On the Double Coset Membership Problem for Permutation Groups

We show that the Double Coset Membership problem for permutation groups possesses perfect zero-knowledge proofs.

[1]  László Babai,et al.  Canonical labeling of graphs , 1983, STOC.

[2]  Hugo Krawczyk,et al.  On the Composition of Zero-Knowledge Proof Systems , 1990, ICALP.

[3]  Silvio Micali,et al.  Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems , 1991, JACM.

[4]  Rafail Ostrovsky,et al.  The (true) complexity of statistical zero knowledge , 1990, STOC '90.

[5]  Shafi Goldwasser,et al.  Private coins versus public coins in interactive proof systems , 1986, STOC '86.

[6]  Christoph M. Hoffmann,et al.  Group-Theoretic Algorithms and Graph Isomorphism , 1982, Lecture Notes in Computer Science.

[7]  John E. Hopcroft,et al.  Polynomial-time algorithms for permutation groups , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[8]  Eugene M. Luks,et al.  Isomorphism of graphs of bounded valence can be tested in polynomial time , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[9]  Amit Sahai,et al.  Honest-verifier statistical zero-knowledge equals general statistical zero-knowledge , 1998, STOC '98.

[10]  Christoph M. Hoffmann Subcomplete Generalizations of Graph Isomorphism , 1982, J. Comput. Syst. Sci..

[11]  László Babai,et al.  Local expansion of vertex-transitive graphs and random generation in finite groups , 1991, STOC '91.

[12]  Johan Håstad,et al.  Perfect zero-knowledge languages can be recognized in two rounds , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[13]  Oded Goldreich,et al.  On the limits of non-approximability of lattice problems , 1998, STOC '98.

[14]  László Babai,et al.  Arthur-Merlin Games: A Randomized Proof System, and a Hierarchy of Complexity Classes , 1988, J. Comput. Syst. Sci..

[15]  Endre Szemerédi,et al.  On the Complexity of Matrix Group Problems I , 1984, FOCS.

[16]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[17]  Uwe Schöning Graph Isomorphism is in the Low Hierarchy , 1988, J. Comput. Syst. Sci..

[18]  Charles C. Sims,et al.  Some group-theoretic algorithms , 1978 .

[19]  Tatsuaki Okamoto,et al.  On relationships between statistical zero-knowledge proofs , 1996, STOC '96.

[20]  Manuel Blum,et al.  Designing programs that check their work , 1989, STOC '89.

[21]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[22]  Stathis Zachos,et al.  Does co-NP Have Short Interactive Proofs? , 1987, Inf. Process. Lett..

[23]  Jacobo Torán,et al.  Graph isomorphism is low for PP , 1992, computational complexity.