Introduction to finite fields and their applications
Introduction to finite fields and their applications
Does co-NP have short interactive proofs?
Information Processing Letters
Graph isomorphism is in the low hierarchy
Journal of Computer and System Sciences
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Derandomization That Is Rarely Wrong from Short Advice That Is Typically Good
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Factorization of polynominals over finite fields in subexponential time under GRH
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
NP-complete decision problems for quadratic polynomials
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Modern Computer Algebra
Solvable Group Isomorphism is (almost) in NP " CoNP
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Equivalence of F-algebras and cubic forms
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Automorphisms of finite rings and applications to complexity of problems
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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We study the complexity of the isomorphism and automorphism problems for finite rings. We show that both integer factorization and graph isomorphism reduce to the problem of counting automorphisms of a ring. This counting problem is shown to be in the functional version of the complexity class AM 驴 coAM and hence is not NP-complete unless the polynomial hierarchy collapses. As a "positive" result we show that deciding whether a given ring has a non-trivial automorphism can be done in deterministic polynomial time. Finding such an automorphism is, however, shown to be randomly equivalent to integer factorization.