Introduction to finite fields and their applications
Introduction to finite fields and their applications
Almost all primes can be quickly certified
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
The quadratic sieve factoring algorithm
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
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Modern computer algebra
Riemann's hypothesis and tests for primality
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EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Complexity of Ring Morphism Problems
Computational Complexity
On Black-Box Ring Extraction and Integer Factorization
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Equivalence of F-algebras and cubic forms
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
On graph isomorphism for restricted graph classes
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
The complexity of black-box ring problems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
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In mathematics, automorphisms of algebraic structures play an important role. Automorphisms capture the symmetries inherent in the structures and many important results have been proved by analyzing the automorphism group of the structure. For example, Galois characterized degree five univariate polynomials f over rationals whose roots can be expressed using radicals (using addition, subtraction, multiplication, division and taking roots) via the structure of automorphism group of the splitting field of f. In computer science too, automorphisms have played a useful role in our understanding of the complexity of many algebraic problems. From a computer science perspective, perhaps the most important structure is that of finite rings. This is because a number of algebraic problems efficiently reduce to questions about automorphisms and isomorphisms of finite rings. In this paper, we collect several examples of this from the literature as well as providing some new and interesting connections.