Telescope Simple Lottery Construction #52
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The code here checks that we are above the bounds, and try to modify rs and rc to lower the u_bound as much as possible.
We need to do one more step: ensuring that our u (u=rs * p * nf) is as close as possible to the minimal bound. To do so, we can decrease rs (which increases u_bound) until u_bound gets higher than u ; at what point we keep the previous rs,rc and output the previous u.
Note that doing this, we increase rc, and so increase the communication cost. Perhaps we should allow the user to choose between low proof size and low communication size.
| #[derive(Debug, Clone)] | ||
| pub struct LotterySetup { | ||
| /// Proof size (in Sp elements) | ||
| pub u: u64, |
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I thought we want to have these parameters with more descriptive names in the code - e.g., u --> proof_size?
| /// Setup algorithm taking as input the security parameters, the set size, | ||
| /// and the lower bound and returns LotterySetup. | ||
| pub fn new(lambda_sec: f64, lambda_rel: f64, n_p: u64, n_f: u64) -> Self { | ||
| let (u, mu) = Self::compute_u_mu(lambda_sec, lambda_rel, n_p, n_f); |
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Section 4.1 introduces the parameter mu (the expected number of network participants) - not sure how exactly we measure expectation here. It might be helpful to clarify what expected exactly means - is the expectation calculated over a long period of network activity where nodes go online/offline?
Also, let's stick to the descriptive naming for the variables.
| } | ||
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| // Setup algorithm taking as input the security parameters, the set size, | ||
| /// and the lower bound and returns the minimum number of participants |
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I am confused about this function - minimal over what? Also, mu in the paper is defined as some expected value. What does minimal number of participants mean - minimal over what?
Content
This PR implements the simple lottery construction given in Section 4.1 of the ALBA paper.
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Closes #37