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Coleman's theory of p-adic integration figures prominently in several number-theoretic applications, such as finding torsion and rational points on curves, and computing p-adic regulators in K-theory (including p-adic heights on elliptic curves). We describe an algorithm for computing Coleman integrals on hyperelliptic curves, and its implementation in Sage. Q P ω i } 2g−1 i=0 .

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Hidden credentials are useful in protecting sensitive resource requests, resources, policies, and credentials. We propose a significant performance improvement when implementing hidden credentials using Boneh/Franklin Identity Based Encryption. We also propose a substantially improved secret splitting scheme for enforcing complex policies, and show how it improves concealment of policies from nonsatisfying recipients.

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