What are some ways to produce a pre-determined sequence of a large number of dice rolls (on the order of 100-1000 times) using biased dice or a biased human roller given the constraints that multiple dice (more than 2) have to be projected in one go from a height of at least 1 meter onto a transparent (acrylic/glass) platform? I'm looking for potential security concerns for a proposed method to generate a publicly verifiable random seed. If an attack vector can get one to be sure of a narrow set of possible outcomes (in lower 1000s), it could potentially harm the security of the system.

  • 2
    $\begingroup$ I don't get what's asked. The question states it wants to produce 100-1000 dice rolls, when the reference consumes 100-1000 (8-sided, sequential) dice rolls. Do we want to produce meta-rolls from physical rolls? Do we want unbiased meta-rolls although that's not needed in the reference? What's the desired balance between simplicity, no bias, and number of physical throws? Can we recognize multiple physical dice thrown together (e.g. by color)? Can we assume dice bias is fixed and throws independent (hard to prove for a human roller)? [off-topic: acrylic shatters; use polycarbonate] $\endgroup$
    – fgrieu
    Commented May 10, 2023 at 16:44
  • $\begingroup$ The linked reference has a theoretical flaw: if we hypothesize that an adversary can intentionally and significantly influence the outcome of a throw (which is hard to disprove), and can make the last throw (or the last few throws) with knowledge of the previous ones, then they can use that to influence the outcome. Independently: IMHO it's too complex to be socially acceptable. $\endgroup$
    – fgrieu
    Commented May 10, 2023 at 17:06
  • 1
    $\begingroup$ Of course though, it doesn't matter if the dice are biased. You'd need lead spots on one face to reduce the entropy from 3000 bits to something useful for an attacker (< 16 bits?). $\endgroup$
    – Paul Uszak
    Commented May 11, 2023 at 1:31
  • $\begingroup$ @Paul Uszak: When throwing a die at short distance without a goblet on a soft surface, it's plausible one can measurably influence the outcome. It's enough an issue that dice goblets with bumps on the exit are used in some Backgammon circles. People can discuss endlessly on the effectiveness of controlled dice throw. If that works, then that allows the last throw (made with knowledge of earlier ones) to influence decisions made on the basis of the SHA-512 of the throws, regardless of how many entropy bits there are in the throws. $\endgroup$
    – fgrieu
    Commented May 11, 2023 at 15:34
  • $\begingroup$ I think that there is a difference between the entropy of the throws and the expected (maximum?) entropy of the dice. If those are the same then Paul is right, otherwise fgrieu is right - but that would be more a question of definition than a difference of opinion. $\endgroup$
    – Maarten Bodewes
    Commented May 12, 2023 at 0:13