Yitao Duan and John Canny Computer Science Division University of California, Berkeley PODC 2007, August 12, Portland OR. Practical Private Computation of Vector Addition-Based Functions. Overview.
Computer Science Division
University of California, Berkeley
PODC 2007, August 12, Portland ORPractical Private Computation of Vector Addition-Based Functions
A method for performing privacy preserving distributed computation of many algorithms that is practical and secure in a realistic threat model at large scale
Provably strong (information-theoretic) privacy
Efficient ZKP to deal with cheating users
Challenge: standard cryptographic tools not feasible at this scale
The server asks for N random projections of the user’s vector, the user proves the square sum of them is small.
Projections are done in small field. The only large field operations are N encryptions and boundedness ZKP
O(log m) public key crypto operations (instead of O(m)) to prove that the L-2 norm of an m-dim vector is smaller than L.
(a) Linear and (b) log plots of probability of user input acceptance as a function of |d|/L for N = 50. (b) also includes probability of rejection. In each case, the steepest (jagged curve) is the single-value vector (case 3), the middle curve is Zipf vector (case 2) and the shallow curve is uniform vector (case 1)
(a) Verifier and (b) prover times in seconds with N = 50, where (from top to bottom) L has 40, 20, or 10 bits. The x-axis is the vector length m.