Scalable Multiparty Computation with Nearly Optimal Work and Resilience
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Secure Multi-party Computation Minimizing Online Rounds
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient non-interactive secure computation
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Constant-round multiparty computation using a black-box pseudorandom generator
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Scalable secure multiparty computation
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Multiparty computation with low communication, computation and interaction via threshold FHE
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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Randomizing polynomials allow to represent a function f(x) by a low-degree randomized mapping f(x, r) whose output distribution on an input x is a randomized encoding of f(x). It is known that any function f in 驴L/poly (and in particular in NC鹿) can be efficiently represented bydegree-3 randomizing polynomials. Such a degree-3 representation gives rise to an NC_4^0 representation, in which every bit of the output depends on only 4 bits of the input. In this paper, we study the relaxed notion of computationally private randomizing polynomials, where the output distribution of f(x, r) should only be computationally indistinguishable from a randomized encoding of f(x). We construct degree-3 randomizing polynomials of this type for every polynomial-time computable function, assuming the existence of a cryptographic pseudorandom generator (PRG) in 驴L/poly. (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 then present the following applications: Relaxed assumptions for cryptography in NC驴. Assuming a PRG in 驴L/poly, the existence of an arbitrary public-key encryption, commitment, or signature scheme implies the existence of such a scheme in NC_4^0. Previously, one needed to assume the existence of such schemes in 驴L/poly or similar classes. New parallel reductions between cryptographic primitives. We show that even some relatively complex cryptographic primitives, including (stateless) symmetric encryption and digital signatures, are NC驴-reducible to a PRG. No parallel reductions of this type were previously known, even in NC. Our reductions make a non-black-box use of the underlying PRG. Application to secure multi-party computation. Assuming a PRG in 驴L/poly, the task of computing an arbitrary (polynomial-time computable) function with computational security efficiently reduces to that of securely computing degree-3 polynomials. This gives rise to new, conceptually simpler, constant-round protocols for general functions.