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related-work.jl
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related-work.jl
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#! /usr/bin/env julia
n = 1024
F = 22e6
κ_hash = 32 # Bytes
κ_commit = 48 # Bytes
# κ_sig = 32 # not counting signatures (all VID) and blockchain interaction (ACeD)
ln(x) = log(x)
function repetition(n, t, F)
k = n - 2*t
# client sends full file to all storage nodes
communication = n * F
# all storage nodes store full file
storage = n * F
return (communication, storage)
end
function avid(n, t, F)
k = n - 2*t
# client sends to each storage node: chunk, hash vector
# storage nodes echo their chunks and hash vectors to each other
communication = (F/k + n*κ_hash) * (n + n^2)
# chunk and hash vector are stored at each storage node
storage = n * (F/k + n*κ_hash)
return (communication, storage)
end
function avid_fp(n, t, F)
k = n - 2*t
# (assuming homomorphic fingerprints are only of size of a hash)
# msg = chunk + hash vector + fingerprint vector
# client sends to each storage node one msg,
# storage nodes echo to each other the hash and fingerprint vectors
communication = n * (F/k + (n+k)*κ_hash) + n^2 * (n+k)*κ_hash
# nodes store their messages (for retrieving client)
storage = n * (F/k + (n+k)*κ_hash)
return (communication, storage)
end
function avid_m(n, t, F)
k = n - 2*t
# client sends to storage nodes their chunk + opening wrt Merkle root
# nodes echo to each other the Merkle root
communication = n*(F/k + (1 + log2(n))*κ_hash) + n^2 * κ_hash
# nodes store their chunk + opening (for retrieving client)
storage = n*(F/k + (1 + log2(n))*κ_hash)
return (communication, storage)
end
function aced(n, t, F; c=48e3)
t_ = 16
r = 0.25
q = 8
eta = 0.875
lambda = (1 - 2*t/n) / ln(1 / (1-eta))
d = 8
# source: https://arxiv.org/abs/2011.00102v2
# Theorem 2, 2.) + eqn (5)
communication = n * ( t_ * κ_hash + F/(n*r*lambda) + (2*q - 1)*F*κ_hash/(n*r*c*lambda) * log(F / (c * t_ * r)) / log(q*r) )
# eqn (5)
storage = communication
# eqn (6)
proof = (d-1)*c + d*κ_hash*(q-1) * log(F / (c * t_ * r)) / log(q*r)
return (communication, storage, proof)
end
function semiavidpr(n, t, F)
k = n - 2*t
# communication = n * (F/k + k*κ_commit + κ_sig) # (ignoring signatures)
# client sends to each storage node their chunk + column commitments
communication = n * (F/k + k*κ_commit)
# nodes store their chunks + column commitments (for retrieving client)
storage = n * (F/k + k*κ_commit)
return (communication, storage)
end
t_049 = round(0.49*n)
t_033 = round(0.33*n)
@show (t_049, t_033)
@show repetition(n, t_049, F)
@show avid(n, t_033, F)
@show avid_fp(n, t_033, F)
@show avid_m(n, t_033, F)
@show aced(n, t_033, F; c=40e3)
@show aced(n, t_049, F; c=40e3)
@show semiavidpr(n, t_033, F)
@show semiavidpr(n, t_049, F)
for c in 8e3:8e3:96e3
@show c
(C, S, P) = aced(n, t_033, F; c=c)
@show (C, S, P)
end
println("c proof storage")
for c in 8e3:8e3:96e3
(C, S, P) = aced(n, t_033, F; c=c)
println("$c $P $S")
end