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    SubjectBug in random32.c: all-zero outputs with probability 1/2^32, other seeding bugs

    There appears to be an error in how random seeding is done in the
    random32.c RNG. I am looking at

    For background, that file contains this comment:

    ... the k_j most significant bits of z_j must be non-
    zero, for each j. (Note: this restriction also applies to the
    computer code given in [4], but was mistakenly not mentioned in
    that paper.)

    This affects the seeding procedure by imposing the requirement
    s1 > 1, s2 > 7, s3 > 15.

    The function random32_reseed takes an unsigned long's worth of entropy
    from the entropy pool (get_random_bytes) and passes it to
    __set_random32. That function (seemingly attempts) to impose the
    requirement mentioned above by first checking if the seed is == 0, and
    if so setting it to one, then setting s2 to s*69069 and s3 to s2*69069

    However this will allow bad seeds. On 64-bit systems, if the low order
    32 bits of the seed are zero, then the check for s == 0 will pass, but
    s1, s2, and s3 will all be initialized to zero due to truncation. This
    will, since there are no additive factors in the RNG sequence, cause
    the RNG to output nothing but zero values. Assuming get_random_bytes
    returns uniform random numbers, this will occur with probability
    around 1/2^32.

    An easy and straightforward fix for this that doesn't require changing
    any interfaces is to add
    s &= 0xFFFFFFFF;
    before the check in __set_random32, which ensures this condition will
    be caught by the check. Alternately, you could replace the check for
    s == 0 with some logic like:
    if((s & 0xFFFFFFFF) == 0)
    s += 1;
    since just chopping the seed to 32 bits does throw away some of your
    seed input (with sizeof(long) == 8, at least; doesn't make any
    difference for sizeof(long) == 4)

    There are also many other seeds which will cause some (but not all) of
    the seeding requirements to be violated. Which seeds will cause this
    problem depend on the size of unsigned long, since the multiplications
    by 69069 are done in that size.

    For instance on 32-bit systems, a seed of 0x4BC54E0A will generate
    the state:
    s1 = 0x4BC54E0A
    s2 = (s1 * 69069) % 2^32 = 2
    s3 = 2*69069 = 138138

    In general, there seem to be large numbers of seeds that cause at
    least one of the restrictions on s1, s2, s3 to be false. The paper
    referenced in the source is not clear exactly how badly the generator
    fails when only one of the restrictions is violated. Certainly it
    seems much less serious than the 64-bit specific bug described above;
    which is fortunate since it seems to occur much more often. A trivial
    patch for both problems is attached.

    Please Cc: me on any replies as I am not subscribed to the list.

    --- random32.c.orig 2008-06-19 11:21:57.000000000 -0400
    +++ random32.c 2008-06-19 11:23:05.000000000 -0400
    @@ -58,13 +58,17 @@

    static void __set_random32(struct rnd_state *state, unsigned long s)
    + s &= 0xFFFFFFFF;
    if (s == 0)
    s = 1; /* default seed is 1 */

    #define LCG(n) (69069 * n)
    state->s1 = LCG(s);
    + if(state->s1 < 2) state->s1 += 2;
    state->s2 = LCG(state->s1);
    + if(state->s2 < 8) state->s2 += 8;
    state->s3 = LCG(state->s2);
    + if(state->s3 < 16) state->s3 += 16;

    /* "warm it up" */
     \ /
      Last update: 2008-06-19 17:43    [W:0.026 / U:47.264 seconds]
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