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We introduce the Euclid–Mullin graph, which encodes all instances of Euclid's proof of the infinitude of primes. We investigate structural properties of the graph both theoretically and numerically; in particular, we prove that it is not a tree.
Arithmetic coding is a technique which converts a given probability distribution into an optimal code and is commonly used in compression schemes. The use of arithmetic coding as an encryption scheme is considered. The simple case of a single binary probability distribution with a fixed (but unknown) probability is considered. We show that for a chosen plaintext attack w + 2 symbols is sufficient...
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