By Eyal Kushilevitz, Tal Malkin
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Additional resources for Theory of Cryptography: 13th International Conference, TCC 2016-A, Tel Aviv, Israel, January 10-13, 2016, Proceedings, Part II
We denote by F[X1 , . . , Xm ] the ring of polynomials in m variables over F; given a polynomial P in F[X1 , . . , Xm ], degXi (P ) is the degree of P in the variable Xi ; the total degree of P is the sum of all of these individual degrees. Linear Spaces. Given n ∈ N, a subset S of Fn is an F-linear space if αx+βy ∈ S for all α, β ∈ F and x, y ∈ S. Languages and Relations. We denote by R a relation consisting of pairs (x, w), where x is the instance and w is the witness. We denote by Lan(R) the language corresponding to R, and by R|x the set of witnesses in R for x.
We use WIPCPs (respectively, CZKPCPs) to construct a 3-round distributed-WI proof system (respectively, CZK proof system in the CRS model) which, at a high level, operates as follows. In the ﬁrst round the prover distributes a WIPCP (respectively, a CZKPCP) between the servers, and in the second and third rounds the veriﬁer and servers emulate the WIPCP (respectively, CZKPCP) veriﬁcation procedure (the veriﬁer sends the proof queries of the WIPCP or CZKPCP veriﬁer, and the servers provide the corresponding proof bits).
711–720, Seattle, WA, USA, 21–23 May 2006 10. : Leakage-resilient circuits without computational assumptions. In: Cramer, R. ) TCC 2012. LNCS, vol. 7194, pp. 230–247. Springer, Heidelberg (2012) 11. : Protecting circuits from leakage: the computationally-bounded and noisy cases. In: Gilbert, H. ) EUROCRYPT 2010. LNCS, vol. 6110, pp. 135–156. Springer, Heidelberg (2010) 12. : Multiple non-interactive zero knowledge proofs based on a single random string (extended abstract). In: 31st Annual Symposium 32 13.