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Foundations of Pairing-Based Cryptography: A Comprehensive Proposal

This document outlines the foundational elements of pairing-based cryptography, focusing on key areas including mathematical foundations, and the roles of various fields, curves, and extensions. It reviews necessary definitions and pairing primitives, while detailing algorithm building blocks and a skeletal outline for implementation. Emphasis is placed on specific curve families, including supersingular curves and techniques like the Miyaji-Nakabayashi-Takano and Cocks-Pinch constructions. The proposal culminates in a clear organizational framework aimed at developing secure and efficient key agreement protocols.

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Foundations of Pairing-Based Cryptography: A Comprehensive Proposal

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  1. 1363.3 Foundations Mike Scott Hovav Shacham Terence Spies

  2. Agenda • Mathematical foundations (Mike Scott) • What fields, curves, and extensions to include • Review of definitions section (section 5) • Pairing primitives (Hovav Shacham) • Algorithm building blocks • Skeleton outline (Terence Spies) • Next Steps

  3. Foundations Proposal • Fields • Characteristic p only (no 2 or 3) • Embedding degree • Even only • Curve families • Supersingular (k = 2) • Miyaji-Nakabayashi-Takano • Cocks-Pinch • Barretto-Naehrig • Brezing-Weng

  4. Definitions Section • Review of included document

  5. Pairing Primitives • Taxonomy of pairing based building blocks • Organization follows Boyen’s schema • Sufficient for implementing: • BF1, BB1, Waters, SK, BB2 IBE/KEM • BLS, Waters, BB2 Signatures • Description is general enough to capture any needed KEM / IBE variant, with CCA strengthening • Extensible to any id-based key agreements and id-based sigs needed

  6. 1363 Outline • Top level outline • Sanity check on what’s included and structure • Included techniques • KEM, IBE, signature, signcryption • Computational methods (miller’s algorithm) • In annex A

  7. Next Steps • Build a clean list of candidates for each category • Make case for inclusion for each algorithm • Cleanly write out each algorithm in terms of the primitives

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