bit of an understatement. I just tried cat /dev/random /tmp/z1 With me moving the mouse around, pressing keys, doing
                      Message 10 of 13 , Feb 11, 2002
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                        On Mon, Feb 11, 2002, Shlomi Fish wrote about "[hackers-il] Re: RE: Re: To Hash or not to Hash [was Re: \\\"On Lisp\ \\" now a=":
                        > > > The Linux Kernel has a random number device, which uses timings of events
                        > > > to generate random numbers, which are more true.
                        > >
                        > > It is very random (a colleague of mine and I submitted it, among quite
                        > > a few others, to a battery of tests), but not very efficient. It might
                        >...
                        >
                        > I did not know it was not very fast. That does make it problematic.

                        /dev/random's not being fast is a bit of an understatement. I just tried
                        cat /dev/random >/tmp/z1

                        With me moving the mouse around, pressing keys, doing things on the network,
                        playing music, and a lot of other stuff going on for random events - and
                        after 56 seconds I got 6952 bytes in /tmp/z1. That's 124 random bytes (992
                        random bits) per second - slow by any kind of standard. And there's nothing
                        much that can be done about this - a faster CPU wouldn't help a bit.

                        Intel's on-chip random number generator (which has more physical sources of
                        randomness) generates what they call an "exceptional performance": 75 Kbit/sec
                        which is enough for many applications, but not all (it is certainly not enough
                        for Monte-Carlo or similar simulations, but you don't need cryptographic-
                        quality RNG for that anyway).

                        /dev/urandom will of course get you bits faster (I measured 5.8Mbit/sec),
                        but it is essentially a PRNG seeded once in a while by "real" random events -
                        which you seem not to like (but I think is good enough).

                        P.S. Guess what? Intel's paper "Analysis of the Intel Random Number Generator"
                        also includes the following quote:
                        Anyone who considers arithmetical methods of producing random
                        digits is, of course, in a state of sin. (John Von Neumann, 1951)
                        :)
                        See http://nadav.harel.org.il/pub/CRIwp.pdf for the full paper.

                        --
                        Nadav Har'El | Monday, Feb 11 2002, 29 Shevat 5762
                        nyh@... |-----------------------------------------
                        Phone: +972-53-245868, ICQ 13349191 |What's the difference between roast beef
                        http://nadav.harel.org.il |and pea soup? Anyone can roast beef.
                      • mulix
                        just a quick note that there s a kernel patch to allow all or most of the network devices to contribute to /dev/random s entropy pool, rather than just a few.
                        Message 11 of 13 , Feb 11, 2002
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                          just a quick note that there's a kernel patch to allow all or most of
                          the network devices to contribute to /dev/random's entropy pool, rather
                          than just a few. no idea if it's applied in the mainline kernel, though.
                          --
                          mulix

                          http://vipe.technion.ac.il/~mulix/
                          http://syscalltrack.sf.net/
                        • Adi Stav
                          ... A controvertial patch, since relying on the randomness of externally connected devices such as network cards would open a security hole. Any software on
                          Message 12 of 13 , Feb 11, 2002
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                            On Mon, Feb 11, 2002 at 12:59:03PM +0200, mulix wrote:
                            > just a quick note that there's a kernel patch to allow all or most of
                            > the network devices to contribute to /dev/random's entropy pool, rather
                            > than just a few. no idea if it's applied in the mainline kernel, though.

                            A controvertial patch, since relying on the randomness of
                            externally connected devices such as network cards would open
                            a security hole. Any software on the machine that relies on
                            randomness will risk having its random number source not only
                            /read/ but actually /affected/ by an attacker that can, e.g.,
                            send packets to the network card with careful timing.

                            This reminds me an old Gaal Yahas (where /is/ he lately?) sig:

                            "Real programmers type `cat /dev/random >a.out' and affect the
                            universe randomisity field."

                            which could actually be made reality.

                            A better idea was for servers to open up their on-board
                            unconnected microphone ports and use the static. Which relates
                            to yet another "Real Programmers" sig.
                          • Adi Stav
                            ... A controvertial patch, since relying on the randomness of externally connected devices such as network cards would open a security hole. Any software on
                            Message 13 of 13 , Feb 11, 2002
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                              On Mon, Feb 11, 2002 at 12:59:03PM +0200, mulix wrote:
                              > just a quick note that there's a kernel patch to allow all or most of
                              > the network devices to contribute to /dev/random's entropy pool, rather
                              > than just a few. no idea if it's applied in the mainline kernel, though.

                              A controvertial patch, since relying on the randomness of
                              externally connected devices such as network cards would open
                              a security hole. Any software on the machine that relies on
                              randomness will risk having its random number source not only
                              /read/ but actually /affected/ by an attacker that can, e.g.,
                              send packets to the network card with careful timing.

                              This reminds me an old Gaal Yahas (where /is/ he lately?) sig:

                              "Real programmers type `cat /dev/random >a.out' and affect the
                              universe randomisity field."

                              which could actually be made reality.

                              A better idea was for servers to open up their on-board
                              unconnected microphone ports and use the static. Which relates
                              to yet another "Real Programmers" sig.
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