44 lines
1.4 KiB
Python
44 lines
1.4 KiB
Python
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def fac(n): return 1 if n==0 else n * fac(n-1)
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def choose(n,k): return fac(n) / fac(k) / fac(n-k)
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def prob(n,k,p): return choose(n,k) * p ** k * (1-p) ** (n-k)
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def prob_lt(n,k,p): return sum([prob(n,i,p) for i in range(p)])
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SIGS = 30
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ACTUALSIGS = 10
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POWRETURN = 0.03
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POSRETURN = 0.01
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# Expected number of signatures on a block
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def ev(pos):
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return SIGS * pos
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# Chance you have at least k sigs
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def at_least_k(pos, k):
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return sum([prob(SIGS, i, pos) for i in range(k, SIGS + 1)])
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# Expected number of signatures on a block filtering all <k
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def ev_atleast_k(pos, k):
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total, subprob = 0, 0
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for i in range(k, SIGS + 1):
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p = prob(SIGS, i, pos)
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subprob += p
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total += i * p
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return total / subprob
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def normal_mining_return(pow, pos):
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return pow * POWRETURN + ev(pos) * POSRETURN / ACTUALSIGS
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def attack_mining_return(pow, pos, k):
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powtotal, postotal, subprob = 0, 0, 0
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# Case 1: mined PoW block, PoS at least k instances
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case_1_prob = pow * at_least_k(pos, k)
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subprob += case_1_prob
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postotal += case_1_prob * ev_atleast_k(pos, k) * POSRETURN / ACTUALSIGS
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powtotal += case_1_prob * POWRETURN
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# Case 2: mined PoW block, PoS less than k: discard
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# Case 3: others mined PoW block
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subprob += (1 - pow)
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postotal += (1 - pow) * ev(pos) * POSRETURN / ACTUALSIGS
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return powtotal / subprob + postotal / subprob
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