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Completeness theorems for non-cryptographic fault-tolerant distributed computation
Every function of <italic>n</italic> inputs can be efficiently computed by a complete network of <italic>n</italic> processors in such a way that:<list><item>If no faults occur, no set of size
How to play ANY mental game
We present a polynomial-time algorithm that, given as a input the description of a game with incomplete information and any number of players, produces a protocol for playing the game that leaks no
Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems
In this paper the generality and wide applicability of Zero-knowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs
How to play any mental game, or a completeness theorem for protocols with honest majority
Permission to copy without fee all or part of this material is granted provided that the copies are not made or Idistributed for direct commercial advantage, the ACM copyright notice and the title of
Short proofs are narrow—resolution made simple
TLDR
This paper relates proof width to proof length (=size), in both general Resolution, and its tree-like variant, and presents a family of tautologies on which it is exponentially faster.
On span programs
TLDR
A linear algebraic model of computation the span program, a variant of Razborov's general approximation method, is introduced, and several upper and lower bounds on it are proved.
Hardness vs. randomness
  • N. Nisan, A. Wigderson
  • Mathematics, Computer Science
    [Proceedings ] 29th Annual Symposium on…
  • 24 October 1988
TLDR
This generator reveals an equivalence between the problems of proving lower bounds and the problem of generating good pseudorandom sequences, and combines this construction with other arguments, a number of consequences are obtained.
Hardness vs Randomness
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
TLDR
A pseudo-random generator which produces n instances of a problem for which the analog of the XOR lemma holds is given, and it is shown that if any problem in E = DTIAl E(2°t”j) has circuit complexity 2Q(”), then P = BPP.
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