Expected number of bad committees per year === The following script suggests ~31 bad committees per year. ```python import math def factorial(n): return n * factorial(n - 1) if n else 1 def choose(n, k): return factorial(n) / factorial(k) / factorial(n - k) def eq_k_probability(n, k, p): return p**k * (1 - p)**(n - k) * choose(n, k) def ge_k_probability(n, k, p): return sum([eq_k_probability(n, i, p) for i in range(k, n + 1)]) # Protocol parameters SECONDS_PER_SLOT = 12 MAX_COMMITTEES_PER_SLOT = 64 SLOTS_PER_EPOCH = 32 TARGET_COMMITTEE_SIZE = 128 BAD_COMMITTEE_THRESHOLD = math.ceil(2 / 3 * TARGET_COMMITTEE_SIZE) SLOTS_PER_YEAR = 365.25 * 24 * 60 * 60 / SECONDS_PER_SLOT COMMITEES_PER_YEAR = MAX_COMMITTEES_PER_SLOT * SLOTS_PER_YEAR # Security assumptions RANDAO_BIAS_BITS = 25 # Optimistic (no SSLE makes forcing RANDAO no-reveals easy by DoSing proposers) ATTACKER_CONTROL = 1/3 bad_committee_probability = ge_k_probability(TARGET_COMMITTEE_SIZE, BAD_COMMITTEE_THRESHOLD, ATTACKER_CONTROL) bad_committees_per_year = 2**RANDAO_BIAS_BITS * COMMITEES_PER_YEAR * bad_committee_probability print("Expected number of bad committees per year:", bad_committees_per_year) ```
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Post-quantum VDF challenge (draft!)

The VDF Alliance is looking for a team to design and implement a concretely-efficient post-quantum prover system for certain Sloth-like delay statements. Such a prover system would yield a concretely-efficient post-quantum VDF which may be used by L1 projects such as Cosmos, Ethereum, Filecoin, Tezos as well as L2 applications. Delay function The delay function is the following Python delay function. p = 3*2**124 + 3*2**96 + 2**64 + 1 def cube_root(n): return pow(n, (2*p - 1)//3, p)

2/8/2021
Halo Infinite reading notes

[x] (page 1) "zk-SNARKs" => "zkSNARK" (the reasoning is that the long-form "zero knowledge SNARK" doe not have a dash, and that similarly prefixed terms such as "zkRollup" and "zkVM" do not usually have a dash) [x] (page 1) "both private and public" => "private or public" [x] (page 1) "a polynomial f ∈ F[x]" => "a polynomial f ∈ F[X]" [x] (page 1) "of degree d" => "of degree at most d" [x] (page 1) consider adding an index after the abstract (the paper is long with many sections) [x] (page 2) "o(d log F)" => "o(d log |F|)" [ ] (page 2) " including DARK, FRI, and Dory" => consider adding a footnote explaining the slight abuse of notation for FRI which is natively a low-degree test [x] (page 2) "or equivalently Algebraic Holographic Proofs" => "or a equivalently Algebraic Holographic Proof" [x] (page 2) "or no trusted setup [BFS20]" => may be worth adding references for Dory and FRI [x] (page 2) "where the operators of the blockchain only need to store the latest proof that attests to the entire correct history of all transactions" => This sweeps under the rug important details such as data availability and the type of "operator" involved. A more restricted (and technically correct) statement could be "where the latest proof attests to the validity of state transitions in the blockchain history".

1/4/2021
StarkEx Validium ransom attack

9/7/2020
Modular squaring bounties

7/14/2020
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