Uses of randomness in algorithms and protocols

By Joe Kilian. 1990

"Uses of Randomness in Algorithms and Protocols" makes fundamental contributions to two different fields of complexity theory: computational number theory and cryptography. The most famous result is Goldwasser and Kilian's invention of a new approach to distinguish prime numbers from composites, using methods from the theory of elliptic curves over finite fields.The Goldwasser-Kilian algorithm is the first to yield a polynomial size proof of its assertions, ensuring correctness while still provably running fast on most inputs. This new primality test implies for the first time and without any assumptions that large certified primes can be generated in expected polynomial time under a distribution that is close to uniform. It provides a provocative new link between algebraic geometry and primality testing, one of the most ancient algorithmic problems in number theory. Heuristic implementations of the algorithm are currently considered to be the fastest existing methods to certify primes.Kilian also provides two elegant and original contributions to theoretical cryptography. He shows how to base general two-party protocols on a simple protocol, known as "oblivious transfer," proving the first completeness result of this kind. He also introduces a generalization of interactive proof systems, known as "multi-prover interactive proof systems," and shows that anything provable in this model is provable in zero knowledge.Joe Kilian is a National Science Foundation Postdoctoral Fellow at MIT and Harvard.Contents: Introduction. New Techniques in Primality Testing. Committing Bits Using Oblivious Transfer. Circuit Evaluation Using Oblivious Transfer: The NC1 Circuit Base. ObliviousEvaluation of Arbitrary Circuits. Interactive Proof Systems with Multiple Provers.

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Citations in the corpus

Geppetto: Versatile Verifiable Computation (2015, methodology): “To our knowledge, commit-and-prove (CP) schemes are ﬁrst mentioned by Kilian [37].”
Non-interactive cryptocomputing for NC/sup 1/ (1999, background): “) as a basic tool upon which secure circuit evaluation can be constructed [27].”
Advances in Cryptology — ASIACRYPT 2000 (2000, methodology): “Specifically, the scheme is based on a generalized version of Micali’s signature scheme [17], which is in many ways similar to the schemes of Ong-Schnorr [16], Guillou-Quisquater [13] and Ohta-Okamoto [19].”
Universally composable two-party and multi-party secure computation (2002, unknown): “(This notion is implicit in the work of [gmw87], and was also discussed by Kilian [ k89 ].”
On the Power of Multi-Prover Interactive Protocols (1994, result): “Complete proofs of these results appeared in [25].”
Privacy Preserving Data Mining (2000, unknown): “1 One of the rst examples of a secure two party protocol for a speci c problem is that of oblivious transfer [20, 8], which proved to be a very useful primitive for many applications as for circuit evaluation [14].”
Secure Games with Polynomial Expressions (2001, background): “One of the most important results on the foundations of cryptography (suggested by Yao [Yao86], generalized to multi-party by Goldreich, Micali and Wigderson [GMW87], and characterized based on the Oblivious Transfer primitive by Kilian [ Kil90 ]) is that given any polynomially computable function f”
Computationally Secure Oblivious Transfer (2004, methodology): “Kilian [ 35 ] and Goldreich and Vainish [32] have shown how to use OT in order to implement general oblivious function evaluation, i.e., to enable Alice and Bob to evaluate”
Universally Composable Two-Party and Multi-party Secure Computation (unknown): “(This notion was implicitly present in the work of Goldreich, Micali, and Wigderson [33], and explicitly proposed by Kilian [37].”
Quantum data hiding (2001, methodology): “Conditionally Secure Quantum Bit Commitment Bit commitment [28] is a cryptographic protocol with two parties, Alice and Bob.”