outsourced computation verification
Post on 31-Dec-2015
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Large amounts of data, limited memory E.g. Router observing network traffic Want to answer questions about data
going through
You(verifier) and a 3rd party (helper)• Both read entire data stream once, helper gives
you answer and (interactive) proof of correctness
Proof must be verifiable in limited space
Data comes as updates to vector [a1…au]
Want to calculate , k>0
Can generalize solution of this problem to solve inner product, range-sum
Interpolating polynomial f(x,y) defined over finite field Zp
V calculates f(1,r)…f(v,r) online
H sends s(x) = j[v] f(x, j)k
V verifies s(r)=f(1,r)k+…+f(v,r)k
If s(x) checks out, return
i [h] s(i)
Let length of vector = n = h•v
Verifier Space: O(v•Log(p)), v=O(√n)
Helper Space: O(n)
Communication: O(k•h•Log(p)) for the kth frequency moment, h=O(√n)
Index vector using {0,1}d in d = Log(N) dimensional space
Interpolate with d-variate polynomial f(x1 … xd) in Zp
Verifier picks [r1 … rd] [p]d, and calculates fk(r1, r2, … rd) online
Round 1:
• H sends g1(x1)=x2…xd fk(x1, x2…xd),
• V sends r1 Round i:
• H sends gi(xi) = xi+1…xdfk(r1, r2…ri-1, xi, xi+1…xd)
• V checks gi-1(ri-1) = gi(0) + gi(1), sends ri Round d:
• H sends gd(xd) = fk(r1, … rd-1, xd)
• V checks gd(rd) = fk(r1, r2, … rd) Dishonest H can only fool V with prob. < O(Log(n)/p)
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