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Number-theoretic aspects of computational complexity.
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Irreducibility testing and factorization of polynomials
It is shown that under certain hypotheses, irreducibility testing and factorization of polynomials with integer coefficients are polynomial time reducible to primality testing and factorization ofExpand
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The first case of Fermat's last theorem
Fermat’s Last Theorem (FLT) states that x + y = z has no integer solution for n > 2. It is easy to show that if the theorem is true when n equals some integer r, then it is true when n equals anyExpand
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Proof of proposition 3
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Proof of proposition 2
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Proof of proposition 1
Before we look at the MMD calculations in various cases, we prove the following useful characterization of MMD for translation invariant kernels like the Gaussian and Laplace kernels. Lemma 1. ForExpand
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The use of public key cryptography in communication system design
TLDR
We present a review of public key cryptosystems, followed by examples of communications systems which make particularly elegant use of their properties. Expand
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An application of higher reciprocity to computational number theory
TLDR
We explore the power of the Higher Reciprocity Laws in number theoretic algorithms. Expand
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