Computationally private randomizing polynomials and their applications

In this chapter, we study the notion of computational randomized encoding (cf. Definition 3.6) which relaxes the privacy property of statistical randomized encoding. We construct a computational encoding in $\mathbf {NC}^{0}_{4}$ for every polynomial-time computable function, assuming the existence of a one-way function (OWF) in SREN. (The latter assumption is implied by most standard intractability assumptions used in cryptography.) This result is obtained by combining a variant of Yao’s garbled circuit technique with previous “information-theoretic” constructions of randomizing polynomials. We present several applications of computational randomized encoding. In particular, we relax the sufficient assumptions for parallel constructions of cryptographic primitives, obtain new parallel reductions between primitives, and simplify the design of constant-round protocols for multiparty computation.