Charles Rackoff

The knowledge complexity of interactive proof-systems

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How to construct pseudorandom permutations from pseudorandom functions

We show how to efficiently construct a pseudorandom invertible permutation generator from a pseudorandom function generator. Goldreich, Goldwasser and Micali [“How to construct random functions,” Proc. 25th Annual Symposium on Foundations of Computer Science, October 24–26, 1984.] introduce the notion of a pseudorandom function generator and show how to efficiently construct a pseudorandom function generator from a pseudorandom bit generator. We use some of the ideas behind the design of the Data Encryption Standard for our construction. A practical implication of our result is that any pseudorandom bit generator can be used to construct a block private key cryptosystem which is secure against chosen plaintext attack, which is one of the strongest known attacks against a cryptosystem.

Random walks, universal traversal sequences, and the complexity of maze problems

It is well known that the reachability problem for directed graphs is logspace-complete for the complexity class NSPACE(log n) , and thus holds the key to the open question of whether DSPACE(logn)= NSPACE(logn) ([3,4,5,6]). Here as usual OSPACE(logn) is the class of languages that are accepted in logn space by deterministic Turing Ma chi nes, wh i 1eNSPACE( log n) i s the c1ass 0 f 1anguages that are accepted in log n space by nondeterministic ones. The reachability problem for undirected graphs has also been considered ([5]), but it has remained an open question whether undirected graph reachability is logspace-complete for NSPACE(logn). Here we derive results suggesting that the undirected reachability problem is structurally different from, and easier than, the directed version. These results are an affirmative answer to a question of S. Cook.

The covering and boundedness problems for vector addition systems

Abstract New decision procedures for the covering and boundedness problems for vector addition systems are obtained. These procedures require at most space 2cn log n for some constant c. The procedures nearly achieve recently established lower bounds on the amount of space inherently required to solve these problems, and so are much more efficient than previously known non-primitive-recursive decision procedures.

Fast Parallel Computation of Polynomials Using Few Processors

It is shown that any multivariate polynomial of degree d that can be computed sequentially in C steps can be computed in parallel in

A Decision Procedure for the First Order Theory of Real Addition with Order

O((\log d)(\log C + \log d))

CBC MAC for Real-Time Data Sources

steps using only

Cryptographic defense against traffic analysis

(Cd)^{O(1)}

Space Lower Bounds for Maze Threadability on Restricted Machines

processors.

Lower bounds for zero knowledge on the Internet

Consider the first order theory of the real numbers with the function + (plus) and the predicate